‘—----I‘-—-- "_“ NUCLEAR SPECTROSCOPIC STUDIES OF SHORT - LIVED NEUTRON - DEFICIENT SPECIES IN THE f7/2-SHELL REGION Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY JERRY NELSON BLACK 1971 th~w This is to certify that the thesis entitled NUCLEAR SPECTROSCOPIC STUDIES OF SHORT-LIVED NEUTRON-DEFICIENT SPECIES IN THE fj/z-SHELL REGION presented by Jerry Nelson Black has been accepted towards fulfillment of the requirements for Ph 0 D 0 degree in Chemistry Mud ”flame Major professor Wm. C. McHarris Date 1971 December 23 0-7639 t: amomo av "=- IIIIAII & SIINS' 300K BINIIEIII INC. LIBRAB! ”MR5 I . NUCLEAR SPECTROSCOPIC STUDIES OF SHORT-LIVED NEUTRON-DEFICIENT SPECIES IN THE f 7/2 —— SHELL REGION. by Jerry Nelson Black ABSTRACT NUCLEAR SPECTROSCOPIC STUDIES OF SHORT-LIVED NEUTRON-DEFICIENT SPECIES IN THE 1“ -SHELL REGION 7/2 BY Jerry Nelson Black The decay schemes of 539Fe and 53”'Fe were studied by the use of standard techniques for 8- and y-ray spectroscopy. The y—decay of ”OSC also was investigated by means of on-line, pulsed-beam techniques. An extensive search was conducted for y-ray evidence to support the existence of high-spin metastable states in 53Co, l+3T1 and 1+38c. Although normal spectroscopic methods using high-resolution Ge(Li) and Si(Li) detectors were employed in most of these studies, the development of cyclotron pulsing, data routing and other on-line techniques for the investigation of short-lived species was a significant part of this work. A pneumatic rabbit system and a helium-jet thermalizer also were utilized in many of the experiments. At least two new y-rays were observed in the decay of 8.5 m S3gFe. These y-rays allowed the establishment of a decay scheme with levels at 0, 377.9, 1288.0 and 1619.0 keV. The 8+ decay was found to have end-point energies of 2.8, 2.4 and 1.7 MeV. Subsequent B+-y coincidence experiments demon— strated that the 2.8- and 2.4-MeV groups feed the ground state and first excited Jerry Nelson Black state, respectively. The decay of 2.5 m 53"Fe was found to have six y rays which could be placed in a consistent decay scheme with levels at 0, 1328.1, 2339.6 and 3040.6 keV. Careful examination of the y rays de-exciting this 19/2- metastable state resulted in the direct observation of transitions of multipolarities ofIMS and E6 -- the highest ever observed experimentally. The Oak Ridge Shell Model Code of French, et al., was utilized to predict the level schemes of 53Mn and 53Fe. The results were compared with other calculations and with the experimentally determined values. Partial half-lives for the y rays de-exciting 5”Fe also were calculated and compared with experimental results. Using on-line, pulsed-beam techniques, seven y rays were observed in the decay of 0.183 s “OSC, and subsequently placed in a consistent decay scheme with levels at 0, 3736.9, 4491.3, 5612.7 and 7656.3 keV. Based on the y-ray intensities observed, 8+ feeding values and log ft values were deduced. Various y-ray techniques were used to conduct an exhaustive search for three-particle metastable states analogous to that observed in 53"We. The nuclei 53Co, l*3Ti and 1+3Sc were studied carefully in order to determine if y rays were present which could be attributed to the decay of metastable states. The results of this study failed to establish the existence of y rays which could be attributed to such states in these nuclei. If these states exist, then either the y-branch of their decay is very small or the cross section for their formation by the reactions used is very low. NUCLEAR SPECTROSCOPIC STUDIES OF SHORT-LIVED NEUTRON-DEFICIENT SPECIES IN THE f7/2-SHELL REGION BY Jerry Nelson Black A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1971 To My Parents :0 XL r. ACKNOWLEDGMENTS I wish to thank Dr. Wm. C. McHarris not only for suggesting this region of study but also for his guidance, support and enthusiasm throughout the various facets of the investigation. His encourage- ment and constant interest during the experimental work and the thesis preparation are greatly appreciated. I also wish to thank Dr. W. H. Kelly of the Physics Department for his advice and assistance. His cooperation and discussions during this project were invaluable. Dr. F. M. Bernthal has provided many useful discussions and advice during the latter part of this study. I wish to acknowledge Dr. B. H. Wildenthal for his advice and help with the Oak Ridge Shell Model Codes. His calculation of the 53’"Fe transition probabilities required considerable effort and I am grateful for the results which he provided. Dr. H. G. Blosser, Mr. H. Hilbert and Dr. W. P. Johnson assisted with the operation and maintenance of the Michigan State University Sector-Focused Cyclotron, which was used for the various irradiations required in this investigation. Dr. P. Miller and Mr. P. Sigg assisted in the development of beam pulsing techniques for the cyclotron. The members of our research group have all helped in some way in the course of this study. Dr. D. Beery, Mr. w. Chaffee, Dr. J. Cross, Dr. R. Doebler, Dr. R. Eppley, Mr. R. Firestone, Dr. G. Giesler, Dr. R. Goles, Mr. K. Kosanke, Mr. C. Morgan, Mr. L. Samuelson, Dr. R. Todd and Dr. R. Warner have provided assistance and advice during various phases of experimentation and analysis. Dr. D. Beery and Dr. R. Warner iii deserve special mention for their assistance with experimental problems. Mr. K. Kosanke has provided valuable help with the pneumatic rabbit and Helium-jet thermalizer systems. Mr. R. Au, Mr. and Mrs. W. Merritt, and the cyclotron computer staff have aided greatly in the data acquisition and evaluation through the use of the laboratory's XDS Sigma-7 computer. Their assistance in various programing problems is greatly appreciated. Help also has been received from Mr. R. Mercer and his staff in the cyclotron machine shop, and from Mr. W. Harder and the cyclotron electronics shop. The cyclotron drafting staff, especially Mr. A. Daudi, have been very helpful in preparing the drawings for this thesis. Our secretary Mrs. P. Warstler typed much of this thesis. Her efficiency, expertise, and patience have greatly facilitated its prepara- tion. I acknowledge the financial assistance of the National Aeronautics and Space Administration, National Science Foundation, U.S. Atomic Energy Commission, and Michigan State University. iv TABLE OF CONTENTS Page DEDICATION. ......... OOOOOOOOOOOOOOOOO00...... t“. t“. ACKNOWLEDGMENTS................................................. iii LIST OF TABLES.................................................. xii LIST OF FIGURES................................................. xiv Chapter I. INTRODUCTION...‘OOOOOOOOOOIOOOOOOO0.0000000000000000000 1 II. EXPERIMENTAL APPARATUS AND METHODS.. ......... . ......... 7 2.1 The Cyclotron and Beam Transport systemOOOOOOOOOCOOOOOO0.00... ...... 0...... ........ 7 2.1.1 The Cyclotron. .................... ......... 7 2.1.2 The Beam TranSport systemOOOOIOOIOOOOIOO OOOOOOOOOOOOOOOOOOOOOO 9 2.2 Cyclotron Beam Pulsing and Timing ...... ........... 13 2.2.1 RF Mbdulation Techniques................... 13 2.2.1A The Clock Module..... ....... . ...... 14 2.2.1B The Beam Pulser. ..... .............. 22 2.2.2 Deflection Plate Method. ................... 29 2.2.3 Utilization of the Microscopic Beam StructureOOCOIOOOOOOOOOOOOOOOOOOO0.... 30 2.3 Activation Chambers for On-Line y-Ray SpectrOSCOPYOOOOOOOOOOOOOIOOOOOIOOIOOOOOOO00...... 33 2.3.1 The Goniometer Chamber..................... 33 2.3.2 The Coincidence Chamber...... ............ .. 39 2.3.3 The Vacuum Transfer Chamber ................ 41 2.3.4 Discussion and Improvements ................ 44 2.4 Rabbit-Pneumatic Target System...... ......... ..... 46 2.5 Helium Thermalizer and Jet Transport .............. 53 Chapter III. Page 2.6 y-Ray Spectrometer Systems........................ 57 2.6.1 Ge(Li) Singles Spectrometer................ 53 2.6.2 Ge(Li)-NaI(Tl) Coincidence Spectrometer systems000...00000000000000.0000000.0.00000 62 2.6.2A Ge(Li) vs 3X3-in. NaI(Tl) SPeCtromter.000.000.000.0000000000 62 2.6.23 Ge(Li) vs 8X8-in. NaI(Tl) Split-Annulus Spectrometer ......... 66 2.6.3 Ge(Li) - Ge(Li) Coincidence Spectromtem000000000000000. ..... 0000 ..... 72 I 2.6.3A TWO-Dimensional Data Acquisition Using Routing ..... ..... 72 2.6.38 Multi-Dimensional Data Acqu181tion000000000000000 ..... 0000 75 2.7 Beta Spectrometers............ ................ .... 77 2.7.1 Beta Singles Spectrometers ........... ...... 77 2.7.2 Si(Li) vs NaI(Tl) e+-y Coincidence Spectrometer ........ .......... 78 2.8 Fe-Mn Chemical Separation... ................ . ..... 79 DATA ANALYSIS............................... ........... 80 3.1 y-Ray Energy and Intensity Analysis ............... 81 3.1.1 Program MDIRAE......... ................. ... 81 3.1.2 Program MOD 7... ....................... .... 91 301.3 Program SW0000000 000000000000 000000000000 92 3.1.4 y-Ray Energy and Intensity calculation 000.00.00.0000000 0000000 00.0000 99 3.2 Double and Single Escape Peaks......... ..... ...... 103 3.3 The PDP-9 Computer and Related Programs.......................... ............. ... 104 3.4 The Analysis of Beta Spectra............. ......... 106 3.4.1 Principles of Beta Analysis..... ........... 106 vi Chapter Page 3.4.1A Beta-Ray Spectraoooooo000.000.0000. 106 3.4.1B The Statistical Weight FaCtOI... ..... coo 000000000000000000 107 3.4.1C Energy and Momentum FormUIaSo0000.00.00.00... ...... too. 108 3.4.1D The First Step of the Analys180000000000000000...00000000109 3.4.1E Maximum Beta Energy Determination ..... . ................ 110 3.4.1F Effect of Electrostatic FOICBS.............. oooooo 00.00.00. 110 3.4.10 The Second Step of The AnaIYS1So00000000000000.0000... 113 3.4.1H Allowed and Forbidden Spectra..... ....... . ............... 114 3.4.11 The F(Z,n) Factor for Allowed Spectra.................... 116 3.4.1J Screening Corrections ......... ..... 118 3.4.1K The Total Beta Emission Probability......... ..... .......... 120 3.4.2 Preparation of Fermi Plots ................. 121 3.4.3 Program FERM 3.... ...... . ....... ........... 123 3.4.4 Program FERMPLOT ...................... ..... 124 IV. THE DECAYS 0F 539Fe AND 53mFe......... ............ 126 4.1 Introduction ...................................... 126 4.2 Source Preparation.... ............ ......... ..... .. 123 4.3 y-Ray Experimental Data. ......... .. ............... 131 4.3.1 y-Ray Singles Spectra ...................... 131 40302 Y-Ray COinCidence Spectraooooooo0.0.0.0000. 135 4.3.2A Anticoincidence Spectra ............ 135 vii Chapter Page 4.3.28 Any-Coincidence Spectra............. ......... . ..... 139 4.3.20 Spectra in Coincidence with the 377.9-keV 7 Ray ........... 139 4.3.2D Two-Parameter Coincidence Experiments.......... ........... ... 142 4.3.2E 511 keV-511 keV-y Coincidence (Pair) Spectra. 0 0 0 0 0 0 0 0 0 0 0 0 0 0000000 142 4.3.3 High Multipolarity y-Ra Transitions Following the Decay of 3”’Fe...... ......... 145 4.3.4 On-Line y-Ray Spectra ...................... 150 4.4 8+ Experimental Data .............................. 154 4.4.1 8+ Singles Spectra ................... . ..... 154 4.4.2 8+-y Coincidence Spectra..... .............. 156 4.4.2A 8+ Spectra in Coincidence with the 377.9-keV y Ray ....... .... 156 4.4.28 8+ Spectra in Coincidence with 7 Rays above 511 keV .......... 160 4.5 Proposed Decay Schemes.. ......................... . 162 4.5.1 539Fe Results.............. ................ 162 4.5.1A The 53Mn Ground State ......... ..... 162 4.5.18 The 377.9-keV Level ............ .... 162 4.5.1c The 1288.0-keV Level .......... ..... 164 4.5.10 The 1619.9-keV Level ............... 165 4.5.1E The 2750.7-keV Level ............... 165 4.5.1F Other Possible Levels.............. 165 4.5.2 53mFe Results ........................ ...... 166 4.5.2A The 53Fe Ground State.. ............ 166 4. 5 . 23 The 3040.6-kev Metastable State0000000 000000000 0 0000000000000 166 viii Chapter Page 4.5.2C The 2339.6-keV Level ............... 167 4.5.2D The 1328.1-keV Level ..... . ..... .... 167 4.6 Discussion.............. ..... ..................... 169 v. SHELL MODEL CALCULATIONS FOR 53Fe AND 53Mn ....... ...... 170 5.1 Introduction... ................................... 170 5.2 The Shell Mbdel......... ....................... ... 171 5.2.1 General Description ........................ 171 5.2.2 Formulation of the Problem ................. 172 5.3 53Fe Ca1culations............ ..................... 182 5.3.1 Predicted Level Scheme ..................... 182 5.3.2 Comparison with Other Model Calculations and with Experimental Results .............. 185 5.4 53Mn Ca1culations........ ......... ................ 188 5.4.1 Predicted Level Scheme....... .............. 188 5.4.2 Comparison with Other Model Calculations and with Experimental Results......... ..... 188 5.5 Calculation of 53Fe Transition Probabilities............... ...................... 194 5.5.1 Methods of Calculation ..................... 194 5.5.1A Mbszkowski Single Particle Estimates..... ............ 194 5.5.18 Shell Model Methods ................ 200 5.5.2 Results... ............ . .................... 208 5.5.2A Single Particle Estimate....... ................ .... 203 5.5.23 Shell Model Results................ 208 50503 DiSCUSSionoooooo000000.000so0.000.000.0000. 210 Chapter page VI. THE DECAY OF L+Ost...................................... 213 6.1 Introduction...................................... 213 6.2 Target Preparation................................ 214 6.3 y-Ray Spectra..................... ..... ........... 217 6.4 Proposed Decay Scheme.................. ...... ..... 221 6.5 Discussion............... ........ ................. 224 VII. THE DECAY OF 53"Co................... ...... ............ 226 7.1 Introduction...... ...... . ..... .... ........ . ...... . 225 7.2 Target Preparation................................ 227 7.3 Experimental Results.............................. 229 7.3.1 Proton Decay. ....... . ......... ............. 229 7.3.2 y-Ray Spectra.......... ...... ........ ...... 229 7.4 Discussion............................... ...... ... 234 VIII. THE SEARCH FOR 3-PARTICLE ISOMERIC STATES IN “31:1 AND uBSCooooooooooooooooooooso... ooooooooo 0.... 237 8.1 Introduction.............. ........ ......... ....... 237 8.2 Target Preparation.............. ........ .. ...... .. 238 8.3 y-Ray Spectra.......... ...... ..................... 240 8.4 Discussion................... ........... .......... 245 Ix. SUMMARY AND CONCLUSIONS................................ 247 BIBLIOGRAPHY.................................................... 250 APPENDICES...................................................... 260 A. FERMPLOT FORTRAN Listing............... ................ 260 8. Input Instructions for the Oak Ridge Shell I wdel COdeS000000000.000000000000000...0000.00.00.00... 265 C. Energies of 7 Rays Observed in the 53”’Co Search............................... ............ 272 Chapter Page Energies of y Rays Observed in the “3mTi and “a"Sc Searches............................... 274 Energies of y Rays Observed in the 53"H'gFe Investigation....................... ..... ...... 277 Table 2-2 4-1 4-3 4-4 4-6 5-1 5-4 LIST OF TABLES Page Ge(Li) Detector SpeC1ficationSOOOOOOOOOO00000000000000. 59 Multichannel Analyzer Specifications................... 53 y-Ray Energy Standards Used in the SWgFe Investigation000000000.000000000000090000000000 13“ SyFe Y kys and Intensities000000.0.00...0.00 0000000 .0 137 53"Fe 7 Rays and Intensities........................... 133 Coincidence Relations between y Rays Observed in the Decay of 53"Fe......................... 144 Electron Energy Standards Used in the 539Fe 8+ StUdieSOOOOOO0.00.00.000.00...000000000000.00.00.000... 155 53gFe....... 159 Resolved 8+ End-point Energies for Effective Proton-Neutron Interactions in the (11f7/2)"1(vf7/2)-1 Configuration................... 183 Predicted Levels and Spins for 53Fe from Shell Mbdel Calculations Using the Interaction from Vervier........................ ........ ........... 134 Predicted Levels and Spins for 53Mn from Shell Model Calculations Using an Interaction fromverv1er000000000000000000000.000000000000000000000190 Single-Particle Estimates for the Transition Probability of a Single Proton.... .............. . ...... 193 Comparison of Experimental Results with Mbszkowski Single Particle Values for Partial Half-11fe00000000.00000000000000000000000000000...00... 209 xii Table Page 5-6 Comparison of Experimental Results with Shell Model Values for Partial Half-life.............. 211 6-1 Isotopic and Spectrographic Analysis of ”OCa Target Used in This Study.............. .......... 215 6-2 y-Ray Energies and Intensities from the Decay of ”08c ...... ...... ........................ . 220 6-3 1+08c y-Ray Energies and Intensities from This Investigation Compared with the Results from PreVious work000000000.000.000.000.00 OOOOOOOOOOOO 223 6-4 Comparison of the Experimental Results of 1+0Sc with Intermediate-Coupling Shell-Model caICUIationSo......e.................................. 225 xiii Figure 1-1 2-4 2-8 LIST OF FIGURES Portion of the Chart of the Nuclides, showing the calcium through cobalt region involved in this study. This section was taken from the Chart of the Nuclides, compiled by the Knolls Atomic Power Laboratory, Ninth Edition.................. Diagram of Particle Energy vs Orbital Frequency for the MSU Cyclotron........ ..... ............ Diagram of the external beam transport system used in this study......... ....... ............... Front and rear views of the routing timer (clock) module, showing the various controls and outputs available on the unit.............. Diagram of the logic pulses available from the routing timer module........................... Oscillosc0pe tracings of the outputs from the routing timer module, illustrating the beam-on, beam-off signals of the master clock (top) and the inhibition period before routing begins (bottom)............. ...... . ........ ..... Oscilloscope tracings illustrating the routing signals (top), generated within the beam-off period (bottom)....................... ..... Staircase generated by the routing pulses............... Wiring setup for using the routing timer module with three ADC's each having a five-way fanout............... ....... .... ............. .. xiv Page 10 15 17 18 18 19 21 Figure 2-9 2-10 2-11 2-12 2-13 2-14 2-15 2-16 2-17 2—18 2-19 2-20 Page Front view of the beam pulser, showing various controls and outlets....................... ..... 23 Block diagram of electronics used for energy vs time experiments under TOOTSIE000000000.000000000000000... 000000000000000000 .00 25 Two-dimensional oscilloscope display produced by TOOTSIE in the Setup made.00.0.0.0.00000000000000.000000000000000. 00000000000 27 Three-dimensional display available from TOOTSIE in the Setup mode... ..... . ............. .... 27 Oscilloscope display produced by TOOTSIE in theRun mOde000000000 0000000000000000 0000000. 28 Block diagram of the electronics setup for utilization of the cyclotron beam merostructure for pulsing00000000000.0000000000000 31 The goniometer facility, showing the 8-inch activation chamber and detector mounting000000000000000000000000000.... 000000000 00.00... 34 Remote control panel for the goniometer........................ ...................... 36 Local control box for the goniometer000000000000000000.0000.000000 00000 00000000000 38 The coincidence chamber. ........ ...... ........... ....... 40 Vacuum transfer chamber, valve, and transfer lock assembly......... ............. ........ 42 Typical "rabbit" used in the pneumatic target system, with foil target packet in place............... .......................... 47 Figure Page 2-21A Interior terminal of the rabbit system.................. 48 2-218 Exterior terminal of the rabbit system.................. 49 2-22 Block diagram of the rabbit system...................... 51 2-23 Interior of the thermalizer box, showing the aluminum hemisphere and target holder ..... .. ........ 54 2-24 Block diagram of a typical Ge(Li)-NaI(T1) coincidence experiment................ ......... ......... 65 2-25 Detector—source geometries for several experiments utilizing the 8XB-in.NaI(Tl) split-annulus spectrometer.............. ............... . 68 2-26 Block diagram of the electronics setup for an anticoincidence experiment using the split annulus. The same equipment is used for obtaining pair spectra after elimination of the 3X3-in. NaI(Tl) detector and the AND/0R gate ........... . ................................. 70 2-27 Block diagram of the electronics used in a typical two-dimensional Y-y coincidence experiment0000000000000000000000000000000000000000.0000. 73 3-1 MOIRAE display oscilloscope and sense switches.......... 82 3-2 MOIRAE oscilloscope display of an unexpanded 4096-channe1 spectrum from the “3mTi search ............. 34 3-3 Partial expansion of the spectrum from Figure 3-2, showing the limits chosen for father expan81on00.000000000000000000000 00000 0 000000000 84 3-4 Display of the expanded segment from Figure 3-3. A third order background has been fitted “SingtheMCK1routineO00000000000000000000000.0000... 85 xvi Figure Page Display of the spectrum as shown in Figure 3-4, including the peaks after subtraction of the third order background. The selected peak limits and calculated centroid are shown for the 270-keV peak....................................... 85 Sample of the line-printer output from MOIRAE. The data are the same as shown in Figures 3-2 to 3.5000000.0.0000000000000000000000000 OOOOOOOOOOOOOOO 88 The storage scope and sense switches used with mD 7.00.0 00000 000.0... 00000 0 00000 0 00000000000000000000 93 Photograph of a portion of the line-printer output from a SAMPO analysis. The peaks shown are the same as illustrated in section 3.1.1............... 95 A typical detector efficiency curve for Ge(Li) detectors. This curve is for a 10.4% efficient Ge(Li) detector with a source-detector distance Of 10 inCheS00000000000....00000000 oooooo 00.00.000.000. 102 Excitation functions from (Esk67) for the 55Mn- (p,3n)53”fi?Fe reaction. The upper curve repre- sents the 8.5m- activity, and the lower one the 205m- isomer actiVity0000000000000 000000 0000000 0000000 0 129 y-Ray singles spectrum of 53m'I'QFe taken with the 2.52 detector.......... ..... . ...................... 133 53m+gFe anticoincidence spectrum....... ....... ......... 136 53“HgFe any-coincidence spectrum ....................... 140 53m+9Fe coincidence spectrum with the gate on the 377.9-keV transition....... ........................ 141 xvii Figure 4-9 4-10 4—11 4-12 4-13 5-1 6-1 6-2 Page 5390'") Fe 511 keV-511 keV-y triple coincidence spectrum........ .......... . ............... 143 53""I'gFe singles y-ray spectrum taken with a 3.6% efficient Ge(Li) detector. This spectrum represents a 24-hour accumu- lation during which sources were prepared every two minutes ........... . ........................ 148 Linear blowup of the 2029.2-keV region from Figure 4-7, showing the absence of cascade-type summing..... ............... . ............. 149 53”H'QFe beam-on singles spectrum ...................... 152 539(+m)Fe 8+ singles spectrum taken with a 200 mm2 Si(Li) detector....... .................. .... 157 539 + Fermi plot for the Fe 8 singles spectrum shown in Figure 4-10 ........... . ........... . .......... 153 + 53"H'gFe B spectrum taken in coincidence with the 377.9-keV y ray using a 200 mm2 Si(Li) detector0000 000000 000000000000 000000000000000000000000 161 539 53m Proposed decay schemes for Fe and Fe ............ 163 Schematic comparison of 53Fe level schemes predicted by two calculations versus the experimental results obtained in this Study ........... 186 Schematic comparison of 53Mn level schemes predicted by various calculations versus the experimental results obtained in this study.. ........ . 189 Beam-off, routed y-ray spectra from the decay Of “OSC00000000 000000 0000000000 0000000 0 000000000000000 218 Proposed decay scheme for “08c ........................ 222 xviii Figure 7-3 7-4 Page Excitation function for the 51+Fe(p,2n)53mCo reaction reported by Cerny, et a1. (Cer70).............................. 228 Four routed beam-off spectra from the S3mCo search using the "slow— pulsing" technique.................... .............. .. 231 y-ray singles spectrum from the 53”’00 search using the helium-jet thermalizer technique.............. ................... 233 Proposed decay scheme for 53’"Co showing the known modes of decay for the isomer00000000000.000.000.000.0.00.000000000000000 235 Four beam-off routed spectra from the ”3mTi, “3mSc search using the "slow-pulsing" technique.......... ..... .......... ..... 241 Routed spectra from the 1+3mTi, 1+3mSc search utilizing the microscopic structure of the cyclotron beam for timing00000000000000000000000000000000.000. 0000000000 . 242 Proposed decay scheme for ”3mSc reported by Sawa and Bergstrfim (Ann70)......................... 244 xix CHAPTER I INTRODUCTION ". . . . There are two ways in which physics tries to obtain a consistent picture of the structure of the atomic nucleus. One of these is the study of the elementary particles, their properties and mutual interactions. Thus one hopes to obtain a fundamental knowledge of the nuclear forces, from which one can then deductively understand the complicated nuclear structures. The other way consists in gaining, by direct experimentation, as many different data as possible for individual nuclei, and examining the relations among these data. One expects to obtain a network of correlations and connections which indicate some elementary laws of nuclear structure. These two ways have not yet met to establish a complete understanding of the nucleus, although many connections have been found . . . ." (May55). Even though these words were written some sixteen years ago, they remain a very basic description of the motivation for modern research in nuclear physics and chemistry. In spite of the tremendous advances in experimental technology and theoretical methods, the long awaited meeting of experimental fact and theoretical prediction has not yet been realized in the nuclear prOblem. Notwithstanding the success cfi'various specialized semi-empirical models, the goal of developing aicomplete comprehensive nuclear theory has not been attained. Although a large number of correlations have been established, no "fundamental” laws have been discovered which simplify or completely resolve the problemiof predicting nuclear structure and properties. As Blatt and .011- .u t." v“. Weisskopf state in their preface: "Nuclear physics is by no means a finished edifice" (81a52). Thus, one finds that the basic impetus for performing nuclear spectroscopy is not the acquisition of knowledge for its own sake, but instead represents another step towards understanding the entire nuclear problem. Each small contribution to the ever growing body of knowledge both experimental and theoretical relating to nuclear structure, brings one closer to the realization of a complete solution. The many correlations and systematics may eventually reveal the true nature of the nuclear force, and consequently the ability to predict nuclear properties from first principles. Since an overall understanding of nuclear structure has not been achieved, current descriptions must rely on various semi-empirical models developed for specific types of nuclei. While these models cannot predict accurately all of the properties of various nuclei, each has been reasonably successful in its particular region of applica- tion. Since these models are semi-empirical, that is they utilize experimentally determined results to establish required parameters, the availability and quality of experimental results may limit the extent to which the model is capable of accurately predicting nuclear properties. In addition, the model itself may need to be modified and inmroved as the quality and quantity of available data increase. Thus, fluaacquisition of nuclear data is justified not only as a contribution tn the general body of knowledge concerning nuclei, but also as a stimulant for testing and modifying present nuclear models. One of the most successful and popular of the present nuclear models is the so-called shell model. This description of the nucleus, detailed in Chapter V, envisions the nuclear protons and neutrons as circulating about in orbits analogous to the atomic electron shell structure. Closed shells are found to occur at proton or neutron "magic" numbers of 2, 8, 20, 28, 50, 82, and 126. The model has achieved its greatest success in treating nuclei near these closed shells. As the model has developed, interest has increased in extending its application to nuclei containing particles outside closed shells. This thesis encompasses a number of such nuclei in the fj/z - shell region, particularly 53Mn and 53Fe. A portion of the Chart of the Nuclides covering the region studied here is shown in Figure 1-1. The original objective of this investiga- tion was simply to elucidate the levels in 53Mn populated by the B+le decay of 53Fe. However, the discovery of a high-spin, three—quasiparticle metastable state in 53Fe by Eskola (Esk66,67) motivated a comprehensive study of the 53”""9Fe decay. A brief investigation of the decay of l‘OSc to levels in 1”Ca was performed both to ascertain the levels so populated and to learn something about the structure of “08c. This investigation was also used to develop cyclotron pulsing and data routing techniques for studying short-lived species. Next, an extensive search was carried out to look for high-spin, three-quasi— particle states analogous to 53"Fe in 53Co, 1+3T1 and l‘38c. These muflei were examined carefully to determine if y rays were present whhfiicould be attributed to the decay of possible three-quasiparticle metastable states. The experimental equipment and techniques employed during this 3.00:0 .:o .mwwwwuwmummuong 530m own—cue. maaocx 05 .3 ewawwwww no 955 05 Eouw co m . :39; 35 5" ES x u mus :owuuow mach. H025 cowmmu uHmnou swaou . 5 E: o no Menu 9539? 333:2 on”. mo :98 05 mo comm—om .HIH muewee investigation are discussed in Chapter II. A number of methods which were deve10ped for the pulsed in-beam study of short-lived species are covered, as well as conventional techniques for B- and y-ray spectroscopy. The use of the pneumatic target (rabbit) and helium- jet transport systems for studying moderately short-lived isotopes also is described. Since the analysis of acquired data is often quite complex, a complete chapter has been devoted to the methods of data analysis. Chapter III describes the various procedures used for analyzing B- and y-ray spectra -- including various computer programs written for or adapted to the XDS Sigma 7 computer at the Michigan State University Cyclotron Laboratory. The rather extensive y- and B— spectroscopic studies of the decays of 539Fe and 53’"Fe are presented in Chapter IV. Level schemes for both species are deduced. The study is highlighted by the elucidation of the metastable state 53’"Fe and the discovery of transitions having multipolarities of.M5 and E6 -- the highest ever observed experimentally. In Chapter V the nuclear'Shell Model is described and utilized to predict the structure of 53Fe and 53Mn. Level schemes are predicted for both isotopes and compared with other calCulations and with the experimental results contained in Chapter IV. In addition, partial half-lives for those y rays de-exciting 53mFe are predicted both from the simple Moszkowski single particle estimates and from the more elaborate Shell Medel theory. These results are then compared with the experimental values obtained earlier. A brief study of the decay of l*OSc comprises Chapter VI. Pulsed— beam routing techniques were used to study the y-decay of l“08c to obtain the levels populated in ”Ca with a relatively high degree of accuracy. Chapters VII and VIII are concerned with the search for high—Spin, three-quasiparticle metastable states in nuclei analogous to 53Fe. Chapter VII presents the known facts about the existence of 53’"Co, together with the results of this study. The search for y rays de- exciting possible 19/2- states in “3T1 and 1”SC is discussed in Chapter VIII. A short summary and discussion of the above investigations is presented in Chapter IX. CHAPTER II EXPERIMENTAL APPARATUS AND METHODS 2.1 The Cyclotron and Beam Transport System 2.1.1 The Cyclotron The performance of pulsed-beam experiments and the production of short activations require a reliable, high-quality cyclotron. At Michigan State University we are fortunate to have such a machine, in the form of a variable-energy, sector-focused cyclotron (81061). The principle and design details of this accelerator together with its Operation have been reported previously (81066, Gor68). A diagram of particle energy vs orbital frequency for the MSU cyclotron is shown in Figure 2-1. This figure illustrates the possible energies of various particles and the harmonic (N) on which they are accelerated. At the present time, protons, deuterons, helium—3 and alpha particles are routinely accelerated using the first and second harmonics. The develop- ment of heavy-ion beams is underway. The bulk of the material reported here was obtained using 24-45 MeV proton beams. In the operation of the cyclotron the most important objective is to produce a well-tuned beam with a high extraction efficiency. 'flus condition can be established by: (l) precise setting of the main magnetic field, (2) careful centering of the beam in order to reduce fluzeffect of RF ripple and (3) good selection of a narrow phase group :hiorder to produce an Optimum single turn extraction. The proton (H+) beam is extracted at a radius of approximately Energy (Mev) I25 5 6 7 8 9 IO IS 20 25 Orbital Frequency (MHz) Figure 2-1. Diagram of Particle Energy vs Orbital Frequency for the MSU Cyclotron. _,‘ . I‘L", , env‘b' . .0-0 0‘ - -... bl 00 ~0E0 ‘ 0 "0‘4. . A ' u... -- u... A..- 29 inches (212 turns), using a first harmonic bump field to induce a coherent radial oscillation. An electrostatic deflector and a focusing air-core magnetic channel are used to guide the beam from the machine. After extraction, the beam is balanced on the exit slits 81, illustrated in Figure 2-2. For our activation experiments, internal beam currents were typically 2 to 6 microamperes with almost 100% extraction efficiencies. l; 1.2 The Beam Transport System The portion of the external beam transport system used in these experiments is shown in Figure 2-2. The details of the optical properties of the beam and of the energy analysis system have been dis- cussed in previous publications (Mac67, Sne67, Ben68). M1 and M2 are horizontal bending magnets for alignment of the beam through the object Slit SB. 82 is a vertical slit which was not used in most experiments. The beam is focused on 83 by means of two quadrupole doublets Q1’ Q2 and Q3, Q4. The distance between $3 and S4 is about four feet. The divergence of the beam is determined by the openings of S3 and S4. M3 and M4 are two 45° analyzing magnets, whose fields are adjusted in such a manner as to direct the beam on the image slit, SS. The magnetic f1elds in M3 and M4, which determine the beam energy, are measured by In-1<.‘.1ear magnetic resonance fluxmeters (Scanditronix, NMR-656C). Q5 and Q6 are quadrupole magnets used for refocusing. The beam must be balanced simultaneously on 83, S4 and $5. This balance can be achieved by equalizing the current on the sides of each individual slit. The 81mape (focus) of the beam can be examined directly with scintillators in front of S3 and 85. After the beam is properly aligned through SS, it is bent into the 45° goniometer line by the distributing magnet 10 \\\\\\\\X 0 5 IO FEET We: MSU 01C E\\\\\\\\ \\\n\\\|\\\ 7‘ VM/LZ .- f .. E 11 M5. Two more quadrupole doublets Q7, Q8 and Q9, Q10 are used to focus the beam on the target. When using the various target chambers in the Goniometer line, the final beam focusing and alignment was performed by inserting a plastic scintillator in the target position and viewing the beam spot directly with a TV camera. With the enlarged image of the scin- tillator the beam could be focused and centered quite easily. The beam current on the rear Faraday Cup was monitored to assure that none of the beam was being lost on the beamline and chamber. No additional methods were used in aligning and maintaining the beam during the course of the experiment. First, the neutron background Was carefully monitored in the vicinity of the target chamber, so that if the beam wandered and struck the target frame or the chamber, an immediate increase in the neutron counting rate would be observed. Second, when possible, the front collimator and/or rear exit pipe of the chamber was isolated and the current from it monitored. For optimum cOnditions, both the neutron background and the collimator current were ulinimized with respect to the beam current measured at the Faraday Cup. For most on-line, pulsed-beam experiments a very low beam current (0.3-30.0 nanoamperes) was adequate. These currents were achieved by Qireulating a minimum current within the machine and then closing the water-cooled slits ($1 and S4) as necessary. The Faraday Cup consisted of a half—inch aluminum beam stop, isOlated from the target chamber and shielded by concrete blocks stacked 6 feet wide and 7 feet high. Additional shielding was provided by a c3"].zlnder of paraffin surrounding the beam pipe about 3 feet from the tat‘get chamber. These shielding measures reduced the neutron background 12 by a factor of ten. This resulted not only in cleaner data, but also in significantly extended detector lifetimes. 13 2.2 Cyclotron Beam Pulsing and Timing Conventional methods of target handling are not suitable for the study of short-lived radioactive species (i.e., those with half- lives in the nanosecond to millisecond region). With such short half- lives, these targets cannot be moved, and therefore must be counted in Hue same position as they occupied during the irradiation. (A few "plunger" and "rotating-wheel" devices have been tried, but were found to be relatively slow and unreliable.) Since only the y rays from the radio- active decay of these isotopes were of interest to us (as opposed to direct excitation y rays from (p,ny) type reactions), it was imperative that the beam was turned off during the counting intervals. The only method that can satisfy all of the above conditions is that of pulsing the cyclotron beam. Although pulsed-beam experiments present a number of difficulties, they are a very powerful tool for studying short-lived isotopes. A number of different techniques are used, depending on the eXperimental requirements and the half-life one wishes to investigate. 2;2,1 RF Modulation Techniques For many of the on-line y-ray spectroscopy experiments rEportedhere, the so-called "slow-pulsing" mode was utilized. This lNflsing is accomplished by modulation of the RF accelerating voltage ‘With a rectangular wave form, effectively turning the beam off and on. The minimum pulsing period is limited to a few hundred milliseconds, however, because of the time constant associated with the dees. Two 'Variations of this technique have been employed, each using a different Pu181ng device together with a suitable data-taking program. l4 2.2.1A The Clock Module The basis of the simplest and most popular method for slow pulsing is a routing-timer module designed by Dr. Peter Miller of the MSU Cyclotron Laboratory. The front and rear controls and outputs for this unit are shown in Figure 2-3. Within certain time limits, this module is ideally suited for pulsed-beam y-ray work. It can provide beam-on (or beam-off) times ranging from 0.4 to 4.0 sec. Both positive and negative outputs are available on the rear of the module for beam pulsing. We have found it desirable to select the RF amplitude that maximizes beam current while there is no output from the timer module, and then use the module output (added algebraically to the amplitude so selected) to detune the beam. This is in contrast to the alternate condition where the RF is tuned while the module voltage is on. This choice was dictated by the fact that the timer output voltage is less stable than its zero level. Understandably, the cyclotron operator must exercise some care when optimizing the RF during an experiment, since it is possible to change from one to the other of the above con- ditions simply by a coarse adjustment of the cyclotron RF voltage control. In practice, such a coarse RF adjustment can result in routing the data taken with the beam on, into locations previously reserved for counts accumulated with the beam off - an undesirable condition wherein one 399-8 his data gradually sink into a sea of meaningless background. An inhibit feature of the clock module may be used to delay the counting for any interval desired after the beam is turned off. This provision is useful for eliminating very hot, short-lived back- ground contaminants, and in the event of very high beam-on counting 15 Figure 2-3. Front and rear views of the routing timer (clock) module, showing the various controls and outputs available on the unit. j... NIIIJ. 16 rates, provides a period for the electronics to recover. In addition, logic signals are output from connectors on the front of the module and may be used to route the data into as many as seven beam-off spectra, plus an additional spectrun of the total beam-on data. Each routed spectrum contains only the counts for a specific time interval after the counting begins. For example, one might wish to route seven 0.1 sec intervals following a beam pulse and a preset inhibition period. The durations of all routed spectra are set simultaneously, there being no provision for routing different spectra for different lengths of time in the same beam-off period. One can, however fill the beam-off period with any nmnber of routed spectra from only one to a total of seven. A timing staircase made up of the routing pulses is available for computer programs which require this type of input. A target position switch generates either manual or automatic signals for use with plunger-type devices where the target is moved out of the immediate beam area for counting. Some of the logic pulses available from this module are illustrated in Figure 2-4. The range of the routing pulses is 0.04 to 2.0 sec per pulse. A routing frequency range switch located on the rear of the unit must be set to designate the appropriate range (high or 10W). The limits on the routing range are determined by the frequency 0f the routing clock. If one wished to extend the range, the installa- tion 015 a different multivibrator clock would be necessary. Oscilloscope tracings of the outputs from this timer module during a typical experiment are pictured in Figures 2-5, 2-6 and 2-7. In Figure 2-5, the top trace shows the beam-on, beam-off signals generated by the master clock. (The beam-off period is in the center of the picture, i.e., the lower portion of the trace.) The bottom 17 LOGIC PULSES FOR SLOW PULSING AVAILABLE FROM CLOCK MODULE T R - '36ch __ I J 1:.” IOBEAM-ONOIOEAM-OFF'I INHIBIT ’ ' PULSE J I __| |._DELAY BEFORE COUNTING BEGINS ROUTING fl PULSES . (UP TO 7 AVAILABLE ' fl RANGES MASTER CLOCK (I/2 CYCLE) 0.4+ 4.0 SEC. ROUTING PULSES .O4-'2.0 SECOND STEP FUNCTION FORMED FROM ROUTING PULSES F18 "r 6 2-4 Diagram of the logic pulses available from the routing timer module. 18 Figure 2—5. Oscilloscope tracings of the outputs from the routing timer module, illustrating the beam-on, beam-off signals of the master clock (top) and the inhibition period before routing begins (bottom). Figure 2- 6 Oscilloscope tracings illustrating the routing signals (top), generated within the beam-off period (bottom). l9 Figure 2-7. Staircase generated by the routing pulses. —._'_ 20 trace shows the inhibition period within the beam-off time before routing begins. This time is shown by the difference in drop off between the top and bottom traces - in this case 20,05 sec. (horizontal scale approxi- mately 1 cm s 0.1 sec). In Figure 2-6 the bottom trace is the same as in the bottom pulse of Figure 2-5, i.e., it is the beam-off time after the inhibition period. This part of the cycle represents the time available for counting, =0.38 sec in this example. The top trace in Figure 2-6 shows the routing pulses that were chosen to fill the counting interval. Note that the first routing interval begins when the inhibition period is over and lasts for 30.09 sec before the next routing pulse appears. In most experiments, four of these routing periods were used, plus a fifth which was just allowed to start within the beam-off interval. This fifth pulse was started to assure that no beam-on spillover into the fourth routed spectrum could occur. Figure 2-7 shows the staircase generated by the routing pulses for use as required in some computer programs. The XDS )3-7 computer and the data acquisition program HYDRA were used With the above clock module. This program, written by Richard Au of the MSU Cyclotron Laboratory, is a time-shared task which can handle four 13- bit ADC's independently with an eight-way fanout for each. For a typical eRPeriment only one ADC is used, with five-4096 channel spectra being routed ‘ one for beam-on data and four for the beam-off data. As many as three ADC ' s , each with a five-way fanout, have been used with the clock module r:outing outputs. (Since the routing box inputs for our ADC's cannot be °°nnected internally, this requires teeing all the inputs together - see Figure 2-8.) Each ADC is controlled independently by the program. During an experiment, the contents of any ADC, or portion thereof, can b e analyzed, printed, plotted or punched. The processing time per count ---:l-SII’ if \. ...I\1-a 1H.i<\ 1|! .usoamm .3179»: m muffin sumo m.on< mmnnu EH3 wasvofi Moan wafiusou mnu mafia: wow 95mm wean—H3 .wlm 9.5me $9.47. . a... E. . nos/ii.“ . (42.. .4. r, .4 , I ,, 22 for this system is the ADC conversion time plus 8 usec, or 30 usec, whichever is longer. The ABC's employed were Northern Scientific 629's, which have a digitizing rate of 50 MHz. Under HYDRA each channel of data is stored in a half-word of the 22-7, so that overflow occurs at 64,000 counts -- the maximum number that can be contained in a half-word. (Since this number is sometimes insufficient, a full-word option soon may be added to the program.) The combination of the clock module and HYDRA has been found to be a very effective means for performing pulsed-beam experiments. This system has the advantage of simplicity and reliability. For many experiments it is ideal, for others, less so. The principal dis- advantages of the routing clock module are: (1) the time limits of both the master and routing clocks may be too narrow for the half-life one wishes to study, (2) the beam-on and beam-off times are not independently adj ustable, (3) the routing intervals are all of the same duration. 2.2.13 The Beam Pulser When the pulsing periods available from the clock module are not; suitable for a particular experiment or when unequal counting intervals are desired, a second method is available. This method makes Use of another beam pulser, which modulates the RF as described above, but which can provide a wider range of pulse times -- with adjustable beam-on times from 0.01 to 24.0 sec and beam-off times from 0.01 to 100 sec. These on and off times are independently adjustable for this pulsar. (The pulse: and its controls are shown in Figure 2-9.) Since this device does not provide routing outputs or do internal timing other than pulsing the beam, the following method is used for obtaining the desired time intervals for counting- 23 .mumfluso mam mHouucou macaum> waaBonm .uumfian anon unu mo Buw> udouh .mIN shaman 0 0 .o _o nww > .(Z‘ won—.3}: m £24,405 «OJuOWWb .1 r 25 «I 1333‘ av. » bu no...“ Ab..~ ,».m OKHN ..nwn 1! :12. ....w, 1 .53: as: .\ . . ....n V . _ _ . _ .. ’ :i : _ cf... 5. 1,; : _ , ..f, , J V _ .. _ _ . _ / , . ... _. _::_ 7;, a : _. ..i. :: , : 2 ,4 , ...,. ;.,,,..:, L E ,_._, ,. .,., l. , ,. . /.._ ., . I... 24 When the pulser turns the beam on, it simultaneously outputs a logic pulse that is used to reset a timing ramp -- usually created by using an operational amplifier to integrate a +12-V signal. Two ADC's are then operated in the synchronous mode, with one receiving the Ge (Li) pulses and the other receiving the timing ramp as gated by the Ge (Li) pulses. The data from these two ADC's are sent to the XDS Sigma 7 computer where they are processed by a time-shared software called TOOTSIE - a versatile multidimensional program written by D. L. Bayer of the MSU Physics Department (Bay7l). Although originally written for particle identification, TOOTSIE is suitable for general multiparameter data acquisition, and has been used unmodified for these energy vs time experiments. A block diagram for such an experiment is shown in Figme 2-10. The program TOOTSIE operates in two modes — Setup and Run. When in the Setup mode the program functions as a two-dimensional analyzer of maximum size 128x 128 channels, using the seven most signifi— cant bits of the ABC's. A horizontal slice of the two-dimensional array (in this case the two dimensions are energy and time) is then chosen for display and appropriate bands are drawn - each band corresponding to a time spectrum in the Run mode. The maximum number of bands is a f‘nlCtion of the size of the spectra. For example, only five bands are allowed if one needs 4096 channels per spectrum. After selection of the appropriate number and width of bands (the width of each band is PrOportional to the time interval viewed by that particular spectrum), th? Program is switched to Run mode. Each band then becomes a normal, °ne‘d1mensional spectrum of the designated size. A display generated by TOOTSIE while in the Setup mode is 25 RF ACCELERATING VOLTAGE ...... .... W INPUT TO RF MODLI. ATOR __ ,ft. GE(LII DETECTOR BEAM PULSER SPECT - , LOGIC OUTPUT USED To ‘m'F'ER RsET INTEGRATOR ~ I fig t- l 5 g "“'R§§f"1 I g * I I I 7“!“ I RAMP OUTPUT TIMING : INTEGRATOR I FROM INTEGRATOR CHANNEL Dc L ' ! ANALYZER ““““““ N I- E z '— % RAMP SAMPLEO , FOR EACH ANALOG TO ANALOG TO GAMMA PULSE DIGITAL INTERFACE DIGITAL , CONVERTER CONVERTER II" ”II” T xos 3:: COMPUTER ENERGY PROGRAM TOOTSIE, A TASK OF “'5 THE JANUS TIME- SHARING SYSTEM TIME AXIS Figure 2-10. Block diagram of electronics used for energy vs time experiments under TOOTSIE. 26 shown in Figure 2-11. This display represents a horizontal slice parallel to the energy-time plane, showing all the locations containing counts between two specified limits. The vertical axis is the time axis and the horizontal axis is the energy axis. Arrows and numbers showing the channel numbers as well as the horizontal slice limits can be displayed but were suppressed in this picture. The data shown are from a “3’"Ti search, using the microstructure Of the beam to set half- 1ife limits. The display represents y rays from one complete beam burst, the beam-off period, and another beam burst. The horizontal lines represent the lower and upper limits of the five bands. The same line that forms the upper limit Of one band may be defined as the lower limit of the next hand. These bands can be of any desired size (i.e., time). If desired, the limits need not be straight lines, but can be curves of any order polynomial up to 10. Figure 2-12 shows a three-dimensional display of the “3’"Ti data. This is a 64X64 section Of the two-dimensional display, shown as an approximate isometric display. Figure 2-11 is a horizontal slice of 3110-11 a contour. A scope display of TOOTSIE in the Run mode is shown in Figure 2‘13. The top spectrum is the first band (i.e. the beam-on spectrum), and the bottom spectrum is the fifth band (i.e. the fourth beam—Off time interval) from a l*3”’Ti experiment. The arrows and numbers at eafih end of a spectrum indicate the limits of the expanded region. The intermediate arrow and number show the marker, which can be moved back and forth for further expansion or channel number determination. In the upper left corner of each spectrum, the number of counts in the highest channel of the spectrum is shown. The number of the band 27 Figure 2-11. Two-dimensional oscilloscope display produced by TOOTSIE in the Setup mode. ......"muIIIllIWIHNHIIIIIIIMH.... " iiliiiiii"“"' Figure 2—12. Three-dimensional display available from TOOTSIE in the Setup mode. 28 Figure 2-13. Oscilloscope display produced by TOOTSIE in the Run mode. 29 being displayed is shown below this maximum-count channel number. (The bands are numbered from 0 to 11-1.) Any two spectra from the selected bands may be displayed simultaneously. The program and displays are controlled by sense switches together with a teletype. The use of the slow beam pulser combined with program TOOTSIE has provided an extremely versatile system for pulsed-beam studies of short-lived species. Half-lives from a few milliseconds to tens of seconds can be examined without difficulty. The experimenter is free to choose any time intervals he desires for Optimum half-life discrimina- tion. This method provides for successive spectra taken for independently selected time intervals out of a total period limited only by the pulser time ranges and the duration of the timing ramp. (Use Of the Operational amplifier for integration gives a ramp time range from about 10-4 sec to 10 sec. However, since linearity of the ramp is quite essential, long time periods should be avoided.) This method has all the advantages of that using the routing timer module, with the additional features of individually adjustable Counting periods for the "routed" spectra; individually adjustable beam-on, beam-Off times; and a larger range of beam on-Off times. The only disadvantages of the TOOTSIE approach are that it requires two ADC's and is initially more complex to set up and calibrate. $2.2 Deflection Plate Method An alternate method to the RF modulation type of pulsing is that of Llaing the pulser output to drive electrostatic deflection plates located so 513» to be able to deflect the cyclotron beam in its first turn. Thus, shortly after leaving the ion source, the beam is periodically diverted from the path 30 traversing a set of slits near the center of the machine. This technique is very adaptable and can be used for pulsing over wide range of times from nanoseconds to seconds. "Fast" pulsing (in the nanosecond region) is available by using these plates to eliminate, for example, nine of every ten bunches from the RF microstructure of the beam. Likewise, both beam pulsers discussed in Section 2.2.1 can be used to power the same plates for slow pulsing. Since the plates physically intercept the beam when it is pulsed, they must be located near the center of the machine before the particles are accelerated. Although this method is potentially a very useful technique for beam pulsing, it has not been utilized fully. Operation of the RF modulation pulsing has been so successful that other means of achieving the same goal have not been tried. Recent attempts to use the plates for microsecond range pulsing have been thwarted by thermally-induced geom- etry changes within the center region of the cyclotron, and consequent Redesign of the center region in order to misalignment of the plates. The method itself is Prevent this difficulty is currently underway. a proven technique, having been used routinely in the past for fast PUlsing. L-ZJ Utilization of the Microscopic Beam Structure By virtue of having a cyclotron, one always possesses a "pulsed" beam - albeit rather fast. At a typical proton energy of 36.0 MeV, one pulse occurs every 56.68 nsec with a duration of about 0.5 nsec, depending On the phase width. This pulse rate is very convenient for measuring the life-times of certain states or setting limits on very short-lived species. A block diagram of a typical electronics setup for utilization of this beam 31 .thOObs 54520. mmoz: (wad 4<4wo . r IIIIII L 9 mUu3Q2< mdwz... IIIIIIIII iTIIIIIIIIIIIII IIIIIeIIIIJ §33 [Im' 04... 20:04:... Tl, much-u Tull. . «=2» 6 on u Padbmzoo ozash _ _ _ _ . _ _ * 3.8 assume _ _ . _ r Block diagram of the electronics setup for utiliza- Figure 2—14. tion of the cyclotron beam microstructure for pulsing. 32 microstructure is shown in Figure 2-14. The program TOOTSIE is used in the same manner as described in Section 2.2.1B, with the setting Of time bands and the resulting spectra for intervals chosen. Calibration of the time is achieved by introducing a delay into the RF side and observing the shift in the two-dimensional display under the Setup mode. The bands drawn in Figure 2-11 are from an experiment of this type. The small bands for the "routed" s ectra represent a period of P about 4.2 nsec each. A set of time spectra from this experiment are shown in Figure 8-2 . Since beam pulsing in the microsecond range has not been available, employment of the microscopic beam structure to- gether with slow (milliseconds) pulsing has allowed the "bracketing" of half-lives in this time range. 33 2.3 Activation Chambers for On-Line l—Ray Spectroscopy 2.3.1 The Goniometer Chamber When this project was begun there had been little previous effort toward performing on-line y-ray spectroscopy at our facility. As a result, no specific equipment was available for this type of experi- ment. However, an elaborate goniometer had been constructed for charged particle scattering experiments (Tho68, Tho69),and its adaptation to on-line, y-ray work was a natural first step. A portion of the goniometer in one of its many experimental configurations is shown in Figure 2-15. The 8-inch diameter chamber shown in the picture was tised almost exclusively, in preference to a larger 16-inch one. The top of the chamber contains a 4-inch Marman flange, which is the type of standard coupling used in the beam line. The square box located on tap of the chamber is part of the vacuum manifold, which leads to a diffusion pump on the left. The top of this box is also fitted with a 4-inch Marman flange,which is used with a target transfer system to allow installation of targets under vacuum. The beam enters the chamber from the beampipe on the left. The beam input port consists of a coupling that fastens to the standard beam pipe and tapers down to slip into a l-inch diameter hole in the target chamber through a double O-ring seal. To aid in alignment Of the beam into the chamber, there is an insulated, 9/16 inch inside diameter, annular, tantalum slit located just before the restricted section. An exit port similar to this entrance port is provided for use with the 16-inch chamber. However, the smaller 8-inch chamber does not have a primary beam exit port, but instead has a slot in its side extending from -15° to +177°. INA: -.I K I r S ’Q { h i" The goniometer facility, showing the 8-inch activation Figure 2-15. chamber and detector mounting. 35 An O-ring groove is located l/16 inch outside of this slot on the out- side surface of the chamber. This slot port can be used in two different configurations. One configuration utilizes a foil window for the beam to pass through, while the other employs a sliding vacuum seal for precise scattering work. For on-line y-ray experiments the foil window was used, as shown in Figure 2-15. This window consisted of a 1/2 mil Rapton foil glued to an aluminum frame, which was bolted to the target chamber through the O-ring seal. The goniometer facility provides a number of other conveniences that are useful for y-ray spectroscopy experiments. A large arm extends to both sides of the unit and provides a mounting for one or more detector packages (cryostat, dewar, preamp, etc.). This arm rotates about the vertical axis of the main body and is controlled either by the local control box or a remote control panel. The targets are held in a vertical ladder arrangement in the center of the chamber. Three 1x2-in. target frames may be mounted in this holder. Vertical movement of the ladder for target selection, as well as rotation of the target plane with respect to the beam, can be controlled remotely or locally. A small manually positioned arm is located under the chamber and is quite convenient for mounting counters, accessories, and the like. The remote control panel, located in the data room, is shown in Figure 2-16. The various controls are in three vertical groups. The controls and digital counter for the target angle are located can the right hand side. In the center are the target height controls aund.counter. Automatic positioning of any one of the three targets 113 achieved merely by pushing the corresponding numbered buttons. Figure 2-16. 36 Remote control panel for the goniometer. 37 A manual mode allows further vertical positioning of a target in case of non-uniform or poorly centered materials. The group of controls on the left side are for positioning the main arm. In addition, this remote control panel has a graphic display which shows the relative angular positions of the incident beam, the main arm, the target, and the manually positioned arm. This display is located in the lower portion of the panel and is coupled to the digital readout system for both the main arm and the target. The local control box, shown in Figure 2-17, contains essen- tially the same functions as found on the remote control panel. How- ever, in addition to these controls, the local box has a main arm limit override switch, permitting the detector to be driven through zero degrees. This feature was not incorporated into the remote panel because of the possibility of crunching a detector into the beam-pipe when using an exit port with pipe extending into the beam dump. The local control box is portable, being connected to the power supply and relays through 30 feet of multiconductor cable. This mobility feature is very handy for alignment and positioning of the various components. The goniometer has been used in many on-line, pulsed-beam y-ray experiments with reasonable success. The most successful configuration has been the 8-inch chamber with the Kapton window. Although this system provides several conveniences, it suffers the following disadvantages: (1) The narrow (l/2-inch) section of the front (and rear) collimators as well as the Kapton foil and surrounding air, produce large amounts of unwanted y-ray activities when struck by the primary and scattered beam. This 38 Figure 2-17. Local control box for the goniometer. it"s-‘3’: I‘d. J. .4 .Iul , .. . fi 39 problem can be severe to the point of sometimes masking the target activity. (2) The distance from the target to the detector is quite large (>4 inches). As a result the relatively inefficient Ge(Li) detector subtends only a small solid angle with respect to the target. For y-ray singles experiments this can mean a higher unwanted-to-wanted y-ray ratio due to beam- pipe activation. For coincidence experiments, the counting rate becomes prohibitively low. 2.3.2 The Coincidence Chamber In order to overcome the disadvantages of the conventional goniometer chambers, a new chamber was designed for y-ray singles and coincidence studies. This rather simple unit is shown in Figure 2-18. Although the chamber can be fitted any place in the beamline, it is used primarily in the goniometer line -where the necessary focusing magnets and beam dump already exist. The chamber is a rectangular box, l-l/2 inches in width, 3 inches long, and 7-1/2 inches high. The sides are l/2-inch plexiglass and are removable. Different sides of various materials, thickness, and windows can be made up to suit a particular experiment. The present setup uses l/4-inch plexiglass sides with 1x2 l/2-inch windows covered with l/2-mil Kapton. The beam enters and emerges from the chamber through 45° aluminum conical adaptors having a minimum inside diameter of one inch. These adapters slip into holes in the chamber through O-ring seals and attach to the beampipe with a standard 4-inch Marman flange. A brass rod with a split end and set screw holds the aluminum target frame in position. This rod passes through a sliding seal at 40 Figure 2-18. The coincidence chamber 41 the top of the chamber, allowing the removal of fragile targets from the direct air stream while the beam line is being pumped down or let up to atmospheric pressure. The large scattering tolerance allowed by this design has resulted in a significant decrease in the-y—ray back- ground spectrum. In addition, the target-to-detector cryostat distance has been reduced to only one inch, with the provision for a detector on each side of the chamber for performing two-dimensional gamma-gamma coincidence experiments on line. 2.3.3 The Vacuum Transfer Chamber The design of the coincidence chamber did not include a provision for the mounting of targets which, because of their chemical reactivity, had to be maintained in a vacuum. When the use of such targets became necessary, a suitable chamber was assembled from various components with little modification. The chamber configuration that was used is shown in Figure 2-19. The body of the chamber is part of the vacuum manifold assembly from the goniometer. Thistxnc is merely a S-inch cube of aluminum, with two 3-1/2-inch holes milled completely through from two sides and a third such hole milled through a remaining side to within about 1/4 inch of the final side. The four holes opposite each other were each fitted with a standard 4-inch Marman flange. An O-ring groove was milled around the fifth opening and a l/2-inch plexi- glass window bolted into place. (For y-ray experiments this plexiglass plate has been fitted with a thin Kapton window.) The box is placed in the beamline with the window on one side, as shown in Figure 2-19. A rOund aluminum plate with a ladder-type target holder attached is fitted to the bottom flange. The angle of the target plane with respect to the Figure 2-19. Vacuum transfer chamber, valve, and transfer lock assembly. 43 beam may be determined by rotation of the bottom plate before tightening its clamp. The vacuum transfer lock then attaches to the top flange. As shown, the transfer lock consists of two parts -a valve, and a small, cylindrical vacuum chamber. The valve can be opened to an aperture of 3/4x2-1/2 inches, and will close vacuum tight. In the top and on the axis of the vacuum chamber there is a target transfer mechanism. This mechanism consists of a 3/16—inch steel rod inside of a S/B-inch steel shaft. The larger shaft enters the top vacuum chamber through a double 0-ring seal, while the smaller one enters the vacuum chamber through a double O-ring seal in the top of the larger shaft. The part which grasps the target frame is a split, conical, phosphor-bronze jaw. This fits into a conical hole in the lower end of the 5/8-inch shaft. The smaller shaft is screwed into the top of the jaw and is spring loaded to keep an upward pressure on the jaw mechanism. Each target storage chamber is equipped with a valve like the one shown under the vacuum chamber. In order to transfer a target, one first removes the storage chamber and valve from the cryogenic pump system used for storage. The vacuum chamber is then attached to the other side of the valve and pumped down to a pressure similar to that in the storage chamber. The valve is opened, the inner shaft of the transfer mechanism is depressed to open the jaws, and the rod assembly is pushed in until the jaws are over the target frame on the storage ladder. The shaft is then released, allowing the spring to tighten fluajaws on the target frame. The frame is withdrawn into the vacuum chamber, the valve is closed, and the storage chamber is removed. The storage chamber and valve unit is then fastened to the top flange of 44 the activation chamber. The beamline and chamber are evacuated. The valve is opened, and, while being sure that the frame is aligned properly, the target is lowered through the hole in the valve and into the target ladder. A clamp around the shaft is provided on the top of the vacuum chamber and prevents the transfer shaft from being drawn unexpectedly into the evacuated chamber. The removal of the target and return to storage is just the reverse of the above procedure. In practice, this system has been used almost exclusively for the transfer and irradiation of 1“)Ca and 1+8Ca targets. Since y-ray singles experiments were the primary objective of most of these studies, the current configuration of the chamber has proven very satisfactory. Since the narrowest constriction in the chamber is 3-1/2 inches in diameter, activation of Inaterial other than the target has not been a problem. The rather large target-to-detector distance (3 inches) has not caused any difficulty in singles experiments. However, this dimension, together with the need for a second thin window, seriously limits the use of the chamber for y-y coincidence experiments. 2.3.4 Discussion and Improvements All of the on-line activation chambers discussed above were designed or adapted to solve a particular set of problems. No one of these combines all of the desirable features into one unit, although these features are not mutually exclusive. A relatively easy and very useful improvement could be achieved by designing a standard, 4-inch flange assembly to fit on the top of the coincidence chamber. This would allow coincidence experiments to be performed on targets which are maintained under vacuum, with all the inherent advantages offered by 45 the coincidence chamber. In order to take advantage of the existing features of the goniometer the construction of a completely new chamber would be necessary. Such a chamber would combine the various aspects of the above chambers with those of one which was compatible with the basic goniometer mountings, thereby retaining the remote control arm and ladder arrangement. Since the goniometer facility is of modular design, compatibility is only a matter of providing the correct size flanges. The beam entrance and exit ports should be made as large as possible (the 3-1/2-inch size on the vacuum transfer chamber seems to be quite adequate). A standard 4-inch flange on top of the chamber would insure fitting of the target lock and transfer mechanism. Shallow detector wells should be included in the sides of the chamber to allow the detectors as close to the target as possible. Interchangeable windows on the inside of these wells would allow flexibility in the thickness and type of materials used as windows. Construction of a target chamber incor- porating these features would provide a versatile unit capable of handling many kinds of on-line y-ray experiments. 46 2.4 Rabbit - Pneumatic Tagget System The B- and. y-Spectroscopic study of moderately short-lived species (t§10 sec) is best performed in off-line facilities where the background radiation is low and the highest-quality detectors can be used without fear of neutron damage. In order to accomplish this, the irradiated target must be transferred first to a low-background area for preparation. Early irradiations were carried out near the cyclotron, through a thin Havar window,which was part of a Faraday cnqrbeampipe cap assembly. Each target was carried into the vault by the experimenter and subsequently retrieved by him. For shorter- lived isotopes, this required a mad dashing over top of the lowering vault door, seizing the sample and Sprinting to the preparation room. As more experiments were performed and the half-lives of interest grew even shorter, the need for a better target transfer system became quite obvious. After consideration of the various possibilities, a very successful pneumatic target system or "rabbit" was developed (K0369). One of the standard rabbits, i.e. the moving target holders, is shown in Figure 2-20. These units are 1-13/16 inches in diameter and 3 inChes long, with teflon ends and a central frame of aluminum. A l-l/8-inch square opening in the middle of the frame provides a place for carrying the target material and any needed absorbers. The rabbit shown in Figure 2-20 is equipped with a fast-transfer, disposable, aluminum foil target packet of the type used for irradiation of manganese powder in the 53mFe study. The interior and exterior terminals ‘Of the system are shown in Figures 2-21A and 2-21B, respectively. The interior terminal is located in the cyclotron vault, just beyond 47 Figure 2-20. Typical "rabbit" used in the pneumatic target system, with foil target packet in place. 48 Figure 2-21A. Interior terminal of the rabbit system. 49 Figure 2-213. Exterior terminal of the rabbit system. 50 the first large bending magnet (M3), which is used to divert the beam from the 0° line into the terminal. A plunging scintillator and viewing port as well as a water-cooled Faraday cup are provided for alignment of the beam. The exterior terminal is located in the target preparation room and is mounted on a cabinet containing the local control electronics. The rabbit is propelled between these terminals through a 2-inch clear cellulose acetate pipe (with bends made of the more easily bent poly- vinyl-chloride pipe) by creating a pressure differential across the rabbit. A large commercial vacuum cleaner is used to create a partial vacuum on one side, while air pressure (‘3 psi) is applied to the other side. To prevent the rabbit from crashing into the terminals, an air cushion is used for braking. A small sensor attached to the rabbit pipe detects the passage of the orientation magnet in the rabbit and turns on the braking air. The transit time for the target is about 4-8 sec, although this can be shortened to 2-4 sec by increasing the working pressures. The length of the rabbit tubing between terminals is now 2150 ft. Upon reaching the interior terminal, the rabbit can be oriented with respect to the cyclotron beam. This orientation is achieved by first rotating the rabbit with a jet of air directed on a set of fins near its base. The rotation is stopped in the correct orientation by the attraction between a small permanent magnet in the top portion of the rabbit (Figure 2-20) and an electromagnet in the terminal. The target is air cooled directly and water cooled by conduction through the aluminum frame. A block diagram of the rabbit system is shown in Figure 2-22. I Several new features such as a remote control panel for the cyclotron C£Hm501e and an automatic retrieval and ADC control device are being added to the system. 51 3.5980 EDI—05 PS mug—60 kaEmm m .5] Ton; I— ».84 :25 8 o J mazes 0.2.2054 _IB W mug mu; «.4 ma . a .58 I III, 3,5661 21 .355 Some . .6528 m4 0 .325» ..z... .azimms ..So. Ve/JJI . Jr “11$ .2. 53. szw .59 55.41 52 The rabbit has proven quite successful for irradiation of targets for off-line study. Because of its convenience, long-lived species as well as short-lived ones are routinely prepared using it. The system has been invaluable for experiments like the 53mFe E6 search, in which over 300 individual targets were irradiated and counted within a 24-h period. Without the rabbit such experiments would not be feasible. 53 2.5 Helium Thermalizer and Jet Transport When half-lives in the 10.0 to 0.010-sec. time range are to be investigated, the simplest method is to utilize a helium thermalizer jet transport system. The system at the MSU Cyclotron Laboratory was constructed by K. Kosanke (K0370) and patterned after that developed by R. D. MacFarlane (Mac63). The thermalizer box configuration as used in the experiments reported here is shown in Figure 2—23. The beam enters the box from the top through a thin Havar window. The target (usually a foil) is mounted in the water-cooled block directly behind the beam entrance. Recoils from the target are thermalized in helium (the box is maintained under 1-3 atmospheres of helium) and swept into the chromed-aluminum collecting hemisphere. This hemisphere is water-cooled and also serves as a Faraday Cup. The recoils, together with the helium, flow through a small hole in the rear of the hemisphere into a polyethylene capillary (ID 30.034 in.) where they are trans- ported at sonic velocities over a distance of :50 ft, to a counting chamber on the roof of the cyclotron vault. This chamber is evacuated to ”10—2 torr by means of a vacuum pump-Rootes blower system. A fixed collector consisting of a thin layer of vacuum grease on masking tape is used for most experiments. This collector is fixed to a thin plexi- glass window directly opposite a Ge(Li) y-ray detector. The tip of the capillary is placed perpendicular to the plane of the collector and about 1 cm from the surface. As the helium-recoil mixture flows from the capillary, the helium diverges rapidly, allowing the heavy recoils to continue more or less straight onto the collecting surface. The decay of the recoils is then detected in a relatively low-background area. Interior of the thermalizer box, showing the aluminum hemisphere and target holder. Figure 2—23. 55 One problem with this system has been the buildup of long-lived contaminants on the fixed collector. A tape transport unit has been designed to provide a moving collecting surface that will alleviate this problem (K0871). Two additional improvements need to be made on the system. The target holder and top plate of the thermalizer box need to be modified so that targets normally stored under vacuum can be inserted into the helium filled chamber without exposure to the atmos- phere. This step would prevent some target oxidation, although the impuri- ties in the helium would eventually damage thin targets of high chemical reactivity. The thermalizer-transport system will not function with highly purified helium. The slight impurities in the helium are thought to interact with the beam plasma to form very high molecular weight conglomerates, which serve as carriers for the recoils (Mac7l). The second modification needed is the installation of a seal between the Havar window and the target holder in the thermalizer box. This would prevent unwanted recoils from the window being transported to the counting chamber. With the present apparatus significant amounts of y-ray background from the window are observed. MOre efficient devices incorporating multiple targets and recoil collection at 90° to the beam have been developed (K0871). These offer increased recoil intensity and lower window background but require a significantly longer collection time. For investigation of short-lived species, the hemisphere collector‘has proven quite adequate. In the work reported here, the helium-jet thermalizer system has been used mostly for the three—particle isomer searches (see Chapters VII and VIII). Although the system allows relatively clean spectra to be taken with the best detectors, it has the disadvantage of not providing any 56 type offast time discrimination. When looking for unknown species, the ability to route successive spectra in time becomes very important, since it permits elimination of many y rays on the basis of half-life. Because the collection time within the thermalizer is stretched over a relatively long period, the system is not adaptable to pulsed-beam type experiments. However, for obtaining clean singles and coincidence spectra of short— lived species the helium-jet system is indispensable. 57 2.6 -¥-Ray Spectrometer Systems The development of Ge(Li) detectors in the early 1960's did much to revitalize the field of y-ray spectroscopy. Complex nuclear structures having numerous y-ray de-excitations, which were impossible to resolve previously, could now be studied with ease. This motivated the study of new decay schemes as well as the reinvestigation of earlier ones. As Ge(Li) detectors have grown in pOpularity and usage, their relative efficiencies and resolution have improved constantly. Early detectors were of the "homemade" variety, i.e.,fabricated entirely within each laboratory. As detector technology has increased, de- manding better materials and facilities, this "black art" has been relegated to commercial vendors. During the relatively short period of this study (three and one-half years), the improvement in the quality of our detectors has been quite dramatic. Early experiments were performed with a "homemade" detector having a resolution of 25.6 keV FWHM (for the 1333-keV y of 60Co) and an efficiency of (0.4%) (as compared to a 3-inx3-in NaI(Tl) detector 25 cm from a 60C0 source). Our latest detector was purchased from Nuclear Diodes and has a resolution of 2.1 keV and an efficiency of 10.42. The quality of other components of our Spectrometer systems has kept pace with the detector improvements. The preamplifiers, once mounted in external units with room-temperature FET's, are now an integral part of the detector cryostat. sometimes utilizing cooled FET'S for maximum noise reduction. Better protection circuits allow the detec- ’t0rs to be biased rapidly without damage to the FET's. MOdern spectros- copy amplifiers have undergone many improvements, including such features as adjustable base-line restoration and pole-zero cancellation. 58 The multichannel analyzers (MCA's) have increased in number, capacity, speed and versatility. Early experiments utilized a hardwired MBA with 1024 channels and a digitizing rate of 4 MHz. Current experiments use up to four computer-interfaced, analog-to-digital converters (ADC's) with 8192 channels each and a digitizing rate of 50MHz. Minor changes in cryostat design and dewar capacity have added con- venience to the systems. 2.6.1 Ge(Li) Simgles Spectrometer The Ge(Li) y-ray singles spectrometer system contains several components, each of which contributes to the overall quality of the final spectrum. A typical singles spectrometer includes a Ge(Li) detector and its bias supply, a charge sensitive FET preamplifier, a "spectroscopy" amplifier, an analog-to-digital converter (ADC), and a memory storage unit together with a readout mechanism (usually for "hard" copy, such as cards or paper tape). With the exception of some preamplifiers, the majority of the electronics equipment is modular and more or less mutually compatible. Thus, different modules from various manu- facturers can be combined to achieve the best results for a given type of experiment. A brief description of each of these components is helpful in understanding the system. The Ge(Li) detectors have already been previewed above. Several different detectors have been used for the experiments reported in this study. The specifications of some of these detectors are listed in Table 2-1. This table presents the detectors in chronological order, ‘clearly indicating the trend toward greater efficiency and better resolution. The choice of detectors for a given experiment will vary with the desired goal and conditions under which the experiment Vt..- 59 .000m to ease sea mmma was com saga n .uOuo0u0n AHHvaz eHImxm m Eoum a0 mm 00 OUom m0 3m0e >03 NMMH 0:0 00 uooemou 30H3m monOHn Ho0H0=z o0Hooo Hmemoo onus H 00 mm >03 H.~ N¢.OH omsmo muoumu0ea0u Boon Hmeooo 00ue H on em >03 m.H No.e omamo Ououmu0mawu aoou Hmemoo onus H 00 NN >03 o.~ Nc.m moeoee “moaosz emaoou Hmeeoumemue H as m.oa >03 ~.~ um.~ 00o0Hn uo0Hooz 0uoumu0o30quou HmmHon0omuH H 00 m >03 c.m No.N .an conuOHomo Dmx 0u0u0u0ee00 Soon HmoHouoomus H on 0 >03 ~.m No.Hn .nog e0u00H0>o sz muoumuoaaou soon Hmoflowoemua H 00 m.e >03 o.m N~¢.o u0uouommoomz 8mm nam0um 0omnm OHumm noOHuoHom03 «>0e0H0Hmwm 0003500 on 300m mGOHumoHuHomem Houoouon AHavoo HIN 0Han 60 is to be carried out. Generally speaking, the detector with the best resolution and the highest efficiency is most desirable -- all other factors being the same. However, facts like the precision with which the efficiency curve is known at a certain distance, the amount of jitter associated with a given detector, or whether the detector Should be exposed to in-beam conditions, may govern the choice of a detector. Simple matters like experimental priority and the availability of a given detector on a given date can dictate the final choice. The bias voltage for these detectors varies from a few hundred volts to a few thousand volts. Choice of a power supply is determined both by the capacity of the supply and the noise it may add to the system (thus, reducing the resolution). Large, well-regulated high-voltage supplies such as Fluke and Northeast seem to be much less noisy than the small, module types. Taken in logical sequence, the next component is the charge- sensitive, field-effect transistor (FET) preamplifier. This pre- amplifier integrates and shapes the charge output from the detector and sends a tail pulse to the main amplifier. Typically, this pulse has a rise time of =25 nsec and a decay time of z50 usec. These preamplifiers come both as separate, independent modules or as an integral part attached to a particular detector. The attached units may be of the usual room-temperature FET variety or the cooled FET type . Today's spectroscopy amplifiers offer great versatility, with many features to improve the resolution, particularly at high count rates. Both unipolar and bipolar output pulses shaped with shaping constants ranging from 0.25 usec to 4 usec can be obtained with various maximum amplitudes of either polarity for use as an input to an ADC 61 or for timing purposes. These amplifiers have highly linear amplifica- tion responses and include such features as adjustable pole-zero cancel- lation, base-line restoration, and DC offset. The pole-zero cancellation feature permits precise elimination of undershoots on the amplifier pulse after the first differentiation. This becomes important at high counting rates, where if the undershoot saturates, the amplifier will be blocked not only for the time of the primary pulse, but also for the duration of the undershoot. In addition, the following pulses which fall into the undershoot will have an apparent area smaller than the actual area, therefore causing deterioration of the resolution. High count-rate resolution is also improved by the base-line restoration feature. This device restores the undershoot of the amplifier signals to a DC baseline after all other shaping has been performed. The im— proved resolution is brought about by the reduction of pile-up distortion caused by undershoot. The DC level adjustment matches the DC level of the amplifier unipolar output to the DC level of the direct input to the ADC. Additional features incorporated into some amplifiers are very convenient. The so-called "common mode" found on some amplifiers sometimes provides a solution for noise pickup in long cables. Almost all amplifiers now provide a convenient plug on the rear of the module for powering preamplifiers. Likewise 930 outputs are also found on most units for proper termination. The last component in the spectrometer system is the multi- channel analyzer. During the course of this study a variety of analyzers has been used. As one might expect, the size, versatility and sophis- tication of these devices has improved concurrently with other components of the system. The pertinent characteristics of several multichannel 62 analyzers used in this investigation are given in Table 2-2. As can be seen, the trend here has been toward increasing the number of channels and speeding up the digitizing rate. Tremendous versatility is achieved by interfacing the ADC's to a computer such as the Sigma 7. The on— line manipulation of the data, together with various acquisition modes such as routing, multi-dimensional storage, etc., are extremely power- ful tools. These methods will be discussed in more detail in later sections. 2.6.2 Ge(Li)-NaI(Tl) Coincidence Spectrometer Systems Although y-ray singles experiments can provide very accurate energy and intensity measurements of y rays associated with a decaying nucleus, they reveal nothing concerning the relationships of these y rays to each other. In order to determine these relationships and establish a decay scheme, one must perform a number of coincidence experiments. Several different types of single parameter coincidence spectra are normally utilized. These include anticoincidence spectra, which reveal y rays that are not in coincidence with any others, e.g. direct ground state (if not B+-fed); any- or integral-coincidence spectra, which reveal y rays that are in coincidence with any other event; gated-coincidence spectra, which show y rays that are in coincidence with a particular transition or region; and, 511-511-y coincidence spectra, which emphasize double escape peaks and B+-fed levels. Each of these types will be discussed in the following sections. 2.6.2A Ge (Li) vs 3XB-in.NaI(Tl) Spectrometer Prior to the fabrication of large, relatively efficient Ge(Li) 63 Table 2-2 Multichannel Analyzer Specifications Maximum Number ADC of Channels Digitizing Rate Memory Nuclear Data 150 1024 4 MHz Hard wired Nuclear Data 160 1024 4 MHz Hard wired Nuclear Data 2200 4096 16 MHz Hard wired Northern Scientific 625 2x 4096 40 MHz Interfaced to DEC PDP-9 Northern Scientific 629 4x 8192 50 MHz Interfaced to xns Sigma-7 64 detectors, which allowed Ge(Li) vs Ge(Li) coincidence experiments to be performed, the principal means of obtaining timing pulses for coincidence spectra were NaICTl) scintillators coupled to photo- multiplier tubes. This system utilized the best advantages of the two types of detectors, with the poor-resolution, but highly efficient NaICTl) detector being used as a gate for the inefficient, high-resolution Ge(Li) detector. A block diagram of this type of set-up is shown in Figure 2-24. Besides the usual equipment required for a singles experi- ment, an additional detector and electronics are needed to provide timing information. A 3x3-in NaI(T1) detector was used for this purpose. This detector had an efficiency approximately 10 times that of the best recent Ge(Li) detector (10.4%), and a resolution of =82 (for the 6ll-keV y ray of 137C8). The pulses output from the photo- multiplier were sent to a spectroscopy amplifier through a cathode follower, which serves as an impedance matching device between the tube type photomultiplier and transistor amplifier. After amplification and shaping, the NaI(Tl) signals are input to a timing single channel analyzer (TSCA). The TSCA checks to see if the pulse falls within a predetermined gate (window), and, if it does, outputs a logic pulse to a fast coincidence unit. Likewise, a similar timing signal must be developed from the Ge(Li) linear signal. This is achieved by using a second TSCA which sends a logic signal to the same fast coincidence module. (Normally the gate on this second TSCA is opened completely, giving a timing pulse for each Ge(Li) pulse it receives.) The function of the fast coincidence unit is to output a logic signal only when a Ge(Li) and NaI(Tl) logic pulse arrive within 65 .uo0afiumexo 00o0vHoeHoo aHHvaZIAHAV0o HoOHehu 0 mo awkwMHv 300Hm .eNIN ouome a3 5338.. 5505.. <03 $803 30:20 assume 2:22 masses , 32020.28 Se... IT .2205 _ use x d _ come «03.... w , 2.2: a toga 08:8 uses , c8038 03 :3 02.00 T02 a a... .e o» 2.3 5023 e 50..» use .380 use >53 {oomofiouh 66 a specified time interval of each other. For most coincidence experi- ments, this resolving time (2T) was set at z100 nsec. An external linear gate was used for almost all coincidence set-ups. A logic pulse from the fast coincidence module opens this gate for a predetermined length of time, allowing any linear signal present at the input during that time to pass through the open gate and on to the ADC. Thus, only pulses from y-ray transitions occurring within the specified resolving time are allowed to pass through the linear gate and be processed by the ADC. The delay amplifier in the Ge(Li) linear circuit is merely to compensate for the delay incurred by the timing signals while they are traversing the coincidence units. The delay is adjusted so that the linear signals and the coincidence timing signals arrive simultaneously at the gate. This simple system has been used for several types of experiments. The normal geometry used has the Ge (Li) and NaI (Tl) detectors oriented at 90°, with the radioactive source at the apex. A graded lead absorber is used between the detectors to prevent scattering events in one from reaching the other. For integral coincidence experi- ments, the NaI(Tl) TSCA window is opened completely. Closing this window to a particular peak or region allows gated-coincidence experiments to be performed. If the window is opened but the linear gate is switched to anticoincidence mode, one obtains a very useful anticoincidence spectrum. 2.6.2B Ge(Li) VS BXB-in. NaI(Tl) Split-Annulus Spectrometer The 8x8-in. NaI(Tl) split annulus is the keystone in one of the most useful spectrometer systems available at this facility. The two Optically-isolated halves of this detector can be combined with other detectors to perform a wide variety of experiments. Several configurations 67 using this annulus in conjunction with a Ge(Li) detector have been described by Auble et al. (Aub67). In the work reported here, the annulus has been used for the following types of experiments: anti- coincidence, integral coincidence, gated coincidence, Sll-Sll-y coinci— dence, and Compton suppression. An illustration of the various detector-source geometries for typical experiments is reproduced in Figure 2-25 (from Doe70). A block diagram of the electronics set-up for using the annulus in an anticoincidence experiment is shown in Figure 2-26. As can be seen in Figure 2-25, a 3x3~in. NaI(Tl) detector is placed in one end Of the annular tunnel in order to increase the solid angle sub- tended by the detectors. A Ge(Li) detector is then positioned in the other end of the tunnel, facing the 3X3-in. NaI(T1) detector --with the source in between, approximately in the middle of the tunnel. The electronics for each section is just like that described in the coin- cidence experiment in Section 2.6.2A above. Now, however, there are three NaI(Tl) timing signals instead of just one. These three timing signals are combined in two AND/0R gates that produce a timing signal whenever one or more of these signals is present. This is accomplished by using an ORTEC universal coincidence unit with the number of coinci- dence requirements set to one, as the AND/0R gate. In this mode, the resolving time control on the unit has no effect. The relevant time consideration is that of the fast coincidence module, which is normally set to 100 nsec in these experiments. The output from the ‘fast coincidence unit is then used to trigger a linear gate operated in anticoincidence mode. Such efficient anticoincidence experiments as this have been 68 A. ANTI - COMPTON s. ANTICOINCIDENCE f ”y! a l C. INTEGRAL CONCIDENCE . \\\\h\\\ a. Ge(Li) Detector b. Photomultiplier Tube c. Half of Split Annulus d. Graded Pb Collimator e. 3X3-in. NaI(Tl) Detector f. Radioactive Source Figure 2-25. Detector-source geometries for several experiments utilizing the 8X8-in. NaI(Tl) split-annulus spectrometer. 69 helpful in identifying ground state transitions which were Primarily electron- capture fed and also transitions from isomeric levels, i.e..transitions from levels having half-lives considerably longer than the resolving time of the apparatus. The anticoincidence spectra also show sub- stantial reduction in the Compton background, since any Y-ray scattered in the Ge(Li) detector has a high probability of being detected by one of the surrounding NaI(Tl) detectors. With only slight modification of the anticoincidence set-up, one achieves a "singles" spectrum having a drastically reduced Compton background. This Compton-suppression or "anti-Compton" experiment as it has come to be called, has been very valuable in extracting weak, lower energy peaks from the Compton background. In this type of ex- periment, the 3X3-in. NaI(Tl) detector is replaced by a graded lead collimator containing the source. As a result, the radiation from the source travels into the Ge(Li) detector, while being shielded from the NaI(Tl) annulus. Thus, the annulus sees only y rays which are Compton scattered from the Ge(Li) detector. When such a y ray is recorded by the annulus, the gate is closed and the Compton event observed by the Ge(Li) detector is rejected. The equipment shown in Figure 2-26 can also be modified for use in obtaining integral and gated coincidence spectra. For integral coincidence experiments, the TSCA's in the NaI(Tl) timing circuits are each adjusted to accept all y-ray energies above x-rays, and the linear gate is switched to "normal mode", i.e., closed until opened by a signal from the fast coincidence unit. With these changes, the resultant spectrum should contain only those y rays involved in a cascade within the resolving time of the fast coincidence unit, normally about 100 nsec. (Improved resolving times of 2T :20 nsec are now possible). 70 IUGHOW FOR NbKTn THING IIIUKJ l 0' I?" NHULUS Figure 2-26. I' ---------------------------------- 'I LINEAR AMPLIFIER 7' ° ‘ LINEAR AN DIOR AIIPLIPIER T 3 ‘3‘ 1, LINEAR . AMPLIFIER T SCA L ...................................... - TSCA Jill-m FAST ANPLIRIER ......“ 00m“ SIONALS OATE SIONALS LINEAR , OELAY . LINEAR “c ""LIF'“ AIIPLIIIIER SIONAL “TE ° Block diagram of the electronics setup for an anti- coincidence experiment using the split annulus. The same equipment is used for obtaining pair spectra after elimination of the 3XS—in. NaI(Tl) detector and the AND/OR gate. 71 The equipment needed to perform a gated coincidence is the same as that used for the integral coincidence experiment just described. The only change needed is to set an energy window with the NaI(T1) TSCA's so that only those y rays falling within this window will cause the TSCA's to output a pulse to the fast coincidence unit. The gated spectrum then will contain only those Y rays that are in coincidence with this energy window, which is usually set on a particular transition or region of interest. This teChnique works quite well for simple spectra having only a few well-separated peaks. For complex spectra however, the poor resolution Of the annulus (=102 for the l332-keV y ray of 60Co) makes interpretation of gated spectra quite difficult, since each gate usually contains a number of Y rays. In addition, this technique is inefficient with respect to cyclotron time. In most cases the development of two-dimensional Ge(Li)-Ge(Li) coincidence systems has rendered this type of gated coincidence technique obsolete. The annulus can also be used as a pair spectrometer (511-511-y coincidence spectrometer) for examining the 8+ feeding to various levels. The apparatus needed for this type of experiment is similar to that shown in Figure 2-26, except that the 3X3-in. NaI(Tl) detector and its associated electronics are not required. Since a triple coincidence is required (that is, signals from both halves of the annulus and the Ge(Li) detector must arrive within the resolving time of the fast coincidence unit), the AND/0R gate is not necessary. The TSCA for each annulus half is set to gate on the 511-keV region. Thus, only y rays ~occurring within the fast coincidence unit resolving time of two separate 511-keV y rays are recorded. This results in spectra which show enhancement of those y rays involved in prompt coincidence with levels which are fed by BT'emission. As might be expected, double-escape 72 peaks also are enhanced in these spectra. 2.6.3 Ge(Li)-Ge(Li) Coincidence Spectrometers The development of large volume Ge(Li) detectors having a rela- tively high efficiency has allowed their use not only as primary detectors but also as gate detectors for coincidence experiments. The superior resolution and peak-to-Compton ratios of these detectors now outweigh their characteristic inefficiencies and permit vastly improved coincidence experiments to be carried out. Although simple gated coincidence ex- periments of the type described above can be performed using two Ge(Li) detectors, this method has been superseded by the development of two- dimensional, "megachannel" coincidence techniques. Modifications of this very powerful method allow rather thorough investigation of short-lived isotopes. 2.6.3A Two-Dimensional Data Acqgisition UsingTRoutigg The technique for performing two-dimensional, "megachannel", y-y coincidence experiments has been refined and utilized extensively in this laboratory (Bee69, Epp70a, Doe70). However, application of this method to the investigation of short-lived isotopes (tl/Z -.-~4 » . _. ,. -..... ....s W ' ..-.. 2,7 My??? .2. . . "V4,, . ’v " 3 .. 9,8” ”his. '42: is: . . , . u- n.‘.!. ’. n, b.- Figure 3-1. MDIRAE display oscilloscope and sense switches. 83 spectrum resulting after subtraction of all events below this curve also can be displayed. All display and calculational parameters are controlled by the sense switches, including the type of display (log or linear), the scale, expansion and shifting of the horizontal axis, background order and type of output. A complete, unexpanded 4096-channel spectrum as displayed on the oscilloscope is pictured in Figure 3-2. (This happens to be the first routed spectrum from a “&"Ti search using the microscopic structure of the cyclotron beam.) After chosing the type of display and background order desired, the next step in the analysis under MDIRAE, is to expand the spectrum horizontally to a convenient working size. Figure 3-3 shows a partially expanded segment from the spectrum shown in Figure 3-2, covering the region from channel 100 to channel 550. The numbers across the top indicate (from left to right) the number of counts in the location marked by the tall vertical pointer, the channel number of this location, the run number, the subroutine currently in use, and the order of the background fit being used. When a log display is chosen, instead of the linear one shown, the number of cycles is displayed to the left of the run number. Since the peaks are not clearly discernable in Figure 3-3, a further expansion is necessary for easier determination of the background. As can be seen in Figure 3-3, the subroutine "expand" has been called, and the desired limits are designated on the left by a short channel marker and on the right by the tall pointer. The result of this expansion is . shown in Figure 3-4 and covers approximately 100 channels. This expansion is sufficient to give good separation of the peaks and allow individual channels to be viewed for use in background selection. This same horizontal 84 Figure 3-2. MDIRAE oscilloscope display of an unexpanded 4096- channel spectrum from the ”3WTi search. «00 o 379 ’07 IIPIID 3' Figure 3-3. Partial expansion of the spectrum from Figure 3-2, showing the limits chosen for further expansion. 85 Figure 3—4. Display of the expanded segment from Figure 3-3. A third order background has been fitted using the BACK 1 routine. Figure 3-5. Display of the spectrum as shown in Figure 3-4, including the peaks after subtraction of the third order background. The selected peak limits and calculated centroid are shown for the 270-keV peak. 86 expansion is normally maintained throughout the entire analysis, with the spectrum being scanned across the scOpe by use of a sense switch. The vertical scale is readjusted to maintain a good view of the data as the number of counts varies. A background is then fitted over all or any portion of the segment displayed. This background is comprised of channels chosen by the operator and included in a polynomial least-squares fit. The order of the polynomial can be varied from one to ten at the discretion of the operator. Figure 3-4 shows a background fit using a 3rd order polynomial. The tall vertical pointer on the right is the movable marker used for choosing channels to be used in the analysis. The short, vertical lines along the bottom of the display are markers, indicating which channels were accepted to be used in the least-squares background fit. Two routines are available for background selection: BACK 1 allows the selection of individual points to be used for the polynomial fit. BACK 2 permits the selection of regions or groups of points between two markers to be incorporated into the background fit. If the polynomial curve does not approximate the background (as judged by the operator), the fit can be rejected, and repeated or modified by accepting additional points. Having achieved a satisfactory background fit under a given peak, the operator uses the vertical pointer to select the upper and lower channels to be considered as limits for that peak. A center of gravity calculation is then performed over the channels between the selected limits to determine the centroid of the peak. The sc0pe display for this routine is shown in Figure 3-5. The two tall markers under the 270.5-keV peak (second from the left) indicate the limiting channels 87 used in the centroid calculation. The short vertical line near the top of the peak marks the location of the calculated centroid. Two routines are available for calculating the centroid. PEAK l calculates the centroid on the basis of the total raw peak, whereas PEAK 2 utilizes only that portion of the peak having counts greater than one-third the maximum. In either case the program calculates the peak centroid, area, sum of the raw data and background and the square root of that sum. These results for each peak are stored on a computer disk and are output either at the end of the analysis or when subroutine UNLOAD is called. The results are output on the line printer, punched on cards and/or plotted on a Calcomp plotter, as designated during the analysis. Figure 3-5 shows both the data and the difference spectrum after subtraction of the fitted background from the raw data. The shape of this difference spectrum provides another check on the accuracy of the background fit. The points near the top of the picture indicate the channels which have fewer counts than the fitted background. This process of background fitting and centroid determination is continued until all the resolvable peaks in the spectrum have been analyzed. A sample of the line-printer output from MOIRAE is shown in Figure 3-6. The data are the same as shown in Figures 3-2 to 3-5. The top section gives the counts per channel of the fitted background. By examining the regularity of these numbers, one can determine whether the fitted background varies in a smooth manner. This is important, since the higher order polynomial fits can generate unwanted fluctuations, such as looping back on themselves. The center portion of the figure gives a channel-by-channel listing of the difference between the data and the fitted background. This listing is also helpful in determining the quality 88 RL\ 737 alc40”“g'\: 0'3"" {-7 ..fo 0 1 I I 0 I 0 I 9 290 so! 9$o~ 3995: 3:0 93!! 90 o 90 a 9790 979i 9793 ’7’! ’7 31° 9 918° 978° 979° 97.9 97.! 91.. 37.0 9788 33.0;‘ 3.0 967’ 96¢: 96cc 000929 ”UK 737 Tl"[9"cf ’81-? f"0 "lV? IS Inc .9 -S y 5001! thlna7t or than. sclvrc(chOIO.-vucltcanoot:/N: II 33-0.: RUN 737 CH3 30: visa" stnnc~ CINYIOIO usxuo tor-L Flax ll Iii-III 00H 2! RA. DAY! A~o lacuclouuo II 897600 -—-—* ::t; . 2:39 :: ,;;;; i: r~c Pal‘vs LSC? .r-: 313 )2: Run 707 Cuitggt 71.3" ggAIcu '-———~—-«.__..__. ‘ .Aan_lac:nlouun_&c____—___.. —:IIOO- ccxvaol: ttxxo vuv.L err: 15 Jae-I32 5L” of 3:. TaYA Axe BAC‘G"UVO ls $23256 ‘-———-«— _i__i._i-snaABL_31;i:hf Afifiifi is, alg-e-I (NO 901‘?! USID utlt III I!) \ _________W‘.h__ __- fl___ ii»? 759' WISH“ " '7???- EEE: "“‘ _’ EIF'E‘W‘TL 9:74.“ an :n. A\: nuctsfl'n‘fi IS 960 .‘ a 15 U" “Ab CAYA ARC BACKGIOUVO 13 186.7: SOUA'Q “#97 or per.; 1; 30.0017 -.. LhQ.EDl)1§th£J .LSL, ___" , __ _,., 111 - _i--r_..i.__JJA_. The Figure 3-6. Sample of the line-printer output from MOIRAE. data are the same as shown in Figures 3-2 to 3-5. m u: 4‘ O I I‘i 89 of the background fit. The last three sections shown in the bottom half of Figure 3-6 are the listings of the analyzed parameters for three of the peaks for which the background was determined. (These are the last three peaks to the right in Figure 3—4.) The parameters listed are defined as follows: The "difference between raw data and background" is the net peak area to be used in the determination of the Y—ray intensity. The "centroid" likewise is used for the energy calculation (note that the program lists which routine, total (PEAK 1) or upper two- thirds of the peak (PEAK 2) was used). The "sum of raw data and back- ground" is merely the raw data count of the peak. The "square root of the above" is the square root of the raw data count of the peak. The "end points used" are the lower and upper limit channels of the peak, as chosen for the centroid and net area determinations. Not shown in the figure, but printed out for each spectrum, is a listing of the raw data. Conversion of the centroids and net areas determined by MOIRAE into energies and relative intensities is achieved by the program MDIRAE E(I). This FORTRAN program, written by D. Beery and G. Giesler, utilizes the card output from MOIRAE to read the results of the previous analysis. The centroids of several strong, well-known y rays are used to perform a least-squares fit to a quadratic energy calibration curve. These "standard" centroids may be contained either within the same spectrum as the peaks of interest (internal standards) or in another spectrum taken under the same conditions (external standards). This energy calibration curve then is used to determine the energies of all the peaks in the spectrum. These energies and the corresponding net peak areas are used in conjunction with a predetermined detector 90 efficiency curve to produce the relative intensities. The resultant energies, relative intensities, input information, and calibration fit are output on the line-printer. A program listing of MOIRAE E(I) together with details of the efficiency curVe preparations may be found in (Gie7l). The advantages and disadvantages of MDIRAE must be viewed in the perspective of time. When the program was first introduced it represented the most convenient and fastest method of data analysis. Previous programs required each individual peak interval and its background intervals to be specified on a control card. Obviously, MOIRAE with its live display and sense switch inputs, provided a much improved means of data analysis. Although faster, more sophisticated programs have since become available, MOIRAE retains some advantages. For example, the complete operator control of various subroutines used in the analysis is often very desirable. The background order, back- ground points or intervals, and peak limits can be manipulated until a satisfactory result (in the judgment of the operator) is obtained. This can be important when dealing with complex spectra having irregular backgrounds. Another important feature of the program is its ability to scan through many spectra while maintaining the same expansion and channel location. This is very convenient when one is trying to determine transition half-lives by following a single peak or region in several spectra taken in sequence. One of the principal disadvantages of MDIRAE can be a feature _ just cited as an advantage, i.e., complete operator control. The all important choice of "best" background fit is left up to the judgment of the operator. Such parameters as the interval to be fitted, selection 91 of points to be used, and order of the polynomial to be fitted to the background are all arbitrarily decided. For intense, well-shaped peaks situated on a smooth background, an accurate fit is easily possible. However, in the more realistic case, where one is dealing with many closely spaced peaks with poor statistics on an irregular background, the situation is quite difficult. One does not really know the shape of the underlying background. Normally, various backgrounds are tried, until the operator is satisfied that he has a reasonable approximation of the true background. The length of the interval fitted is usually a compromise between the speed gained in choosing a large interval, and the accuracy of fitting a smaller one. The key to good results lies in the degree of consistency with which operator selects the backgrounds and peak limits throughout the analysis. Since MOIRAE does not utilize a standard peak shape and the backgrounds are chosen at the whim of the operator, consistency is difficult to maintain. It should be noted that the area of the peak is much more sensitive to the background fit than is the centroid. Another disadvantage of MOIRAE is the fact that it cannot strip unresolved peak multiplets -- an important consideration in complex spectra. Compared to other methods of data analysis, MOIRAE is relatively slow, with analysis of a single complex spectrum requiring as much as three hours. Since MOIRAE utilizes a live display, it requires a large amount of computer time. Thus, when several programs are running simultaneously under the time-sharing monitor, all jobs are slowed and the display scope can become erratic. In spite of these difficulties, MOIRAE remains a useful and often convenient method of data analysis. 3.1.2 Prmam WD 7 MOD 7 is actually an adaptation of MOIRAE, retaining most of the 92 subroutines found there. This task, develOped by D. Bayer, utilizes a Tektronix 611 storage oscilloscope for the display and thus alleviates the problem of having to drive a live display from the computer, as with MOIRAE. The storage scope and sense switches used with MOD 7 are shown in Figure 3-7. There are two such terminals interfaced to the Sigma-7 computer, allowing two MOD 7 routines to be operated simultaneously. Being derived from MOIRAE, MOD 7 retains most of the advantages and disadvantages discussed earlier. A very useful modification has been the addition of a third subroutine for background fitting (BACK 3). With this feature, one is not restricted to existing data points, but may choose any number of locations and points, connected by straight lines, to form the desired background. Thus, a very complicated background can be approximated by a sufficient number of these points. Likewise, a simple linear fit can be obtained by selecting only two points. Since one is dealing with a storage scope, the spectrum cannot be continually scanned across the display screen but is shifted right or left by the number of channels between a moveable-cross marker and the corresponding side of the displayed expansion. Otherwise, MOD 7 is quite similar to MOIRAE. The smaller display screen together with smaller switches located in a less convenient arrangement, make data analysis with MOD 7 more difficult and lengthy. However, the increasing use of the computer has made the utilization of storage scopes almost imperative. Because of this restriction, MOD 7 is normally the program used for direct, operator- controlled data analysis. 3.1.3 Program SAMPO SAMPO is a FORTRAN data analysis routine written by J. Routti .. ...... a: “at-LFHHHI-Ir "Nil“! ’ 93 .n no: nuHB pom: monouw3w mmawm was oaoum mwmnoum och .mum oudmfim D9 GIG-I #KC)--I “a- a}... .m. s. a. ) a. w. m, flI‘ll..."‘fll‘Ils‘nlllrlcllllbi'ttliist.l.n.¢.n\l. i.‘ ”01.1.- 94 (Rou69) and adapted for use on the Sigma-7 MSU cyclotron computer by T. Arnette, C. Merritt, and C. Morgan. Communication with the program can be maintained either by FORTRAN control cards or via a storage scope and sense switches. The task includes algorithms for line-shape, energy and efficiency calibrations, and peak-search and peak-fitting routines. The current version of SAMPO can provide most of the features found in previous programs, plus a number of important additions. Among the features used for nuclear spectroscopic data analysis are: a) The fitting and subsequent subtraction of background. b) The fitting of photopeaks to analytical functions and deter- mination of the centroid for each peak. c) The preparation of an internal energy calibration curve, and its application to determine the energy and the statistical error of the energy for each peak. d) The calculation of net peak area and statistical error of the area for each peak and conversion of these to relative intensities via an internally prepared detector efficiency curve. e) The resolving or stripping of multiplets using the peak-fitting parameters. f) The plotting of spectra on the Calcomp or line-printer. g) The calculation of half-life data. The tabulated results of the SAMPO analysis, together with plots of the raw data, fitted background, and peak fits, are output on the line-printer. A section of a SAMPO output for a “3mTi spectrum is shown in Figure 3-8. These peaks are the same ones as used in the MOIRAE Figures and output example from Section 3.1.1. 95 :2; 83. 3:: :3; EF: ..m. ..n...I-L..W.EI\ Er. .5.mb . 3on3 coco. ...—no 33.. ...—n. 73. 93.... 2.9L: :3. ::..: «as... 5.5 «Sid «13.. 1!..." 44.. «44.. «arr-u Ann; Mafia-an. l mono; anon. 0&7; coca." “.05: .3”. nun”.| «VEml {tau} ..lonmhiomlx .52 .52 3.53. :92 3:33. :2! Cu! ..m: ...:u. $.33... ::.:.. 5.1.33 591:: «:3: ...: .3. 2.25.?» :UJIJ BL; .855. ...: 3:. 3:2. .2 3... .35 sleiuuui. a. 2.: . .....3 ..p 2... . $.55 : so... 2...:3 «...-L Y. .L. :2...” .... ..C ...... ml .0... 933...? formuo div-Hm fuunnc ::083 .‘Ill ._ I I .u—I- I h Dyl- u bill. I ufllD . ”.Ifllu A "film“ :5:::_::::::: :_:::. _._... : _ . . . .2: .32 Lp ...: 7 0.... 1: .3: Zoo - .3: T A: .0.~Bon “MOB" . N.» .mnon a. .ucn E .33 L2. \ . .1: oz. 6: L; . |\ . . “Mr... nuns—n ”.32. . 1 . a . a. .33. is: . .2. o. . "cu—2 $00.". .00: ... ..nn 1% I ...... ...... | lllll. v. ..2. .... .... u . .0: u. . .28 .22: ...-3. \ .nn: .. .2. r I did»... 1 Jun o . no a: ocun .132 .13— / .mscu a: £3 ...-a an: . 1%..“ . . ulju‘ . . 3......“ ... ...m." u u ..m . .0 n :3- .oBo ‘\.| I 11 ll 1.. \ -LdunL: Jul. at! .ncna . .nnoo “.nc ”mm” a O I .maoo Ac: {rm-«01; li‘ .\. .3: ..n. .3» 322 :0: o.\|\| .039 a... .0: :::. ”.8: .‘l‘lll‘l‘l‘lll :1] :l I: .Lt‘ rt- .2? I; p . a: a: ..un .33. énoa. “[1. .un; Ta. .2» in»: ...—n. I] ll} . i .03.. lit‘ . u o . .n . .1 a" ”n Lane in: ‘i‘l‘uQ‘tlél 1:1 A: i Photograph of a portion of the line-printer output from a SAHPO analysis . .oo: o. couha .05». . m. .35 0.8 nau on . . ‘ It} .\ _ 2.. Ta. .08 :32 ..22 -.\. _ ”an: o... .3. .32: .: . fi|l‘\\‘|£ LII-tor; Elk—um? ‘ . 33. ... ... .38. 5.3— f u / cl M .0... o... ..8 .8:— .~32 In! _ [Ell Lliul‘ .. . .n .03 3:2 £82 If” .mmuu u: is .88. .....u . r i ltl‘ . .38 o. . .33 .33 7 . 32 a: .03 .38. 3... I \buhfilb’w’lbdl LI|§‘ . . . 0.6— o. .5 .38. 3:2 _. .w-mo. ... .03 ...-oo— "ouoo— . {LE— . .- LE! .. is. .. . .. .33" ”"3”“ . . ...—o. n. .3- . $2.... .2: ....- Z: :3» .32.. The peaks shown are the same as illustrated in section 3.1.1. Figure 3-8. OH I ""libl _ .6253: 18:11} am ' A K {'9 n' 5‘ EDD L . i . .... .ns t I 0.x r- .Hb . F1. Ar” . .“1 Mr“? Irlh I. 96 Each experimental peak is fitted to a Gaussian function having exponential tails. The shape parameters for the peakrfitting routine are obtained from an initial shape calibration using single, well- resolved y peaks distributed over regular intervals throughout the entire spectrum under analysis. These shape parameters are stored and a linear interpolation is used to determine the parameters for fitting the remainder of the peaks in the spectrum. The shape parameters can be punched out and used in subsequent analysis of y-ray spectra taken under the same experimental conditions, thereby providing a considerable savings in computer time. The centroids determined for standard peaks, together with the energies for these standards, are then used to prepare an energy calibra- tion curve. Although a higher-order polynomial can be used to form the calibration curve, the standard calibration method is to perform a piecewise linear fit between succeeding standard points. Likewise, an efficiency calibration curve can be prepared using a number of well- defined peaks and their relative intensities. The data analysis performed under SAMPO can be done in two modes, automatic or manual. The complete analysis of all peaks in a spectrum normally requires utilization of both modes. In the automatic mode, SAMPO scans the spectrum and locates all statistically significant peaks based on the expected line shape. It then determines appropriate fitting intervals and fits the peaks using the shape, energy, and efficiency calibration data. The manual mode is then used for the analysis of peaks missed by the automatic scan. These include weak peaks which fall below the minimum statistical limit for automatic acceptance, multiplets that are not resolved, and other peaks having poor shape. In the manual 97 mode, only those peaks are analyzed for which approximate centroids and fitting intervals have been input. The entire spectrum can be analyzed manually, but in practice the automatic mode is almost always used for the first scan. Thus, a minimum of two passes of SAMPO through the computer is necessary to accomplish the complete analysis of a y—ray spectrum. As illustrated in Figure 3-8, the line-printer output from a SAMPO analysis lists the various parameters in considerable detail. A plot of each fitted interval is provided, showing the raw data, the calculated background, and the resultant fit for each peak. The columns on the right show the counts per channel for the raw data (YDATA) and the counts per channel for the background curve and fitted peak (YFIT). The three columns of numbers to the left of the plot give (from left to right): the channel number of each point contained in the interval shown; the difference between the raw data and the calculated fit at each point; and the calculated background at each location. The key to the symbols used in the plot is given directly under the plot itself. Near the bottom of the figure, the results of the analysis of the plotted section are presented in tabular form. This table includes, for each peak fit, the centroid and its error, the energy, the energy error due to the calibration curve, the overall energy error, the area of the fitted peak together with its error, the relative intensity of the fitted peak, the intensity error introduced by the efficiency calibration curve, and finally the total intensity error. When the intensity calibration data are not read in, only the net peak areas and relative peak areas are given in the output. The statistical error for each area determina- tion is given as a percentage error and therefore reflects the difference bet: wr Cni' cfn 91v.” .1; . 30C 1 -~ ““1 6‘ '- rout 3am Van} in r? >1 ‘5. 05:5 98 between the fitted analytical function and the raw data. Thus, this error indicates the degree to which a given peak shape matches the shapes of nearby standard peaks, as used in the shape-parameter determinations. Although SAMPO offers many advantages over previous data analysis routines, its real forte is its ability to strip or resolve peaks in a multiplet. For complex spectra, containing many unresolved peaks, the amount of time saved by using SAMPO is phenomenal. Spectra which would normally require weeks to strip by hand can be analyzed in a matter of minutes. The sheer speed of the program makes its use desirable for routine analysis. Even though several peaks may require the use of manual mode, SAMPO is considerably faster, more precise and more con- venient than other methods. A relatively complex spectrum (50-75 peaks) can be analyzed in about 20 minutes, whereas the same spectrum analyzed with MOIRAE or MOD 7 would require 2-3 hours. In this study, SAMPO has been used extensively for the analysis of the many complex spectra obtained from pulsed-beam, routing experiments. Although SAMPO has inherently fewer disadvantages than the other programs described here, it does have a number of difficulties. The relatively low order of the background fitted (2nd), together with the short fitting intervals used, result in a poorly approximated background in regions of low statistics and/or near Compton edges. (Higher background orders are now available.) Consequently, these regions must be fitted in the slower manual mode. The use of a standard peak shape sometimes results in many missed peaks. For example, beam-on spectra and high count-rate 8PECtra having irregular peak shapes are often difficult to analyze under SAMPO. 99 An on-line, interactive version of SAMPO also has been adapted to the Sigma-7 system by C. Morgan. In this mode, the data are displayed on a storage oscilloscope and control is maintained through sense switches. Each fit may then be examined visually by the operator before being accepted. If a fit is not acceptable, the operator may change the length of the fitting interval or alter the number of peaks and/or their centroids. However, the background fit is restricted to a second order polynomial. Although the fits obtained using this technique are improved, the direct operator control adds two disadvantages common to other methods, i.e., longer analysis time and further injection of operator bias. Generally speaking, SAMPO represents a significant advancement in the speed and versatility of data analysis. The results of analyses using all three programs are comparable. Intensity determinations show the greatest variation among methods, because of their sensitive dependence on background fit. This variation is especially pronounced for weak, poorly—shaped peaks on irregular backgrounds. The best method of analysis of any particular spectrum must be determined by weighing the character of that spectrum against the advantages and disadvantages of the various data analysis routines. 3.1.4 y-Ray Energy and Intensity Calculation Regardless of the analysis method used, the resultant centroids and areas of the unknown peaks must somehow be related to relative energies and intensities. This is accomplished by calibrating the detector system using well-known standard sources. The y-ray energies are obtained by computing a least-squares quadratic calibration equation from the centroid channel numbers of well-known standard y-rays and then determining the energies of the unknown peaks from their centroids and this calibration curve. These energy calibration curves can be 100 prepared from either "internal" standards or "external" standards. Internal standards are counted simultaneously with the unknown source, and are contained in the same spectrum. External standards are counted under the same experimental conditions as the unknown but are contained in a separate spectrum. Internal standards generally give more accurate calibrations but have the disadvantage of obscuring some of the unknown peaks. Normally, one uses internal standards to establish the energies of several unknown peaks and subsequently uses these established energies in later spectra as secondary internal standards to calibrate weak and previously obscured peaks. In some experiments (e.g., on-line, pulsed—beam experiments), the use of internal standards is quite difficult, and one must rely on external standards. Sometimes side reaction products and contaminants (e.g.,22Na) provide y rays which can be utilized as internal standards in such experiments. The proper selection and utilization of these standard calibration sources are very important factors in determining the accuracy of the energy calibration curve. The ideal selection would consist of a few standards, having only y rays which closely surround the unknown peaks, that are of approximately the same intensity and which cover the entire interval of interest without obscuring any of the unknown y rays. In reality this never happens, and one is forced to compromise the limited number of available standards and the need for good calibration points With the spectral distribution of his unknown. Usually, this requires the bootstrap method of calibrating a few unknown peaks and then employing these as secondary internal standards. The y-ray relative intensities are determined by using previously Prepared detector efficiency curves. Since photopeak efficiencies of 101 Ge(Li) detectors are a function of many factors such as detector size, geometry, total active volume, etc., individual sets of efficiency curves must be tailordmade for each detector. Since the detector efficiency varies with the detector-source geometry, an efficiency curve must be prepared for the various possible geometries. Current calibrations include curves for front-entry geometry with the source at contact, 2 inches and 10 inches from the detectors. These efficiency curves were prepared using Y rays whose relative intensities were well-known. The data were then fitted to a third order polynomial of the form: log (efficiency) - A‘+ B log E + C (log E)2 + D (log E)3, where A, B, C and D are empirical constants and E is the energy in keV. A typical efficiency curve is shown in Figure 3-9. This curve is for a 10.42 Ge(Li) detector with a source-detector distance of 10 inches. A.more complete discussion of the preparation of detector efficiency curves may be found in (Gie7l). These curves have been incorporated into MOIRAE E(I) and are available on cards for SAMPO input. One merely specifies the detector employed and the source distance, and the programs use the calculated energies and appropriate efficiency calibration to convert the net peak areas into relative intensities. 1(32 .monoca OH mo oosmumav nouumuuvuoousom m sues uouuuuov Awuvou usoaoamwo N¢.oa u you we o>uso wank .mu0uuouov Aaavow you o>uso mocoauamwo scuuoumv Hoownzu 4 39. v 35cm >3”. in 00. on CON .sun spawns 88 88 80. com d I I I II I l mmzoz_ O. ._.< mOhHmFMQ ciao o\o v.0. :— _ _ .r..._e _ _ 4:...fiq u b d I I I I I I l. aAuolag mama 103 3.2 Double and Single Escape Peaks Early studies performed with relatively small, inefficient Ge(Li) detectors made extensive use of single escape peaks (i.e., peaks differing from a full-energy photopeak by 511.01 keV) and double escape peaks (peaks having energies 1022.02 keV less than a full-energy photopeak). However, the development of larger, more efficient detectors has relegated this once useful, routine tool to more specialized applications. Only studies of highly energetic y rays (>3000 keV) now utilize escape peaks for routine photopeak energy determination. The 511 keV-511 keV—y triple coinci- dence experiment described in Section 3.6.2B is normally used to determine which peaks in a given spectrum are double escape peaks. Another technique for determining single and double escape peaks is their lack of Compton edges. However, this method is virtually useless in complex spectra. The use of escape peaks for the determination of full-energy photopeaks may be slightly inaccurate, since recent evidence has suggested that the energy differences need to be corrected by a "field increment effect" factor, based upon the detector-source geometry and the electric field in the detector produced by the diode bias voltage (Gun68). (The effect is most important for planar detectors, and is washed out in coaxial ones.) This factor is quite small (<0.l keV) and was not considered in this study, espeCially since escape peaks were not relied on for precise energy determinations. In this study, single and double escape peaks were lltilized to indicate or Confirm the existence of highly energetic y rays from the decay of ”08c and other short-lived species. 104 3.3 The PDP-9 Computer and Related Programs In addition to providing an excellent facility for data acquisi- tion, the Nuclear Chemistry group's PDP-9 computer has been extremely useful for various numerical calculations used in data analysis. The various programs are written in FORTRAN, stored on DECtape and run under a keyboard monitor system. Each program is called from a magnetic tape iJito core, as needed, via an appropriate teletype command. The majority of the present programs were written by R. Eppley of the Nuclear Chemistry group, now at LBL. More complete details of the PDP-9 operation and prxagram descriptions can be found in references (Epp70a) and (Epp69). The following are a few of the programs which were used in this study: 1) ARITH - This program allows the PDP-9 to be used as an electronic desk calculator, capable of performing simple numerical calculations. 2) INTEN - A program used for the calculation and re- ruarmalization of y-ray intensities. 3) FERM 3 - This code calculates Fermi functions for use in Irreparing Fermi-Kurie plots of electron and positron spectra. 4) PROB - This very useful program is for the calculation <1f transition probabilities and half-lives of y-ray transitions based on the single particle equations of Moszkowski. 5) PLYFIT - This is a general polynomial least-squares Program. 6) ICC - This is a program which is used for the interpola— titni of the theoretical internal conversion coefficients from 105 published tables. 7) INTERP - A program similar to ICC, but which is based on the theory of splines and adapted from the program given by Hager and Seltzer (Hag68). 8) VC - This program calculates Clebsch—Gordon coefficients, using Racah's general equation. 9) TRIGA - A program which calculates the expected activity of samples submitted for irradiation.with the MSU TRIGA reactor. In addition to these programs, more complete data analysis routines of the MOIRAE variety are currently being developed for use on the PDP-9. When the present task of interfacing the PDP-9 and the Sigma-7 18 complete, the convenience and versatility of using the PDP-9 for data acquisition and analysis will be greatly enhanced. u‘: I1 106 3.4 The Analysis of Beta Spectra The data obtained from beta singles and beta-gamma coincidence experiments must be analyzed in order to extract the desired beta end— point energies and spectral shapes. The method used is that of preparing Fermi-Kurie plots from the data. Although somewhat complex, this is the standard technique used for the analysis of beta spectra. Since this technique has had little previous use or documentation by the Nuclear Chemistry Group, I would like to discuss the available theory, calculation and codes for beta analysis in some detail, beginning with a general discussion of beta analysis taken from (Tab51). 344-1 Principles of Beta Analysis 3.4.1A Beta-Ray Spectra Positrons or electrons may be ejected in the course of spontaneous decay of atomic nuclei. The kinetic energy of these particles may be measured to a precision of one percent or better, depending upon the detection device. The most widespread instrument for precise measure- ment of electron energies is the magnetic spectrometer, although scintilla— tion devices and solid-state detectors are coumonly used. If one measures the energies of a few electrons emitted in succession by nuclei of a B‘radioactive material, he finds that the energies are spread at random 0 Ver a wide range without apparent continuity. However, upon measuring a large number of such energies a regular pattern emerges, and one can draw a curve representing their statistical distribution in various energy inteIfirals. This distribution is the beta-ray spectrum of the material and is the curve representing the raw data from a typical experiment. The statistical distribution of electrons covers all energies fr or“ zero up to a maximum energy, E0, characteristic of the decay and ‘fiii r«-. . ‘F ., ; at . . fl' . u. up, .u_ A? Hr HQ 107 representative of the total energy actually released by the nucleus in the course of its B-disintegration process. Whenever the electron is ejected with an energy E' < E0, the remainder of the energy is carried away by a neutrino of energy Eo-E. The observed statistical distribution of electron energies reflects the relative probability of the various possible ways in which the total energy, E0, released by a nucleus can be shared between an electron and a neutrino. The theoretical analysis of a beta-ray spectrum attempts to determine the factors that govern this sharing of energy. The first step in the analysis consists of evaluating the in- fluence of the pertinent extranuclear factors, i.e., those factors which are only incidental to the process of the decay and do not depend upon the internal processes of the nucleus. When these factors are properly subtracted, the remaining features of the beta-ray spectrum should reflect the truly nuclear features of the disintegration phenomenon. 3.4.1B The Statistical Weight Factor In general, all beta-ray spectra are characterized by their bell-shaped plots. The electrons may carry away almost all of the available Energy or practically none Of it, although the probability Of either of these conditions is extremely low. The most likely event is that the electron and the neutrino will share the total energy in comparable amo‘mts. From statistical mechanics it is known that, of all modes 0f Elation of two or more particles with a fixed total energy, the great majol. 1ty correspond to approximately an even sharing of energy among t he Particles. More specifically, the types of motions of the electron an ' d of the neutrino, which have been ejected from a nucleus, can be C1 assified on the basis of the components px, py and P2, and qx: qy 108 and qz of their linear momenta. Any particular subdivision of the available energy 1'70, between the electron (E) and the neutrino (EC-E) implies fixing the magnitude of the momenta of the two particles, namely, a: = Y 2 p lp’i + p; + p22 and q qu + qy + qzz. The smaller the value of E, and, consequently, the value of p, the smaller is the range of possible values of Px’ py’ and 192' This means that the variety of modes of motion of the electron is an increasing function of E. However, if E is so large that Eo-E and q become too small, the possible modes of motion of the neutrino become limited. Thus, in order to maintain a large variety of combined motions for both particles, the total energy E0 should be shared comparably. This argument leads one to prove, through a quantum mechanical treatment, that the probability that the magnitude of the electron's momentum lies between p and p + dp is proportional to the product pzqzdp (3-1) This result is frequently expressed by the statement that the value of p2q2dp represents the statistical weight of a particular subdivision of energy. 3.4.lC EnergLand Momentum Formulas The momentum of an electron can be expressed in terms of the product of its mass, m, and the velocity of light, 0, by means of the Symb01 -—11—— (3—2) n = mc LikWise, the energies E and E0 are expressed in terms of the product 2 m0 3 by means of the symbols E E0 (3-3) E = mcz’ 8° = mc 109 The energy, E, includes the rest energy mcz, of the electron, as well as Thus, e is related to n by the equation 5 = V]. + n2 (3‘4) Since the neutrino has a negligible rest mass, the magnitude of its kinetic energy . its momentum, q, is proportional to its energy, so - e. The expression (3-1) for the statistical weight of a particular energy subdivision may be rewritten as 112(80 - e)2dn = nae—+7.3 - mfldn <3-5) The magnetic techniques for measurements of electron energy lead to a direct determination of the momentum, rather than of the energy. The momentum is proportional to the product of the strength, B, of a magnetic field and of the radius of curvature, p , of the path that it forces the electron to follow: Bp = 1704.3n gauss cm (3-6) Consequently, the experimental methods yield directly the statistical distribution of momenta, i.e., the number N(n) dn (3-7) of electrons whose momenta lie between n and n + dn. MD The First Step of the Analysis The significance of the concept of statistical weight is as follows: If all other conditions were discounted such that only the statistical weight could influence the sharing of energy between electron and neutrino, the Ilumber (3-7) should be proportional to (3-5), that is, the ratio of (377) to (3-5) should be a constant, independent of n (although this is not always true). Nevertheless, if one divides the observed distribu- tion (3-7) by the statistical weight (3-5), he achieves a first step in the anal , ySlS of the experimental data. In this way, one eliminates the effect 110 of an extraneous factor that would otherwise obscure the details of the nuclear mechanism . 3.4.1B Maximum Beta Energy Determination Inspection of the plot of N(n) does not enable one to determine go accurately, since the number of electrons observed near the maximum energy is very small. Therefore, in practice, one can use the following procedure. Instead of dividing (3-7) by (3—5), one may divide it by nzdn and then take the square root of the resulting ratio (3-8) W(n)dnfn2dn = «1.77.12 and plot it against a (Kur36). If (3-7) were proportional to (3-5), the ratio (3-8) would be proportional to so - e, and its plot would be a straight line intercepting the e-axis at 50. Although the resulting plots are not really expected to be straight lines, they are reasonably straight near the high-energy limit and serve well for the graphical determination of so as the intercept. 344.1 F Effect of Electrostatic Forces An electron that has been ejected by a nucleus finds itself 31113.1 ect to the electrostatic action of the nucleus, which is attractive or repulsive, depending on whether the electron is negative or positive. This electrostatic force remains appreciable until the electron gets sufficiently far away from the nucleus. The force affects the motion of the electrons to a different extent depending upon their energy. Therefore, it may modify the relative probability that an electron be e 1acted with one energy or another. The qualitative effect of the electrostatic force is readily Lee as- 4 int. ...‘_ .w a.) 111 understandable in the case of positron emission. If a positron were liberated with no kinetic energy at the edge of a nucleus, the repulsion exerted on it by the nuclear charge would speed it up to attain an eventual kinetic energy of the order of millions of electron volts. This circumstance might seem to indicate that positive beta rays necessarily leave a radioactive material with a high kinetic energy. However, they can also come out with a lower energy by "leaking" through the repulsive potential barrier that surrounds the nucleus, just as a particles do. The fact remains that the emission of low-energy positive electrons by nuclei meets unfavorable conditions. The qualitative discussion of the effect of the electrostatic force upon the emission of negative electrons is not so simple. However, this effect is opposite to the effect on positrons. It may be carried out rather conveniently by treating the transit of the electron from the nucleus to the space outside the atom as a problem in electron optics, that is, according to a "wave picture." In this way one arrives at the rule for calculating the effect of the electrostatic force upon the beta- ray spectrum, both for positive and negative electrons. An electron traveling away from a nucleus finds itself in a region Where the electrostatic potential changes very rapidly from one point to the next. It is a fundamental phenomenon of atomic physics that the motion of an electron through a rapidly variable potential causes a Substantial reflection of the electron wave-function, just as a rapid Val-1a tion of the refraction index causes a substantial reflection of light One Can argue rather easily that, in the case of a negative electron, t he reflection effect takes place within the limits of the K shell of 1'. v' std .A‘ ~¢‘ ..J. vi.- “.‘1 O. L. A. II. ..1 PI,‘ (1, .4: 112 the atom. At larger distances from the nucleus the potential experiences only a small fractional change within a wavelength, and this is just the condition for the absence of reflection. Mathematically, this means that one can apply a WKB approximation in this latter region (R0336). For the same reason, the reflected wave that returns to the nucleus interferes constructively with the wave that goes out from there in the opposite direc- tion. This explains why the emission of negative electrons is enhanced by the electrostatic force. The effect of reflection is the more conspicuous, the larger the electrostatic potential with respect to the kinetic energy of the electron, i.e., the larger the atomic number and the smaller the electron energy. As the reflection takes place within the inner part of the atom, we may also assume in practice that the electrostatic force exerted by the nucleus follows the "l/r2" law, i.e., that it is not greatly modified by the presence of the atomic electrons (R0336). The idea of treating the outward travel of the electron as an Optical phenomenon also suggests that one applies a principle of optical reciprocity to the determination of the probability of electron emission. Accordingly, we argue that an electron released at the nucleus has the Same chance of eventually leaving the atom with a certain energy as an electron entering the atom with the same energy has of eventually reaching the nucleus. In fact quantum mechanical calculation (Fer34) Shows that, other conditions being equal, the probability of emission Of a beta ray of given energy is proportional to the ratio F = lw(center)|2/lw(out)l2 (3-9) Where w is the wave function of an electron of that energy in the space co “ta ining the atom, Mcenter) is the value of that function at the 113 center of the atom, i.e., at the nucleus, and w(out) is the value out- side the atom. The ratio F may be calculated from a knowledge of the solution of the wave equation for an electron moving in a "lflPz" field of force. This particular portion of the beta-ray problem appears thus to coincide with a standard problem of atomic physics. Therefore, the numerical calculation of.F represents a contribution to a general problem of atomic physics. The value of the ratio F depends primarily on two quantities: (a) The electric charge of the nucleus, that is, its atomic number Z. The appropriate value of this number is the one pertaining to the end product of the B disintegration, i.e., to the nuclear charge after the emission of the electron. (b) The energy, E, or the momentum, n, of the electron after it has left the atom. 3.4.16 The Second Step of the Analysis From the discussion above, it follows that the statistical diestribution of electron momenta, N(n), should be proportional to the furuetion F(Z,n) alone, if the distribution were determined entirely by the effect of the electrostatic force. This is not the case, but one car: élpply here again the procedure used earlier to deal with the Statistical weight factor: the effect of two incidental factors “pot: the beta-ray spectrum is removed if one divides the distribution NITH>Cln by the statistical weight factor (3-5) and by the electrostatic factor F(Z,n), that is, if he plots the ratio ”(n)dn/[n2(€o - €)2an(Z,n)] (3-10) add A“ a: a) ‘Ia r“. r . ‘. .)|.. 114 against a- Alternately, by analogy to (3-8), one may plot the ratio fN GIT/1125' (Z .11) (3-11) against E. If the effects of statistical weight and of the electro- static force are the only important factors, this plot should be a straight line, intercepting the e-axis at 80' This is actually observed in a large number of beta spectra. One concludes from this result that, in a broad class of beta disintegrations, the truly nuclear effects do not influence the sharing of energy between the electron and the neutrino . The plot of the function (3-ll) against a is usually called a Fermi plot or a Fermi-Kurie plot after the authors who suggested this method of analysis (Kur36). 344.111 Allowed and Forbidden Spectra A particle may be ejected from a nucleus not straight outward bUt, so to speak, tangentially, that is, endowed with a certain angular momentum of orbital motion about the nucleus. Such a particle experiences at once the effect of a powerful centrifugal force that pushes it away from the nucleus. This force acts much like the electrostatic repulsion does upon positive beta particles. As in the case of the electrostatic repulsion, the effect of the centrifugal force may be described as the effect of a potential barrier that surrounds the nucleus. This potential barrier can rise even more shat‘Ply than an electrostatic potential barrier and it may affect the o utgoing neutrino as well as the electron. The orbital angular momentum of an outgoing particle must be 115 a whole multiple of '11, according to quantum mechanics. If this angular momentum amounts to a few units of 'h,_the centrifugal potential barrier reaches such a high level at the edge of a nucleus that the outgoing particle must "leak through" it. This circumstance has two effects. First, any particle that must come out with an orbital angular momentum other than zero is unlikely to take the minor share of the total energy available because this would involve a more difficult leakage through the barrier. Second, if the conditions are such that at least one of the particles must come out with some non-zero angular momentum, the process of disintegra- tion must proceed slowly, at a pace set by the rate of leakage through the barrier. A kind of disintegration that proceeds under these cculditions is said to be "forbidden". A very special interest is attached to the case where the particles 3113 ejected "straight out" from the nucleus, that is, without any This case is particularly easy to handle because angular momentum. no centrifugal effect need be considered. Moreover, this case may be expected to be a most frequent one in practice. In fact, whenever a Process of nuclear disintegration may develop through alternate paths, it naturally has a high probability of following a path that does not require outgoing particles to leak through a potential barrier, other Conditions being equal. Most of the work on beta spectra has been devoted in the past to the study of "allowed" spectra that do not exhibit any effect of centrifugal forces. Fermi's original theory of beta emission dealt particularly with this case. In ,_ - L21, ‘ 116 A few spectra that exhibit the effect of centrifugal forces have been analyzed successfully, beginning about 1949 (Lan49), (Wu49), and (03049). The theoretical analysis of such "forbidden" beta spectra has been the object of a paper by Konopinski and Uhlenbeck (Konél) and is also discussed in Konopinski's review article (Kon43). 3.4.11 The E(ZLnL Factor for Allowed Spectra The motion of an electron in the space around a nucleus proceeds, in the main, according to the Schrfidinger equation. This equation does not apply when the velocity of the electron approaches the velocity of light, but in this case the attraction of the nucleus becomes unim- portant, and there is little need for a special study (except in the immediate proximity of the nucleus, as discussed below). The solution of the Schrodinger equation for an electron moving under the electrostatic attraction or repulsion of a nucleus, without any angular momentum, leads to a well-known expression for F, namely, (Kur36) Fn(Z,n) = y/Il '- exp_-'_( y)| (3'12) Where the upper sign applies to negative and the lower to positive ele c trons , and y = 4n22e2/hv = 21rZ/137(v/c) = 21ry/B = 21er/1 + n2/137n (3—13) and (3"14) 1) = elm/m: cn/e: = 80 is the eventual velocity of the electron after escaping from the atom. The relativistic effect is not quite unimportant because an electron always approaches the speed of light when it moves in the innuediate proximity of the nucleus. Approach to the speed of light b I$11188 about an increase of the apparent mass of the electron, that 117 is, the momentum becomes a more rapidly increasing function of the kinetic energy than it is at lower speeds. In turn, the wavelength experiences a more rapid decrease. Consequently, the relativistic effect enhances the fractional change of the electrostatic potential over one electron wavelength, which is responsible for the reflection effect discussed previously. Therefore, this effect makes the value of l¢(center)|2 and hence that of F(Z,n) larger than they are expected to be on the basis of the nonrelativistic treatment. Relativistic wave functions for the motion of an electron in a "llrz" field of force are known from the solution of the appropriate Dirac equation. The relativistic effect just discussed is so strong that the wave functions would become infinitely large right at the position of the nucleus, if the nucleus were actually a point charge as it is assumed to be in the calculation. Fermi suggested in his original work (Fer34) a practical way of estimating F(Z,n), despite this difficulty. One should first calculate the wave function as if the nucleus were a point charge and then introduce into equa- tion (3-9) in the place of |w(center)|2 the value of lap!2 at: the edge 0f the nucleus. The idea is that the electrostatic force no longer follOWS the "1/r2" law within the nucleus and, therefore, u: should no longer increase very much within the nucleus itself. The value of F(2,n) calculated according to this procedure is F(Z ) = .1122.— 2 M zseino ’" 1"(3+2.s) h S XIF(1 +s+i6)|2(1+§) (3—15) where . . R is the nuclear radius, the i Sign applies to negative or p031tive e1 eQ trons and 118 S = V1 - Z271372 - 1 (S = Zv’l + n2/137n = y/21r This value reduces to (3-12) if one sets 3 = 0, since |F(l + i6)|2 (3-16) Therefore,(3-15) can be written in the form S F(2.n) = Fn(z.n)(-4—“—m,f-“5-)2 F(3)I‘(1+S+i6) 2 g _ I'(3 + 29)r(1 + £5) (1 + 2) (3 l7) = n6/|81nh1r6 This last formula shows c1early.how the relativistic effect depends on the magnitude of S. 3. 4 . lJ Screening Corrections It is pointed out in section F that the presence of the atomic Electrons does not modify the electrostatic force in the space near a nucleus where it matters for the determination of 8 spectra. Never- theless, the attraction or repulsion that the atomic electrons exert farther away from the nucleus does modify to some extent the electro- Static potential near the nucleus. Thismodification of the potential is Called the effect of "outer screening", because the external electrons of the atom screen off the outside space from the electrostatic force of the nucleus . A negative electron of given total energy that penetrates near the nucleus through the outer screen of electrons does not have so high a kinetic energy as it would have in the absence of the screen. Conversely, a positive electron preserves more of its kinetic enerSY- TheI‘efore, Rose pointed out (R0836) that one can take into account the effeczt of outer screening by calculating the electrostatic effect as if the electron energy differed from its actual value by an amount e qua]. to the potential energy, V0, due to the outer screening. 119 The value of V0 is not defined very exactly, as the whole picture that the atomic electrons exert only an effect of outer screening represents only an approximation. The approximation is justifiable insofar as the effect on the 8 spectra is itself quite small. A rather good estimate of V0 can be obtained from the comparison of the experimental binding energies of K electrons with the theoretical values for the hydrogen-like model. This estimate should be good at least for application to the case of electrons whose kinetic energy outside the atom does not greatly exceed the K electron binding energy. In the case of electrons of higher kinetic energy, the important electro- static effect stems from a region closer in than the K shell, and one might use a somewhat higher value of V0, especially for light elements. Another estimate of V0 may be obtained more simply from the Thomas-Fermi distribution of electrons in the atom. The outer screening P°tential is a function of the distance from the nucleus. An average Value pertaining to the interesting range of distances has been estimated (R08 36) to be about 30 Z‘*/3 eV. The Thomas-Fermi value of V0 calculated for an electron right at the center of the atom is 48 ZL'I3 eV and sets an upper limit to the effective value of V0. The evaluation of the effect of outer screening according to the me tl'lod suggested by Rose applies to the calculation of eigenfunctions noI‘Ttlualized "per unit energy". Therefore, one should take the function ”“727“,?” or the equivalent function f(Z,n)V1 + nz/n and find OUt w hat fractional change it experiences if the B-ray energy is reduced b y V0 in the case of negative electrons or increased by V0 in the case 0 f Positive ones . This change turns out to amount to a few percent, at most, 120 except in the case of low energy positrons. The outer screening has a much larger effect upon positive electrons than upon negative ones because it reduces the height and thickness of the potential barrier through which the positive beta rays have to leak. An accurate calculation of the screening effect has been performed by J. R. Rietz (RieSO) for a number of values of the atomic number and of the electron energy. He calculated numerically the relativistic wave function of an electron moving through an atom whose normal comple- ment of electrons follows the Thomas-Fermi distribution. Thereby, Rietz obtained an almost exact evaluation of the "Fermi function" that can be compared with the values uncorrected for screening or with the values corrected by less refined methods. £344. 1K The Total Beta Emission Probability The factors considered in the preceding sections do not influence only the subdivision of energy between electron and neutrino. They affe ct the total rate at which the beta disintegration proceeds. In other words, the absolute probability of beta emission is actually proportional to the statistical weight factor and to F(Z,n), other conditions being equal . Therefore, the total value of this product, covering all possible ways of subdividing the energy between the two particles, namely, —_2' In“ n2(€o- e>2Fdn O = ¢(Z)f'1+"° (so - e>2fdn <3—18) O 1': epresents a determining factor of the disintegration rate, which is 121 incidental to the nuclear process itself. The systematic evaluation of the integral (3-18) for all values of Z andtb involves a substantial amount of labor. Calculations of the integral (3-18) for the values of Z andr1o, which correspond to observed beta radioactivities have been made by S. Moszkowski and by E. Feenberg and G. Trigg (FeeSO). In both cases a preliminary evaluation of the Fermi function was required. This evaluation was carried out by the authors by using approximate formulas to the desired precision. jfigfi.2 Preparation of Fermi Plots Fermi plots of the data obtained in this study were prepared both by ‘the use of tabulated Fermi functions and corrections and by computer Programs designed to calculate these functions. Although considerable Effort was expended in the development of computer programs, the final analyses presented here were performed using tabulated functions (TabSl). The convenience, reliability, and number of corrections (e.g.. screening) Offered in various tables are difficult to beat, unless a large number 0f analyses need to be performed. Since the analysis involves the use of the 1‘ function of a complex argument, a function which cannot be readily evaluated, tabulated results from rather extensive calculations are most convenient for occasional use by the experimentalist. The tables used for the analyses presented in this work were compiled by the National Bureau of Standards and are perhaps the most useful and comprehensive tabulation available (TabSl). The main tables give the value of the so-called "Fermi Function": f(Z.n) = n2+25ei"5|r<1 + s + is>|2 w here the : sign applies to the spectra of negative and positive electrons, 122 respectively, and n - momentum of the electron, after its ejection from the atom, in units of me. 3 = JT‘Z'277T377 - 1 Z = atomic number 6 = Z/l + n2/l37n. The tabulation covers all the values of Z that may be encountered in The set of values of n are sufficient to enable the user to calcu- practice . The late the function at intermediate values readily by interpolation. tabulation extends to n=7 (: 3.5 MeV). Higher values of f(Z,n) may be calculated to within approximately one percent by an empirical expression. Key values of IF(l + S + 16)]2 were obtained by interpolating the table by W. Meissner (Me139). In particular, the table used gives loglo '1" (z)| for the triangular net 2 = (2m+12n/§)/24 and = [(2m+1)+1(2n+1)/§]/24 , 17; n = O, l, . . . , 6, 7. Beyond the range of witl”1m=6,7,... this table use was made of the following relation: |r(a+ib)|2=|r(a)|2nU%[1+b2(n+a)‘2]'1 The right-hand side may be expressed also in the following form, which is more suitable for computation: 2 log|r(a+1b)|2=2 log|1‘(a)| - 108 (1 +57) 2 d2 b“ d1+ [9 “$7108 I‘(a+1)+ fiat 108 F(a+1) - . . Values of F(a). (dz/daz) log F(a+1). and (d”/da“) log F(a+l). e tQ - , were obtained by interpolation in H. T. Davis (Dav35). 123 Key values of‘f(z,n) for Z = 10 to 100 and n a O to 7 were then obtained by adding the logarithms of the P function and of the factors eind and "2+25. These values were then differenced, and subtabulation, using Lagrangian interpolation formulas, was performed on IBM machines. 3.4.3 Program FERM 3 Program FERM 3 is a FORTRAN routine written by R. Eppley (EPP69), WhiCh runs on the PDP-9 computer. It was developed to calculate the values of Fermi functions at intermediate values not included in tabulations. However, the program is not for the interpolation of values, but. instead, actually calculates the Fermi function at each point, using a power series method. This program gives values in good agreement with those found in the tables and could easily be incorporated as a subroutine in a more complete code. The method of calculation is as follows: The Fermi function can be written as (TabSl) f(Z.n) = r12+25efl5l1“(1+S+i37» .NLV 0.93m mums—DZ 4m22<10 .ero 8.52. m ... . . ...e... a .2x9. can. coo. one can can 0 o a q a d S ['7 m n .93» 1.0... s .. a “m . .03.: 3» x. m .0 85... w?! 1 .2qu 'IBNNVHO/ SanOO 133 .uouoouuv um.~ onu nus: comma 0mm mm mo suuuomau nuances haul» .Nuq seamen mum—232 JMZZuxnm.~nm ecu so was» any sue: guuooam oocuowucwoo omthmm .mlq Sawa mmmzaz smzqus ope: Doom Doom Debi o _ _ 1:: é, _ _ .2 qr— 356:; 67.1.9 '" :r :1 GHQ- 28 >2 mg L... o 1 m.“—A E on... “IEJNNUHJ 83c] SINHOZJ 142 transition from 539 Fe. Again, a more complete description of this experiment may be found in Section 2.6.2. The results of such a gated experiment are shown in Figure 4-5. This spectrum represents a 12-hr accumulation of data, using the 7-cm3 Ge(Li) detector in conjunction with the split annulus. Examination of the spectrum reveals that none of the assigned 53”fi7Fe'Y rays 18 in coincidence with the 377.9-keV transition in 53Mn. 4.3.2D Two-Parameter Coincidence Experiments Although the facilities for performing two-parameter "megachannel" type coincidence experiments are readily available in this laboratory, such an experiment was not deemed necessary for the 53"flyFe study. However, Eskola has performed a two-parameter type experiment using a 4096-channel analyzer (Esk67). Although relatively simple, this experi- ment was sufficient to verify the 53'"Fe coincidence relations. These results are summarized in Table 4-4; a plus sign indicates an observed coincidence relation, and a minus sign, the lack of it. 4.3.2E 511 keV-511 keV-y Coincidence (Pair) Spectra The two halves of the 8X8-in. NaI(Tl) split annulus were used in conjunction with a 20-cm3 Ge(Li) detector to determine the 8+ feeding to levels in 53Mn and to identify possible double-escape peaks. Each half of the annulus was gated on the 511-keV yi peak, and a triple coincidence (resolving time, 21 2100 nsec) was required among these and the Ge(Li) detector. The relevant block diagram of the necessary electronics and details of the experiment may be found in Section 2.6.2. The Spectrum resulting from this experiment is shown in Figure 4-6. As can be readily observed, only the 377.9-keV state in 53Mn appears to 1113 8.2 .ssuuomam oucovfiucaoo oaaauu >u>ox Haml>ox Han omAE+vmmm mmmzaz nmzquu seeeeeeo an: a ->s __m->s a mun—A688 (uwzg) bibl— .o-e muswae oom ‘wl CYHC as,“ 6119:— l as -OH -OH TOM -ofi WBNNUHJ 83d SlNflOJ 144 Table 4-4 Coincidence Relations between Y Rays Observed in the Decay of 53”’Fea y-Ray Energy (keV) 701.1 1011.5 1328.1 2339.6 701.1 - + + + 1011.5 + — + - 1328.1 + + - - 2339.6 + - - - aFrom (Esk67). 145 be strongly 8+ fed. Extremely weak transitions like the 1619.9-keV Y ray do not appear in these spectra. The presence of these weakly fed states is verified by their appearance in long singles experiments using chemically separated sources, and by the lower energy 8+ end-point energies found in the Fermi plots of the 539Fe beta spectra. Based simply on the assumed log ft's for the 8+ decay to these weaker states, one finds that the predicted 8+ feeding is as follows: the 8+ feeding to the 1619.9-keV state is at best a factor of =12 less than that to the 377.9-keV state. However, the 1288.0-keV 8+ feeding should be less than the 377.9-keV intensity by a factor of 3108. One finds experimentally that the 1619.9-keV feeding is less than predicted, whereas the 1288.0-keV intensity appears enhanced, based on the observed y-ray intensities from these levels. Note, however, that there exists the possibility of y-feeding to these states from undetected, higher-lying levels. For most of these experiments, the upper limit of detectability for a y ray in the 1200-to 1700—keV region was about 0.5% of the normal 377.9-keV y-ray intensity. 4.3.3 High Multipolarity yfigay Transitions Following the Decay of 53”2176 The discovery of the high-energy, high-spin, three quasiparticle isomer in S3Fe has provided an excellent opportunity for the direct observation of very high multipolarity y-ray transitions. The existence of M5, E6, and higher multipolarities has never been substantiated by experimental fact except for their presence as small admixtures occasionally being invoked to explain small discrepancies in experiments such as angular correlations. Having confirmed Eskola's gamma decay scheme for 53mFe, we initiated 146 a program to search for hitherto unobserved transitions of multipolarity M5 and E6. Source preparation was carried out as described in Section 4.2, with bombardment time, beam energy, and all other parameters adjusted to optimize the production of the metastable state. y rays were detected with a 3.6% efficient true-coaxial Ge(Li) detector having a resolution of 2.0 keV. The remainder of this system consisted of an amplifier having high-rate baseline restoration and a 50-MHz analog-to-digital converter interfaced to a Sigma-7 computer. Graded lead absorbers having a combined thickness of :3 cm were used between the source and the detector to attenuate the lower-energy y rays. Even so, counting rates as high as possible without appreciable deterioration of resolution were maintained throughout the experiments, with an average count rate of about 6700 counts/sec. This combination of isomer optimization, detector efficiency and resolution, and high-count-rate electronics was deemed absolutely necessary in order to obtain the number of events necessary for direct observation of the weak E6 and M5 transitions. Various spectra were taken at different times and with different geometries and produced consistent results. Figure 4-7 shows the spectrum resulting from a 24-hr accumulation of data and front-end detector geometry. During this time a continuous cycle of bombarding and counting was maintained such that a fresh source was counted every 2 min. Definite peaks exist in this spectrum at the energies of 1712.6 and 3040.6 keV, where the M5 and E6 transitions are expected to occur. After careful energy and intensity analysis, these peaks were found to correspond to transitions having intensities of 1.3x10-2 and 6X10—” as compared with the 701.-keV transition. Recent experiments using a large 10.5%- efficient Ge(Li) detector have shown that these peaks decay with the 147 2.5-min half-life of 53mFe and are the only peaks in the spectrum (other than the four well-known, intense 53’7’Fe peaks) that decay with this half-life.‘ Having shown that these peaks are present, one is obligated to demonstrate that they are indeed true peaks and not merely the resultant sum peaks of two or more known constituents. Such sum peaks are known to occur in large-volume detectors under high-count-rate conditions. These can originate from two different physical conditions. First, if the source is sufficiently close to the detector so that the detector presents a large solid angle, summing of events in the same y-ray cascade can occur. Second, if the source is strong, accidental summing of events from the same or different y-ray cascades can occur. With our 53mFe experiments one needs to worry about both effects in turn. This summing problem was examined both in light of the data themselves and also from additional experiments designed to elucidate the summing phenomenon. Considering the 53"Fe data alone, we can formulate several interesting arguments. Examination of the established decay scheme (Figure 4- 13) reveals that two of the most intense transitions, at 701.1 and 1328.1 keV, are in a cascade connected by the 1011.5-keV transition, the third most intense. If indeed cascade-type summing were to occur to an appreciable extent during an experiment such as that recorded in Figure 4-7, one would conclude that these two most intense transitions should give rise to a sum peak at 2029.2 keV. Examination of the spectrum, however, shows no evidence for a y ray at this energy. Figure 4-8 shows a linear blowup of the 2029.2-keV region from the spectrum given in Figure 4-7. This absence was reproducible from experiment to experiment, with widely varying count rates and source-detector distances. One can estimate for this spectrum, for example, that the contributions 148 Singles 53m(*g) Fe (well) E'MSZ ('GGOJ) 9.62:2 ~- or... :-T“.I:‘:‘.“.'ZT..IT——' “““ 6'6022 “rm; / (2'6202) -* 93992-5 ...... ngaj) (9W) 9.311.. (Read) 6'6l9l ‘ (“u") €.v€bI'——" - r-.:'..7" and.“ This spectrum represents a 24-hour accumulation during which sources were prepared SWgFe singles y-ray spectrum taken with a 3.61 1500 2000 2500 3000 3500 4000 CHANNEL NUMBER ICC!) 500 "IBNNVHO 83d .3 O U U 0 u .3 . — MO I. a‘- .-..-. . ‘ . (U ajlgzgl A a d 96922-0 ’ fi ”* 3 ..J :1 V G 8 E 0 ~04 ... U >~ w u w 0 ‘3 5 "" ' («$31) I'IOZ Ions . 7 'T n-m'-‘”H Q _. 8 (mad) 6‘22: 9 no ...q In j J 1 ”J I I . - '9 e 9 9 ~° 9 1119 .wsdussu 093-3330 mo 00:33 05 weasozm .e-e enemas acne seamen eex-~.o~o~ use we assess teases .m-e enemas mum—232 qwzzlqlo 8% 8.8 h J CONN waom 8.58% mm muse.“ see 58¢ >9. - Nam om to 3265 50:3 1 1 u v03... vaxN WBNNVHO 83d SanOC) L!) (‘J *‘7 4;: / 4-»~ 150 of summing to the.M5 and E6 peaks would be considerably less than 0.1% and 10%, respectively, and come almost entirely from chance coincidences. Also, although the 511.01-keV 7: peak was the most intense peak in the spectrum, no evidence was found for vi summing to give a lOZZ-keV peak or of their summing with any of the stronger y rays in the Spectrum. This indicates that chance type summing was not a significant factor in these experiments except for a small (<10%) possible contribution to the weak E6 peak. A third consideration is the peak width. In general, sum peaks or peaks containing significant summing components tend to be wider than their true counterparts. However, here one finds the peaks corresponding to the M5 and E6 transitions to be of normal width, providing further evidence for the fact that they are true peaks. Finally, the E6 and M5 decay with the same half-life as the E4 isomeric transition, and one would expect to measure a different half-life if there were a substantial contri- bution from chance-coincidence summing. To check the internal data, a series of experiments was performed in which 60Co Spectra were taken with various source-detector geometries at a constant count rate. The degree of summing to form a 2505.7l-keV sum peak was observed as a function of geometry. Then,using the same count rates and geometries, an analogous set of 53mFe spectra was taken. The resulting intensity variations of the M5 and E6 peaks as a function of geometry were compared with the variations of the 60Co spectra. This method corroborated the fact that the 1712.6- and 3040.6—keV peaks are not sum peaks but do indeed reflect true transitions in the 53Fe nucleus. 4.3.4 On-Line YtRéYg§P€Ctra A number of pulsed, in-beam experiments have been carried out during 151 the:53M+9Fe investigation. In these experiments, the cyclotron beam was pulsed by RF modulation such that the beam was on for about 0.4 sec and off about 0.4 sec per cycle. The targets consisted of powdered manganese in a Duco cement or polystyrene binder on a thin mylar backing. These targets were placed in a precision goniometer where they were viewed by Ge(Li) detectors through a thin kapton window. A shielded beam dump was located about 8 feet beyond the target position. The principal detector employed in these experiments was a 2% efficient, trapezoidal Ge(Li) detector, having a resolution of about 3.4 keV FWHM. Data were taken on-line with the Sigma-7 computer, using routing. Five 4096- channel spectra were routed as follows: one spectrum was taken during the beam-on portion of each cycle, with four more being taken in 0.1 sec time intervals during the beam-off period. Results of these in-beam experiments served largely to verify the results of our earlier S3m+gFe experiments. A typical in—beam spectrum is shown in Figure 4-9. Since the beam-on spectra were capable of seeing direct excitation decays (as opposed to decays resulting from the B+/€ decay of 539Fe), they proved to be most interesting. Earlier investigations of the 539Fe decay using different reactions such as (a,xn) indicated a state of about 1290 keV (Ju159). Our previous studies of the S3”1+9Fe decay using the 55Mn(p,3n)53Fe reaction did not indicate a level of this energy. However, our in-beam data clearly contain a y-ray at 1288 keV. In addition, two of the E6 search spectra (containing very high numbers of counts and good statistics) show evidence for such a transition. Thus, the 1288-keV level in 53Mn appears to be only very weakly fed by the B+le decay of 539Fe -- although its existence in the decay has been verified. From this SSMn(p,3n) work, 152 In - Beam Singles as,“ 6'619I— “W 29 OWVI "' 896,; 0882!- Ivgz a van- uw,g 9928— 89,.“ 110/.— :2 I018— II)?- 8000 3000 9000 CHBNNEL NUMBER 1000 U7 3' 00 OJ e4 CI) (2) (:3 (2) CI) ‘EINNUEIO 813d STNHOB 0 CI) H 53m+9Fe beam-on singles spectrum. Figure 4-9. 153 no Y ray was seen corresponding to the level of 1440 keV reported from earlier 53Cr(p,nY)53Mn studies (McE68,70). 5 WW A comprehensive list of all Y rays observed in the Fe investigation is given in Appendix E. 154 + 4.4 8 Experimental Data In addition to the y-ray studies of 5%?Fe, an investigation of the 5+ spectrum associated with this nuclide also was carried out. This investigation included not only singles experiments, but also B+-Y coincidence experiments in an effort to ascertain the 8+ end-point energies. 4.4.1 3+ Singles Spectra Although a number of devices were used in studying the 8+ decay of 5%?Fe, the most useful and convenient instrument was a Si(Li) surface- barrier detector. The detector utilized had an area of 200 mm2 with a thickness of 1000p. In order to reduce noise this detector was mounted in a dipstick cryostat immersed in a methanol-dry ice bath (z-77 C). The detector itself was covered by an evacuated Al can with a 0.10~mil Havar window for admission of the positrons. After performing a chemical separation on the target, a drop of the aqueous iron solution was carefully dried on a frame-mounted thin Havar backing and placed in an appropriate holder on the detector can. Each sample was counted for approximately 20 min, with a total counting time of 16-24 hr per run. The usual electronics were utilized, including a 1024-channel analyzer. An energy calibration for these spectra was obtained by using the conversion electrons of several well-known standards. Very thin sources of these standards were prepared by evaporation onto a thin aluminum backing mounted on a small ring holder. The standards used in this study, together with their conversion-electron. energies, are listed in Table 4-5. Since most of these standards are relatively low in energy, one must necessarily extrapolate the energy calibration curve to higher energies -— a somewhat risky procedure, 155 Table 4-5 Electron Energy Standards Used in the 539Fe 8+ Studies Conversion-Electron Energy Source (keV) 137cS 624.15i0.0Ba 655.88i0.10 203Hg 193.64:0.02b 264.49i0.10 2073i 481.6li0.06 554.37i0.10 975.57i0.06 1048.1 :0.1 a(Mulsz),(Lind53),(cra60), (Led67) b(Nij59),(W0156),(Her64), (Led67) C(Bra64), (Yav55), (Led67) 156 requiring cautious evaluation. An 537Fe positron singles spectrum, obtained with the Si(Li) detector is shown in Figure 4-10. Even though the data are plotted on a log scale, the bell-shaped trend of the continuum is apparent. This spectrum represents an l8-hr accumulation of data, using chemically separated sources which were prepared every 15 min. The conversion-electron peaks of the standards used with the above experiment were analyzed using the data analysis task MOIRAE. A first-order background fit was made to the peaks of these standards and their centroids determined. An energy calibration curve was then prepared by making a polynomial fit of energy to channel number, using a standard fitting routine. (The polynomial order was kept low, so that a more reliable high-energy extrapolation could be made.) Then, using the tables of NBS Applied Mathematic Series #13 (Tab51), the corrected Fermi ordinates were obtained and the Fermi plot obtained. Figure 4-11 shows a Fermi plot of an 539Fe singles positron spectrum. The end-point energies of the three resolved beta groups for 539Fe are given in Table 4-6. 4.4.2 B+-YCoincidence Spectra 4.4.2Afi+ Spectra in Coincidence with the 377.9-keV Y Ray In order to elucidate the 3+ feeding to the levels in the 53Mn nucleus, a number of 8+‘Y coincidence experiments were performed. For these experiments a rather efficient 3X3-in. NaI(Tl) detector was used for the y-ray gate, while the Si(Li) surface barrier detector described previously was used to observe the positrons in coincidence with these X rays. The source detector geometries were run at both 90° and 180°. If we assume that the highest end-point group observed at 2.8 MeV feeds 157 .8333 3.33 was 08 m :33 coxmu esuuoonm moawcam +m mmAgv mmm .oauo snow: 39: stem 08m comm 8.3 88 89 coo. 08 o oo. . . 1 _o_ .........,.... .. ......qv) 3 ...w .. «Q O .. n .0. u 5.! AIM“! . I, / .../0 i no_ 0 2 U. x D / U .ue . .o. .I l ..o. 8.9% Seemed mm mm . e0. 158 .oanc was»: a.“ 56% 55.5003 moans: +m whomm 05 now moan «Show 4.7.» was»; $9: >ommzm 83 88 com. 08. com, com .. . _ _ _ . O I..... _ NE a O O 10. [ON 10m 10¢ 10m 10m 19. 10m 10m _ _ — so... mo... 5.: Emma 00. 159 Table 4-6 Resolved 8+ End-point Energies for 539Fe Relative Group Number Energy, MeV Abundance (Z) l 2.80:0.10 56 2 2.40:0.10 41 3 1.71:0.35 z1 160 the ground state of 53Mn, then the 2.4-Nev group should correspond to feeding of the first excited state at 377.9 keV. When such experiments were performed, gating on this 377.9-keV Y-ray, the Fermi plots of the resultant beta spectra revealed a highest end-point group at 2.4-Nev - - 0.4 MeV less than the most energetic group in the ungated spectrum. Thus, these B+FY experiments confirm the earlier hypothesis that the 2.4 MeV group finds the 377.9-keV level in 53Mn. A typical gated coinci- dence spectrum from above is shown in Figure 4-12. 4.4.2B 8+ Spectra in Coincidence with 1;Rays above 511 keV As a matter of interest, an experiment was performed to examine the positron spectrum in coincidence with Y rays above 511 keV. The experi- mental configuration used was the same as described above, except the NaI(Tl) y-ray gate was opened and its lower limit set just above the 511-keV Yi peak. Since the B+ls decay to the ground and the first excited state of 53Mh comprise.over 98% of the available S3gFe decay, the experiment described above was only marginally feasible. Indeed, the results were not clear, but did hint in the appropriate direction. The positron spectrum indicated a weak end-point in the region of 2.2—2.4 MeV, with another strong end-point resolved at 1.2-1.4 MeV. This latter energy is in the region one would expect if feeding to the weak states of 1288.0 and 1619.9 keV were occurring. The higher energy group at 2.4-MeV is not explained but may well be due to chance coincidence. Thus, this experiment seems to confirm the fact that 8+ feeding is occurring to the 1288.0- and 1619.9- keV levels of 53Mn. 1631 A >9: 35cm 83 88 com. 08. 08 — — A 00’. O ...... u..p pgaw no... 28 >2 mNNm 83:0on .Q no on. Pi - b .l A -. .~ O. '9 nauuoqg / slunog O. O. 2 Si(Li) 53M+9Fe 8+ spectrum taken in coincidence with the 377.9-keV Y ray using a 200 mm detector. Figure 4-12. 162 '4.5 Prgposed Decay Schemes The information yielded by the B- and y-ray experiments described above were fitted into consistent decay schemes for 537Fe and 5”Fe. Both of these decay schemes are presented in Figure 4-13. 4.5.1 539Fe Results 4.5.1A The 53Mn Ground State A large portion (257%) of the 5¥7Fe decay proceeds directly to the ground state in 53Mn. This long-lived state (2X106 y) has been shown experimentally to have a spin and parity of 7/2- (Dob56). Positron feeding to this state with an end-point energy of 2.8 MeV has been demonstrated by both 8+ singles and B+Fy coincidence experiments. The 8+ group feeding this level has an allowed shape and a log ft of 5.3. 4.5.18 The 377.9-keV Level The first y ray to be discovered in the 53Fe decay was one reported at 370 keV by Nussbamm et al. in 1953 (Nu853). Previous investigations had characterized the 53Fe decay only as positron emission with an end- point energy of approximately 2.6 MeV (NelSO). The present investiga- tion has assigned an energy of 377.9:0.l keV to the above level. This first excited level is by far the most highly B+/e fed of all the ‘higher states, receiving 398% of the available decay to the excited states in 53un. For many years this Y ray was the only one that could be assigned with certainty to the 53Fe decay. B+-Y coincidence eXperi- lnents in this lab and elsewhere (Ju159) have shown that the 377.9—keV level is fed by a positron group having an end-point energy of about 2.4 MeV. This group appears to have an allowed shape and gives a log ft ‘value of 5.1. A.measurement of the spin for this level has been performed 163 (IOOI '"ZL— (L33) (87) +g «NLS 9/2' l328.l ISZBJ 7,2- I I 31 539 . 26Fe27 8.5 mun 27 7 // -Qh ——————— ~—— / I / l ./ I ,’ . dl 8' . ‘9' 3 ,6 NI 1 I “l I (we-Lass _=+ '3 o l (3/2'Lflflflflle ‘4 l I I a, I B’=4Ix.(5.l) m I e E I ‘8‘ I 5/2“ 77.9 3 .L‘ : B’ = 56%.(53) 7/2- 0 L 1' 53 2 1: IO6 stnza y Figure 4-13. Proposed decay schemes for 539Fe and 53mFe. 164 and confirms the earlier assignment of 5/2— (McE70), (Vui66), (Ju159). This finding is in agreement with other odddmass nuclei in the f7/2 region. 4.5.1C The 1288.0-keV Level This investigation contains definite Y-ray evidence for 8+ feeding to higher levels in S3Mn from the decay of 53 Fe. Heretofore, the only evidence for these levels has been obtained through reactions leading to excited 53Mn states directly -- e.g., 52Cr(p,Y)53Mn. The 1288.0-keV state appears to be populated only very weakly by the decay of 539Fe. Only experiments with very high statistics such as those from the E6 search revealed this level. This state also has been observed rather strongly in the in-beam data, where direct excita- tion is possible. Earlier workers using other reactions together with scattering experiments have reported a level near 1290k£N (Ju159), (McE70). The 3+ spectra analysis indicate group(s) near 1.2-1.4 MeV which may feed this level. A more positive statement about this feeding cannot be easily obtained, since resolution of the 3rd or 4th beta group in a Fermi plot is at best a tedious and somewhat inaccurate procedure. Also, the extremely weak nature of this Y ray does not permit a reliable B+-Y coincidence experiment to be performed. Theoretically, the second excited state should be 3/2-, which would also be consistent with other odd-mass nuclides in this region (Ju159). Recent Y-ray angular distribution measurements by McEllistrem et a1. (McE70) have experimentally verified the 3/2 spin assignment. This assignment would require that the positron group populating the 1288.0-keV state to be second forbidden with a log .ft of approximately 13, and hence a negligibly low relative abundance. 165 Although our experiments show the 1288.0-keV state to be populated very weakly, the abundance is greater than that expected for a log ft of 13. Nevertheless, in view of systematics and the work of McEllistrem et al. an assignment of 3/2- to this level does not seem unreasonable. 4.5.1D The 1619.9-keV Level The population of this level by the 53gFe decay is relatively weak. However, we should recall that there is only about 1% of the total decay populating the higher levels in 53Mn. In this perspective the state is relatively strong. supported by the fact that it was seen in every significant singles spectrum. 8+ experiments described earlier indicate possible feeding to a level of this energy. Half-life measurements show that this level follows the same half-life as 53gFe. Comparison with other scattering transition data confirms the existence of a level of about 1620 keV. The assignment of spin 9/2 to this level has been con- firmed by"Y-ray angular distribution measurements (McE70). 4.5.1E The 2750.7-keV Level Possible evidence for a level at 2750.7 keV has been found during this investigation. A transition of the above energy has been observed in several spectra using chemically separated targets. Half-life measurements have shown that this Y ray follows the 539Fe half-life. This assignment is supported by reports of a level near 2700 keV in several 52Cr(p,Y) experiments (Ste66), (Vui66). No spin assignment was made to this level, although it must be 5/2_, 7/2-, or 9/2-. 4.5.]I' Other Possible Levels Since 99% of the B+le decay of 539Fe goes either to ground or to the first excited state, the task of determining high-lying levels in 166 53Mn by the present approach is quite difficult. Distinguishing possible transitions from contaminants, background and statistical fluctuations also becomes increasingly difficult. Several Y rays seen in this investi- gation remain unidentified even after elimination of contaminants, side reactions, background, etc. All of these are quite weak andnmne can be placed in the decay schemes with confidence. Nevertheless, a coupleof examples will be presented here for completeness. There exists one such Y ray at about 1730 keV which persists after chemical separation and follows approximately the 539Fe half-life. No level of this energy in 53Mn has been reported. Another Y ray at about 3274 keV has been observed in the chemically separated targets and seems to follow a half-life similar to that of 539Fe. From the energetics involved we conclude that it is not fed from the 539Fe ground state. Additional lower-energy Y rays were observed but could not be assigned. 4.5.2 .SgnFe Results 4.5.2A The 53Fe Ground State This ground state has a well-established spin of 7/2— and a measured half life of 8.51 minutes (Ebr65). It is fed by all identified higher states, with the largest contribution (87%) from the first excited state. 4.5.2B The 3040.6-keV Metastable State The Y-rays associated with the metastable state at 3040.6 keV were first: identified by their shorter half-life. During excitation function studies, the concurrent appearance of these Y rays with the known 539Fe Y rays led to the belief that they comprised a metastable state 111 53Fe. Indeed, decay curve studies by Eskola have shown that there 167 is a parent-daughter relationship between the shorter 2.5-min activity and the 8.5-min ground state of 53Fe (Esk67). Comparison of the excitation energy and half-life with single particle estimates (Mos65) indicate that spin values of the metastable and the ground state differ by at least five units. Since the ground state spin is 7/2- this means the spin of the metastable state must be at least 17/2. If the metastable state is interpreted as a three-particle state, one obtains a spin value of 19/2 (Esk67). Gamma-feeding to every established level in 53Fe from 5ynFe has been demonstrated in this investigation. 4.5.2C The 2339.6-keV Level This level was placed on the basis of Y-ray sums and verified by coincidence relations. The spin and parity were assigned on the basis of comparison with the Weisskopf single-particle estimate (Ann70).- Recent experiments by Sawa and Bergster (Ann70) have verified the 11/2- spin and parity assignment of this level. Y-rays were observed from this level which correspond to deexcitation to the ground and first excited states. 4.5.2D The 1328.1-keV Level Based on the present experimental evidence, assignment of the first excited state in 53Fe can be made at either 1328.1 keV or 1011.5 keV. However, shell model calculations indicate that the 1328.1-keV assign- ment is correct (see Section 5.3). The assignment of 9/2- to this lowest excited level is based upon the observed gamma branching ratio for the two Y rays de-exciting the 11/2- level. Assuming that these 1011.5- and 2339.6-keV transitions 168 have multipolarities of M1 and E2 respectively, an estimate derived from the transition probability of a single proton (M0365) yields a branching ratio which is consistent with the observed ratio -- With due regard to the generally observed retardation of M1 transitions with respect to the single particle estimate. The assignment of 9/2- for the spin and parity has also been substantiated by experimental work (Ann‘70 ) . 169 4.6 Discussion In retrospect, the 53m'the investigation has been very rewarding, and certainly turned out to be far more productive than we initially bargained for. The original task of elucidating the levels in 53Mn populated by the B+le decay of 53Fe was accomplished, using both 8+- and Y-ray spectroscopy. However, the salient feature of the investiga- tion was the discovery of several new transitions which were consequently attributed to a high-spin, three-particle isomer in 53Fe. Careful Y-ray studies of this isomer revealed the existence of high multipolarity gamma rays corresponding to M5 and E6 transitions, which were heretofore un- observed. Both 53Fe and 53Mn have interesting structures for shell model studies. 53Fe contains two proton holes and one neutron hole outside the Z228, N828 doubly closed shell. The 53Mn nucleus has a closed N528 neutron shell, and three proton holes outside the Z=28 closed shell. The structure of the isomer, 53mFe, is also of considerable interest. The discussion of the ramifications of these structures and Y-ray transition rates with regard to the shell model has been deferred to the next Chapter (V). CHAPTER V SHELL MODEL CALCULATIONS FOR 53Fe AND 53Mn 5.1 Introduction Our degree of understanding of the nucleus and its processes is measured not only by our ability to make detailed empirical observa— tions but also by our capacity to explain and predict these phenomena from first principles. Therefore, in order to achieve a fuller insight into the nuclear realm the nuclear spectroscopist must not confine himself only to the experimental details, but rather explain and elaborate upon his discoveries through the use or formulation of an appropriate model. Indeed, without some employment of theoretical explanations, the experimentalist becomes merely a nuclear book- keeper. In this spirit of "understanding as well as measuring," I would like to use one such nuclear model in this chapter to describe the data presented in Chapter IV. While the complexity of the nuclear force and its lack of understanding have prevented the formulation of a universal nuclear model, many of the prOperties of nuclei have been explained by a few semi-phenomenological models. Among these, the shell model has been quite successful in many regions, and is the one which I would like to apply here. 170 171 5.2 The Shell Model 5.2.1 General Description Mbtivated by the appearance of the so-called "magic nucleon numbers" (Z or N equal to 2, 8, 20, 28, 50, 82 and 126) where large discontinuities in nuclear binding energy occurred, M. Goeppert-Mayer (Goe49) and Haxel, Jensen, and Suess (Hax49) independently constructed a nuclear model similar to the atomic electron shell structure. In this model, each nucleon is assumed to be moving independently in an average potential due to all of the remaining nucleons. The potential was chosen to be intermediate between that of an isotropic harmonic oscillator and a square well. In order to generate the nuclear orbital spacings to give shell closure at the "magic numbers" a strong spin- orbit coupling term had to be added to the Hamiltonian. This had the effect of splitting each harmonic oscillator level into two levels, j = 2 + 1/2 and j = l - 1/2, which were (2j + l)-fold degenerate. The j = 2 + 1/2 levels were found to lie lower in energy than the j = i - 1/2 levels. This fact gave energy level spacings that were consistent with the "magic numbers." The filling of levels inside a shell must be in accord with the Pauli principle for protons and neutrons separately. In the ground state, the nucleons are paired so that the nuclear properties are determined by the last unpaired nucleon. This prediction has been found accurate for odd mass nuclei having one nucleon just outside a closed shell. The model has failed to predict correctly several properties such as Spin and magnetic moments, for nuclei that have 'several nucleons (or holes) outside a closed shell, i.e. nuclei with only partially filled shells. This is due partly to the fact that the 172 model cannot predict the order of the level filling because of the strengths of the spin-orbit coupling and residual interactions, which cannot be determined accurately. Another example is the failure of the simple shell model to predict the E2 transition rates and electric quadrupole moments in certain nuclei. These are almost invariably larger than the single particle estimates, often by several orders of magnitude. One model which has been used in attempting to account for these effects is the Intermediate Coupling Shell Model. The first attempts to extend the range of validity of shell model calculations consisted of the removal of the requirement that the particles move independently by including two—particle interactions. This was first done for particles in a single configuration, i.e. that giving the lowest energy. This restriction was later removed and "configuration mixing” was introduced. This corresponds to using a wave function which is a linear combination of wave functions for single particle states having nearly degenerate energies and the same total angular momentum. A principal difficulty in using this method is the complexity of the calculations when more than two or three particles are present outside a closed shell. Other modifications of the calculations including residual interactions have been made, but will not be included in this brief description. 5.2.2 Formulation of the Problem In this section, a general outline of the solution of the shell model problem will be presented. This section, as well as much of the calculation, was taken from notes and material provided by Dr. B. H. Wildenthal of the MSU Cyclotron Laboratory and P. W. M. Glaudemans (Gla70). While quite general, this description pertains largely to 173 the Oak Ridge Shell Model Codes. One begins with the basic postulates of the shell model, and in particular makes the assumptions that the single-particle orbits, p(ji)", exist and have a given energy spectrum. In order to do the problem, one must divide these orbits into three distinct groups: 1. The "core", i.e. the "closed shells" or the "inactive particles". 2. The "active" orbits. 3. The "empty" orbits. The core orbits are completely filled with as many nucleons as the Pauli Principle allows, and then dismissed from further orbit calculations. For a nucleus with A nucleons, C nucleons are used to fill the core orbits, and N are left to be distributed over the active orbits in all or some of the distributions allowed by the Pauli Principle. The choice of these "active" orbits also defines the "core" and "empty" groups. A particular number distribution of active particles: n1 n (pi+1) (pi+2) 2 . . . . . . . . . (p. where n1 + 112 + ... +na = N is called a configuration. The occupation numbers n1, n2, .... na can be individually limited either by the Pauli Principle alone or choice. The totality of allowed sets of (n1, n2.... na), presupposing a choice of (01+1, ), constitute the 0.... pi+a "allowable" or "model" configurations, and usually are sufficient to define the model vector space S. The rigorously good quantum numbers of S are N, n, J, and if one uses isospin, T. A basis vector of the space S is then expressed as: 174 TI 111 Hz NJT _ wK ‘ [{(pi+l)jltlx1 (°i+2) I ... (pn ) j2‘2x2 J12T12X12 1$a Jataxa JJT" (5-1) This is an antisymmetric, orthonornal, N-particle ((i ni = N) state of total angular momentum J1 and total i-spin T, with "K" labeling different possible orthonormal vectors for a given N, J, T, n. The x are additional quantum numbers as needed to provide a unique specifica- 1 tion of the single-shell ni-particle wave functions (pini)jiti. The parity of w is determined simply by the number of particles in odd- parity orbits. From this point, attention will be focused on a subspace of S defined by the set of quantum numbers N, J, T, n = s. This subspace is spanned by D vectors SwK. Therefore, the wave functions will be expressed as: D s 2 = S I — W K=l ax wK (5 2) The "dimension" D of the subspace s is a strong function of the number of orbits in S as well as j(pi), J, and T. The wave functions V are eigenfunctions of the shell model Hamiltonian H, and D orthonormal W's can be obtained from the diagonalization of the matrix <¢i|H|wK>. These eigenfunctions are ordered according to the magnitude of their associated eigenvalues and labeled by 0, the order number, with e = 1 corresponding to the lowest energy state of that NJTn(S) and so on. The shell model eigenvalue problem can now be written as: H36 ‘1’ = SBESB ‘I’ (5-3) Or H NJTne > = NJTTreE|NJTne > (5’4) 175 H consists of one-body terms (i.e. the interactions of particles in active orbits with the core), and two-body terms (i.e. the inter- actions of particles in active orbits with each other). 0 0 86 = )3 80 36 = 86 Z 36 SB _ H W H =1 3K, wK E K=1 a 0K (5 5) or U s s D s e '2: e z 3 _ H|s > K=1 aK H K> K;1 aKISK> E (5 6) S ' multiplying by < K I gives: 2 Sa < SK' |H| SK> = 3 Sa 838 . (5-7) K=1 K K=1 K KK This can be rewritten as: D Z s s _ s s _ =1 ax HK'K ' aK' E (5 8) where K' = l ..... 0 These equations form a matrix equation: Y r Y r x S I 3 H11 H12 0 O O O HID a 21 = E (5-9) H01 ”vvJavY "5‘0J 0 6+ For the above matrix equation, there exists 0 solutions (S E,S a). 176 Thus, the shell model problem has been reduced to: 1) Evaluation of the multiparticle matrix elements: . 2) Diagonalization of the resulting matrix. The first problem is by far the more difficult. In order to evaluate the HKK" one must employ the "Fundamental Theorem" of the shell model: If H has only zero-, one-, and two-body forces, thenlany multiparticle matrix element can be written as a linear sum of one- and two-particle matrix elements, and <(0a08)JTIHI(0a'08v)JT>- This can be restated as: M (sz'IHISwK = SHK'K.= mil SCK'Km Xm (5-10) where the xm are the one- and two-body matrix elements. The singular importance of the "Fundamental Theorem" is that, whereas there exists a semi-infinite number of multiparticle matrix elements , there is a relatively small, well-defined number of two-body matrix elements, for any given choice of pi+l’ pi+2’ .... p1+a. From these two-body matrix elements, any multiparticle matrix element in S can be calculated. Thus, the first step of the shell model problem is separated into: 1) Finding the coefficientsSCK.Km which relate the two- body matrix elements and the single-particle matrix elements to the multiparticle matrix elements. This is a very difficult algebraic 'problem, but one which is explicitly defined. The C's are fixed for a given assumption for the model space S. The basic function of the 177 shell model code is to determine these C coefficients. 2) Finding the shell model Hamiltonian, that is the one- and two-body matrix elements. This is not a mathematical problem, but one which is empirically determined from "nature". Some attention will now be given to part two. If one now considers equation (5-6): s s D H|s>=Kg1H|SK> a = Es> Now, multiplying from the left by: D s s , = SE =K i. 188K.SaK (5-11) or rewritten in another form: 0 = 2' (5-12) K,K =1 Thus, the multiparticle matrix elements, are related to the eigenvalues SE. However, the two-body matrix elements and the single-particle matrix elements, the parameters of H, are related to the multiparticle matrix elements by the geometrical coefficients SCR'Km' Inserting this substitution, one obtains: D M M X S S S S S a v a ( 2 C X ) = X F = E (5-13) K,K'-l K K mgl K'Km m m=l mxm where SFIn = K',gsl saKvSaxécKoKm and Xm are the two-body matrix elements and single-particle matrix elements. 178 It should be emphasized that the set of two-body matrix elements and single-particle matrix elements is fixed'for a given shell model, i.e. all eigenvalues in S are derived from them. This allows the shell model problem to be self-contained, or in a sense, self-consistent. The use of the single-particle and two-body matrix elements provides the most general specification possible of the shell model potential. One should also note that: l) The eigenvalues of the multiparticle states are related to parameters of the Hamiltonian through geometrical coefficients and eigenvector amplitudes. 2) These eigenvalues of multiparticle states presumably cor- respond to energies of experimentally observable nuclear levels. One can now require that the two-body matrix elements and the single particle matrix elements be such as to yield a least-squares fit between the calculated SE and the presumed experimental counter- part values, Se. If one knows L experimental energy levels Se, then for each one he can construct an equation: M r ch 2 s s s app oa “1:1 Fm Xm= E -————--+ c (5-14) S = NJTB running over L values. If one can then manage L >> M, he can perhaps determine the Xm meaningfully. First, some initial choice must be made for H (= Ho), Sao 8 determined by XS. m = l,M. One then calculates SE°, k’ F°m. Using ethese, L identities are set up: F° x° = 13° (5-15) 179 Now, one substitutes in these expressions Se for the sE’and treating the xm's as unknowns, least-squares solves for a new set. Suppose that a new set ofSV, 8E has been obtained. After inspection of SE vs. 85, it is appropriate to calculate expectation values of other operators besides H. There are only a very few operators (moments) which have expectation values that are functions of one SW. Most of the s' physically measurable observables connect one SW to another F. If one wishes to evaluate some such operator: (5-16) f0 f where = Z a lf.> i and i D i i W = Z a I £> i=1 2 The first step is the construction of the matrix : ' ) ... ... <0 > = ' (5-17) 0 J L "where the matrix elements connect different basis vectors 180 km (or |K>) of the model space S. 00 can be either one-body or two- body. Most observables correspond to one-body operators -e.g. spectroscopic factors for single nucleon transfer, E2 strengths, inelastic scattering strengths, etc. These observables can all be represented either by a bare or weighted creation operator or a creation- annihilation pair. In either case, . In addition, angular momentum and isospin must be conserved from state "1" through OpJT to state "f". Considering the expression: _ n1 n n [(p)tl(D)Il---(D)vi] 9“ 1 J1°‘l 2 Jzo‘z 8‘ Ja“... i (N'J'T') (5-19) h = w ere N(f) N(i) or N(i) +1 and A(JJ'AJ(Op)) A(TT'AT(00)) + F = I = v . or 00 a a nK nK except for one case, where nK nK + 1 In addition, all non-K J's and T's must satisfy 5(J J ') etc. K’ K For 00 a afa One particle can change orbit (including returning to the same) and so all nK = nK' except for two, . , = v . = v _ which must correlate. nK nK + l, nK nK l. The matrix elements of these operators are constructed with the .aid Of the coefficients of fractional parentage libraries in a manner analogous to the construction of the in terms of the two-body 181 matrix elements times geometrical coefficients. After construction of the matrix , it is multiplied by the amplitude of the eigenvectors: = (fal, fa2, ... fafv) i 00 a (5-20) 1 aiv \ With the shell model code, these procedures are accomplished in two steps, First, the Operator matrices are constructed and stored. Second, the eigenvector amplitudes, saved from a previous eigenvalue-eigenvector calculation, are combined with the matrices to obtain the observable values. In addition to the above general description of the shell model code, I have found that detailed "how-to-do-it" input instructions for the code to be very helpful in understanding the shell model problem, as well as providing the format for running the program. Because of the length and the "secondary relevancy" of these input instructions and comments, I have deferred their discussion to Appendix B. However, anyone who desires a more complete grasp of the problem, or wishes to perform such a calculation.will find this section very valuable. 182 5.3 53Fe Calculations 5.3.1 Predicted Level Scheme The Oak Ridge Shell Model Codes were used first to calculate the energy level spacings for 53Fe. A proton-neutron formalism was chosen, instead of the isospin formalism, and the levels calculated in a pure f7 [2 approximation. Eigenstates of the mass 53 system were calculated assuming 7 active neutrons, 6 active protons, and the proton-neutron interactions of Vervier. (Ver67). Table 5-1 contains this useful list of interactions from Vervier. All three interactions were tried with our code, and found to give very good results. These results are summarized in Table 5-2. Note that agreement with experi— ment is quite satisfactory in all three cases. Also, the large Spin- gap which gives rise to the isomeric character of the 19/2- level is predicted in all cases. (Vervier points out in his paper (Ver67) that the persistence of this isomeric prediction with varying effective interactions is due to the following facts: (1) the 7+ state lies very low in the spectrum of the (fife/2)(vf7/2) interaction, much lower than the 6+, 5+, 4+ and 3+ levels (for the three cases of Table 5-1), indicating a strong attraction between the lf7/2 proton and neutron when their spins are as much aligned as possible. (2) The 6+ and 4+ states of the (nf7/2)'2 configuration are quite close together, indi- cating that the proton-neutron interaction "dominates" the proton- proton interaction and pushes the l9/2- level, where the maximum spin alignment occurs, below the l7/2-, 15/2-, and 13/2- states of the ‘(nf7/2)‘2(vf7/2)_1 configuration. The occurrence of similar spin gaps and their correSponding isomeric levels has been explained 183 Table 5-1 Effective Proton-Neutron Interactions in the -l -l (wf7/2) (vf7/2) Configuration Spin Interaction (1) (2) (3) 0+ 0 0 0 + 1 1.035 0.610 0.618 1.509 1.510 1.590 2.248 1.960 1.518 2.998 2.750 2.844 1.958 2.250 2.220 3.400 3.190 3.191 0.617 0.530 0.526 Interaction (1) has been adapted from the work of McCullen, pg 31, (McC64). The two others are based on more recent experimental data; (2) was deduced by Ball (BalJB) from a least-squares fit of the experimental spectra of 42Sc and 48Sc; (3) differs from (2) mainly in the assignment of the 3+ level based on recent (3He,p) results (Zur66). Predicted Levels and Spins for 5 Shell Model Calculations Using the Interaction from Vervier. 184 Table 5-2 3Fe from Interaction (1) Interaction (2) Interaction (3) Experimental Energy(MeV) Spin Energy Spin Energy Spin Energy Spin 0.00 7/2 0.00 7/2 0.00 7/2 0.00 7/2 1.68 9/2 1.64 9/2 1.66 9/2 1.33 9/2 2.44 11/2 2.50 11/2 2.46 11/2 2.34 11/2 3.25 7/2 3.47 19/2 3.47 19/2 3.04 19/2 3.41 3/2 3.64 5/2 3.50 5/2 3.64 l9/2 3.66 15/2 3.60 7/2 3.71 15/2 3.68 13/2 3.64 13/2 3.85 13/2 3.70 7/2 3.72 3/2 185 previously by essentially the same arguments in 211Po, 212Po (Aue64) and 93Mo (Aue64a). 5.3.2 Comparison with Other Model Calculations and with Experimental Results. A schematic comparison of the results of various calculations with the experimental results obtained in this study is presented in Figure 5-1. The first level scheme is from the work of McCullen, 33 al. (McC64). The wave functions used in this calculation were constructed from a “OCa core plus (Z-20) protons and (N-20) neutrons in the lf7/2 shell. The lf7/2 nucleon-nucleon interaction was determined from the observed levels of ”28c, assuming that they could be interpreted as due to the configuration (lf7/2)2. Using the method of Talmi, the interaction was treated exactly -within the framework of the pure configuration assumption. As shown in Figure 5-1, this model produces a level scheme which is in good agreement with our results from gamma decay. The energies, spins, and parities are in accord with those assigned to the experimental scheme. The second level scheme shown is from Vervier (Ver67). These calculations are similar to those of McCullen, g£_§l,, in that both assume the energy levels of 53Fe arise from the (nf7/2)_2(vf7/2)_1 configuration. The effective proton-proton interaction in the (nfj/Z)‘2 configuration was taken from the experimental spectrum of 5“Fe. Several effective proton-neutron interactions in the (nf7/2)"1 (vf7/2)-1 configu- ‘ration were used (see Table S-l). The level scheme shown was obtained using interaction (3), although all the effective interactions gave N 1 Energy (MeV ) l9/2' lll2' 9/2' 0 _J 7/2' MC Cullen etol. Figure 5-1. 186 Vervier Interaction Expt Schematic comparison of 53Fe level schemes predicted by two calculations versus the experimental results obtained in this study. 187 practically the same results. The isomeric nature of the 19/2- level is predicted in all cases, thus demonstrating that the existence of the isomer does not depend strongly on the details of the effective interactions. Since our calculations using the Oak Ridge Shell Model Codes, utilized the interactions of Vervier, the resultant level scheme is practically the same as that reported by Vervier. Hence, our scheme is not included in Figure 5-1, but may be thought of as being the "Vervier Interaction". However, the results of our calculations are listed in Table 5—2. 188 5.4 53Mn Calculations 5.4.1 Predicted Level Scheme Calculation of the energy level scheme for 53Mn was accomplished using the Oak Ridge Shell Model Codes as described above. The calcu- lations were performed assuming five active protons, in a pure f7/2 approximation. The results of these 53Mn calculations, together with our experimentally determined levels, are given in Table 5—3. 5.4.2 Comparison with Other Model Calculations and with Experimental Results. The levels of 53Mn have been calculated by several workers. For comparison, a few of these level schemes are presented in Figure 5-2, alongside our experimentally determined level structure. The results shown in the first theoretical decay scheme are those of Talmi (Lip58). These calculations are based on a closed core, with only the outer nucleons contributing to the level scheme. When there exist more than one nucleon in definite orbits outside this closed core, there are many levels obtained by the various modes of coupling of the angular momenta of the extra nucleons. Since the energy in the central field is the same for all these nucleons, one must consider their mutual interaction in order to remove the degeneracy and split the levels. Talmi's approach has been to start with the shell model and using jj-coupling wave functions predict the energies. He did not ’make any specific assumption for either the interaction or the radial functions. He assumed only that the effective interaction was a 189 .mvsum mfinu cu voafimuno muasmou Hausoawuooxu «no msmuo> mcoaumasoamo msoaum> so wouowvoun moauzom Ho>oa :zmm mo somwumoaoo oaumeucom .mtm muswfim etc; aft 8.8225 528 .U .0 comcmom an. .229 6832 so: 8:8 0.2 .35 8 39.3% EB -Mz. dz. .3. -3. -S !|.I|..~k I'M: J» J o J Ila}. ..IIIIII RB - ... IR}. .Na .80 l/J J. B - x... 1 _ mm». h» .9» Jn .8» -~\__ Jc. .Illllhz. - -MB .mxn .IIIIIW» -ma |\Il -«3 - n 8: - \n -Nx: IIIIIIIJMv: - - Jo Jo 1 N MB N)... ha .Q. . as. I ..«N IIIIII Illlllhua _ lawn. -msfl .im Illlhlxm. Ablaug (AGIN) 190 Table 5-3 Predicted Levels and Spins for 53Mn from Shell Model Calculations Using an Interaction from Vervier Calculated Experimental Energy (MeV) Spin Energy Spin 0.00 7/2 0.00 7/2 0.32 5/2 0.38 5/2 1.47 3/2 1.29 3/2 1.78 11/2 1.62 9/2 2.15 9/2 2.75 ( ) 3.08 15/2 191 two-body force. The results of his calculations for the first two excited states of 53Mn are in excellent agreement with the experimental facts. The second level scheme shows the results of Kisslinger and Sorensen (K1860). Their model combines features of the unified nuclear model and the independent-particle model, with a two-body residual interaction. The residual action used consists of two parts -a pairing force and a long-range part. Calculations were performed for various values of the two strength parameters, using single-particle levels taken from experiments. Agreement with experimental results for 53Mn was rather poor, although qualitatively correct. Prediction of the ll/2- level being depressed under the 3/2- level is not in agreement with other work. Also, the higher lying excited states are predicted to be somewhat too high in energy. The third level scheme is that from deShalit (deS63). This rather detailed shell model calculation gives levels that are in good agreement with the experimental results. The separation of the higher states appears to be slightly too large. The fourth level scheme is from the work of McCullen gt al. (McC64). The methods of this calculation have already been described (Section 5.3.2). The first excited state is predicted a bit low, while the upper levels are slightly higher and more separated than in deShalit's work. Nevertheless, qualitatively, the level scheme is in agreement with experiment. The fifth level scheme is that predicted by Malik and Scholz (Mal66). Their levels are calculated using a strong-coupling symmetric- rotator model including the Coriolis coupling between bands. The .— single were c split apprc The n exci‘ char were exci term or < wet. res the PI. 192 single-particle energy levels and wave functions in the deformed well were computed for a spin-orbit strength consistent with the observed splitting in “ICa. The band-head energies were calculated from the appropriate summation over the occupied single-particle energy levels. The moment of inertia was taken from the excitation energy of the first excited 2+ state of neighboring even-even nuclei assuming a rotational character for the state. The matrix elements of the Coriolis coupling were computed from the single-particle wave functions. The final excitation spectra were obtained by diagonalizing the Coriolis coupling term with the rotational wave function based on the ten available particle or core excited states in the lf-2p shell. Energy levels and wave functions were calculated as a function of the deformation parameter, 8. The results for 53Mn are shown in Figure 5-3. The scheme agrees well with the experimental results, although the higher levels are a little low. Spin assignments to higher levels are also not in the same order as those of previous calculations shown. The sixth theoretical level scheme presented is that of Auerbach (Aue67). Instead of the pure configuration description, he has employed a configuration mixing approach. A ”BCa nucleus was assumed to be an inert core with the extra n-protons outside this core forming fg/z and f9}; configurations. The calculation was performed by the method of effective interactions. The results of this calculation for 53Mn agree very well with those from the experiment. The last calculation shown, labeled "Vervier Interaction", is _our calculation using the Oak Ridge Shell Model Codes and the same proton-neutron effective interaction as used by Vervier. These levels are tat Sh( vi 90 193 are in good agreement with the experimental results, although quanti- tatively they are not quite as close as some of the other calculations shown. In general, all of the calculations shown are in agreement with the lower-lying levels of 53Mn as determined in our experimental work. 194 5.5 Calculation of 53Fe Transition Probabilities 5.5.1 MEthods of Calculation 5.5.1A Moszkowski Single Particle Estimates Although the single particle estimates are rather crude and are not expected to yield accurate results, they do provide a good starting point for interpretation of ones results. Only a brief description of the derivation of the estimates will be provided here, since these details have been treated previously (Epp70a) (Mos65). The total power radiated by a pure multipole over all angles is given by C P(£,m) = la(£,m)l2 (5-21) 81rk2 where P is the total power radiated and the a's are the multipole coefficients. The transition probability may be written in quantum mechanical terms as P _l=__ _ T-T 1:... (522) where T is the transition probability and T is the mean lifetime of the state. Expressions can now be written for the electric and magnetic transition probabilities: 2wc 22+2 TE(2.m) =- (2+1) k mm + Qémlz (5—23) fiw[(22+1)!!]2 9. _ 2nc 2+1 2£+2 , 2 _ TM(2.m) — (T ) k IMILm + Mm] (5 24) ‘fiw[(2£+1)!!]2 195 These equations still contain the classical expressions for charge and current densities, which must now be transformed to their quantum mechanical equivalents. Performing these transformation” one obtains: l le = e (5‘25) iekfi l 2 :E;E ' a _——_ + + . * * . - sz 2(2+1)M (flpn 0' X r 6(1' Ylm) + 2r Ylm h |i> (5 26) Mun - (2+1)M (5 28) At this point, the calculation of the transition probabilities cannot proceed without having explicit forms for the wave functions involved. Thus, we must invoke some particular nuclear model in order to provide the wave functions, and consequently, the radial matrix elements. The'single—particle model assumes that the structure of the excited nuclear state is determined entirely by the last, unpaired nucleon in the nucleus, either a proton or a neutron. The nuclear properties are therefore established by the properties of this last unpaired nucleon. Y transitions from excited nuclear states are then defined as changes in the state of the odd nucleon under the influence of a spherically symmetric potential created by the remainder of the nucleons in the nucleus. Calculation of the single-particle transition probability is 'usually carried out assuming that the odd particle is a proton, although neutron transitions can be treated by a slight modification of the 196 expressions. If we consider the transitions of a proton in a central, velocity-independent well, equations (5-23) and (5-24) now can be written as: 2' (1) (EL) _ 245M) 93-. .22. £2 _ Ti+f - £[(2£+1)!!IZ—w(hc)(wc) (J Rf(a) Rirzdr)28(ji’£’jf) (5 29) 0 and (ML)- 24m: 23:22.12 ___2__ . 2.2-1 2 2. TL+f _ £[(22+l)!!]2w'fic (: ) (mca) .(upl 2+1)2( Rf(a) Rir dr) 0 where g = the angular momentum carried away by the emitted quantum. Rf = Radial wave functions of the initial and final states, respectively m = (El-Ef)/fi c a velocity of light a = nuclear radius p a proton magnetic moment S = statistical factor The radial integrals can be evaluated explicitly if one makes a few assumptions concerning the nuclear wavefunctions. A very simple view of the nuclear wavefunctions is provided by the assumption that the radial wavefunctions, R, for both the initial and final states are con- stant throughout the interior of the nucleus (for ra) (Bla52), (WeiSl). On the basis of this constant density model, the radial integrals 197 may be rewritten as: r 2 3 I: Rf (E) R1 err = W (5-31) A more detailed calculation of radial integrals, using the radial wavefunctions of a single proton in a Spherical square well was found to give practically the same results as the simple assumption above, except for M1 transitions (Mo853). In order to obtain more accurate results it would be necessary to take into account the diffuseness of the nuclear potential (Blo60). Using the constant density model estimate, the y-decay transition probability for a single proton, equations (5-29) and (5-30), can be written in the following form: T021.) = 4.41m; (3 )2 (Lfm x Sp 2[(22+1)!!]2 2+3 197 Nev (a in 10-13 cm)22 S(j1,£,jf) x lOleec-1 (5-32) and (ML) 0.19 (2+1) 3 2 ___9.__ Tap ‘ g[(2g+1)::i7(g+2) (“pQ 2+1 2£+l '“w (a in 10' 13 (197 MeV) Cm)29.-2 x S(ji,2,jf) x 10213.3(?1 (5—33) A few of these estimates are listed in Table 5-4. These expres- -13 A1/3 Sions include the assumptions that a = l.ZXl0 and up = 2.79. The statistical factor, S, contains the angular dependence of 198 Table 5-4 Single-Particle Estimates for the Transition Probability of a Single Proton. Multipolarity TSp in sec-1 E1 = 1.0x101” - A2/3 - E3 3 E2 = 7.4x107 ' A“/3 - E: 5 E3 = 3.4x1ol - A2 - E; 8 E4 = 1.1><10"S - A8/3 ’ E: 3 E5 = 2.5x10‘12' A1°/3- E;1 3 M1 = 2.94013 - A0 - E3 3 M2 = 8.4Xl07 - 9.2/3 ' E3 3 M3 = 8.7x101 . A‘Vg - E; 3 M4 =- 4.8><10"5 - A2 - 19:3 3 M5 .. 1.7x10‘11- A8/3 ° 15:1 s (a = 1.2x10“13 All3 cm., up = 2.79, EY in MeV) 199 the transition probability, and can be defined as: * .. * S(j ,2,3 ) = 41r(2j +1) 1 2: 2 2| emf Y 9‘“ MP (5-34) 1 f f 4n A simple expression for S can be deduced from the above soimjf) = (23f+1>IC(ji.jf2.%-§o>12 (5-35) where C is a Clebsch-Gordon coefficient (Edm57, R0557). For the special case where Iji-j a 2, the expression for S f| becomes relatively simple: = 13.111211}. x gun)” x (21:)!1 _ 3(31.2.jf) (251)” 2: [(jf-(1/2)1! (5 36) In particular, S(£+l/2, 2,1/2) = 1 (5-37) Viewed strictly from a single particle picture, magnetic transition probabilities in odd-neutron nuclei are expected to be slightly smaller than the corresponding magnetic transition probabilities in odd proton nuclei (Mos65), by the factor n N -1 -2+1 up () (5-38) The equations from Table 5-4 were incorporated into a PDP-9 computer program, PROB, written by Dr. R. Eppley. This program calcu- lates transition probabilities and half-lives of y-ray transitions based on the single particle equations by Moszkowski. The input information consists of the type of transition (neutron or proton), the transition energy, and the value of the statistical factor. The output contains 200 the transition probability and half-life for the transitions El through E5 and.Ml through M5. This program may be found on the library DECtape and is run under the keyboard monitor system. 5.5.18 Shell Model Methods Present day shell model calculations are capable of going far beyond the simple estimates outlined in Section A. Multiparticle con- _ figurations as well as configuration mixing can be treated. While somewhat complex, the formalism for reducing these expressions containing many-particle matrix elements to single particle matrix elements exists and is well-defined (Gla70). This essentially reduces the problem to the evaluation of single particle matrix elements. In this section, I would like to outline the calculation of these single particle matrix elements, which are the basis of the shell model transition probability formalism. In some ways, this amounts to a partial restatement of Section A, but is more complete and provides a good insight into the calculation. We wish to evaluate the following matrix elements for electric transitions: L o L l (5-39) where SL and VL are defined by A e (i)+e (i) A A e (1)-e (i) A L - .2, n L L _ _p_ n L _ Sm(el) — 1:1 2 riYm(r) Vm(el) - 1:1 2 riYm(ri) (5 40) The wave functions |p> can be separated into a radial, spin, and isospin part |p> E IRn £>l2jm>lttz> (5-41) 201 The same can be done for |A>. We can now rewrite the expressions for the matrix elements in (5-39) L , efen L . L A a ( 2 )<£fJfI'Y (r)l|£ij1> and VL 1 _ 32_:_32. L L ‘ 1 - < 2 ><2fJfl|Y ||2111> (5-42) We now consider each part of (5-42). L m * c L “ _ L _ 1. a J Rhf£f(r) r Rh121(r) dr : (5 43) 0 1 .1 A -' A 2 2. <2fjf||YL(r) Ilgiji> = ¥ IIYL(r)||£i.Zfi>S > E M (5‘44) 3f 31 Since YL(r) does not operate on spin we have: £f+ll2+ji+L 2f 2 M = H) /(23f+1) (211m LA .l (zfllY (r)||£i> (5-45) 1 f 2 The last part of 5-45) can be evaluated using equation 17.14 of deShalit and Talmi (Des63b). 2fL£i (2L + 1) (22f + 1) (221 + 1) L * 2 (5-46) <2f||Y (r)||21> = (‘1) f///' 4" o 00 This vanishes for 2f + L + L = odd. 1 Therefore, the resultant expression is: 1 .<2fjf||YL(£)l|ziji> = (-1)22f+'§-+ ji+L¢//K2jf+l)(2ji+l)(2£f+l)(2L+l)(221+1) 4n L L i “f “1 2f 1 1 31 jf 2 o o o (5 47) 202 3. The last part of (5-42) can be calculated directly with the Wigner-Eckart theorem +1 r—-——'—“1 Since 1 - <.E||11||t£> . 5££991££i (2t+l) we get - J2: + 1 (5-48) Likewise, one can prove from t a 2 that - «4(.+1)<2.+1) att. (5—49) + + for t = 1/2 we get using I 2 2t <1/2||1L°||1/2> = /'2‘ (5—50) <1/2||11||1/2> = J? The final expressions for the single-particle matrix element for an electric transition can now be written as: 1 (23f+1)(231+1)(2L+1)(211+1) L o e + en 24j +L «4.4! Is (...... Hw = *7 H) . .. ifliL lfLii L x l /-2_ (r > (5'51) j13£2 203 e - e _l <2fjft| IVL(el)TR'|‘gij1t> a [fig—.11][(_1)2+31+L/(23f+1)(231+1)(2L+1)(221+1) 4n 'zfziL szli x 1 /6 (5-52) jijff 0 00 The curly brackets indicate a 6-j symbol and the parentheses a 3-j symbol. The corresponding calculation of single particle matrix elements for magnetic transitions is more complex and somewhat more difficult. The reduced transition probability for a magnetic transition, B(L) contains many-particle matrix elements 1 Z i i B(L) 3 ~ ~ (2J1+1)(2Tf+1) Jijf J23;:l L__ #1 = 1 ~ ” L x ETiTiOOITfofoTfHIS fl°|||1111> + ~ .. 1 2 -J . = 1 L o (211+1)(2'rf+1) [(Jfoms 1‘- IIIJ1T1>6Tin + 1 .. vL 1 12 (5-53) It can however, be expressed in terms of one-particle matrix elements. (5-54) (5—55) 204 where SL and VL are given by (i) (2) '* A ,. g (1) + s (i) 21 L L "i + Sm(magn.) = Z grad riYm(ri) _p n L+l i-l 2 8:3)(1) + 3:3)(1) 2 :1 Zinc (5-56) P (2) (2) '* A g (i) - g (1) 21 L _ L 11 n i Vm(magn.) - 1:1 grad riYh(ri) 2 L+1 + (S) (S) 8 (i) - g (1) + 99- “ si é“ (5-57) 2 2Mpc Again separating the wave functions |p> in space and isospin parts we have L L o o = <2fjf||S If ||giji> (5-58) and = <2fjf||VL||21ji> (5-59) The matrix elements of the isospin part were calculated above, see (5-50). For the space part, we may use the vaers of L A + (5-60) and <2fjf|[grad]rLYL(r)|'§|Iziji> (5-61) Using the expression (17.19) from deShalit (deS63b), one can perform a calculation for a magnetic dipole (Ml) transition. For the orbital 205 angular momentum part we obtain: <2 1 lgradtr11(£>1-E||z j > =«3 <1 j ||E||z j > (5-62) f f i 1 4n f f i i This can be rewritten as: l ‘l 2 'l + f 2 + 1 2 =< A llzll A > = jf 31 2f+l/2+j1+1 ifli l + (-1) /(231+1)(ij+1) <2f| [2| [11> (5-63) jijfllz Applying the Wigner-Eckart theorem we have: + <2f||1||11> = Jhi(£1+1)(221+1) 6211f (5—64) Substituting (5-64) into (5-63) and (5-63) into (5-62) we get: <£fjf|lgrad[rYl(r)°]Ellliji> - 3 2f+ji+3/2 J/4E; (-1) /(2ji+l)(2jf+l) /11<11+1><221+1) lfli 1 f (5-65) 1,1f1/2 Likewise, a similar expression can be derived for the intrinsic spin part: 206 1 A + <£fjfllgrad[rY (r)]-s|l£ij1> = 1/2 1/2 1 2 +j +3/2 3 _ f f /(23 +1) {2;} +1) 3 /14 ( 1) f 1 //2 ) 6 Final expressions for the magnetic dipole transitions may be written as: For the isoscalar term: 2 f 1 o 3 /2 +1 2 +1 -1 6 x <2fjft||s (M1)ju Ilzijit> ='/Z?' ( j1 )( jf ) ( ) lilf 1 1143/2 8 (2') + g (2.) lffli l {-1) *E—' n «11(21+1)(221+1) + 2 jijf1/2 J (s) (s) ‘ 1/2 1/2 1 “If-Hal2 Ep + 3n 3 eh (~1) E" 1 J? 'EE"E""— (5-67) 2 J jijf f p For the isovector term: ,/ if 1 . 3 2 +1 2 +1 -1 6 x <2fjft||v (M1)T1||1131t> = /Z;' ( 31 )( jf ) ( ) lizf ji+3l2 g (2)_ g (2) lfii 1 (-1) p n /21(21+1)(221+1) + 2 jijf1/2 (s) (s) 1/2 1/2 1 j +3/2 g - g (-1) f ‘2- n J/% 2 J5 Zific (5'68) 2 jijf f p Note that both matrix elements vanish unless Iji - jfl :1 and £1 = if (5-69) 207 Note that the conditions given by (5-69) are the selection rules for M1 transitions. The above discussion was included here to give the reader some feeling for the techniques involved in performing these calculations. The M1 probability calculation outlined above is relatively simple com- pared to higher order magnetic transitions. The 53’"Fe problem contained only one such transition, but it was an.M5! Before continuing it is appropriate to discuss the matter of units. Calculation of the reduced transition probability, B(L,n), yields so-called "natural" units of [ezfmZL] and [uzfmZL-z] for electric and magnetic transitions, respectively. One may wish to go from these to partial half-lives, or vice versa, in order to compare with experir ment. The following formulas and conversions are quite useful in accomplishing the change of units. The partial width of a gamma transition (with angular momentum L, energy Ey, and parity n) from an initial level with spin ji to a final level with jf is given by the expression (Pre62) 8n mu) 3 21‘” L... = L[(2L+1)HF ‘hc mm (5%) P where B(L,w) is the reduced transition probability, in units of 2 2L-2 (ezfmZL) or (uofm ). Convenient units for plugging into this equation are: ‘hc - 1.973 x 10’11 MeV cm e2 8 1.440 MeV fm 1132 = 0.1589 MeV fm3 208 The lifetime of the initial state may be calculated by: F‘r =‘fi = 0.6582 x 10.15 eV sec (5-71) and the half-life obtained with T = 0.693 1 (5-72) 1/2 The above equations allow the results of our calculations to be expressed in various units. 5.5.2 Results 5.5.2A Single Particle Estimate The values of the single particle estimate were obtained using program PROB--which utilizes the formulas listed in Table 5-4. Such a formula was not available for the E6 transition, and it was calculated using formula (5-32). The statistical factor, S, was obtained by use of expression (5-36). The results of these Mbszkowski single particle estimates for the relevant 53mFe transitions together with the experimental data are given in Table 5-5. 5.5.28 Shell Model Results The reduced transition probabilities, B(L,w), and consequently the partial half-lives also were calculated using the Oak Ridge Shell Model Codes. These shell model estimates for the relevant E6, M5, and E4 decays were calculated in an f7/2 approximation. Eigenstates of the mass 53 system were calculated assuming 7 active neutrons, 6 active protons and the'f7/2 interaction of Vervier. The 19/2— state is purely (vf7/2)3=7/2(wf7/2)3=6, whereas the 11/2- and 7/2' states are 209 Table 5-5 Comparison of Experimental Results with Moszkowski Single Particle Values for Partial Half-life. E Photon Retardation (keV) Multipolarity Intensity Expt.a Calc. Expt./Calc. 701.1:0.1 _E_4 100 1.57::102 2.0611101 7.6 1011.5t0.1 51 86:5 1328.110.1 51 87:4 1712.6io.3 gs 1.3.10.1 1.173.104 2.76x103 4.2 2339.6i0.1 _2 13:2 3040.&0.5 _E_6 0.06:.01 2.6x105 6.1711104 4.3 a The 701.1-keV transition was corrected for conversion using a value of (1k - 0.003, which we obtained by a linear extrapolation from the tables of R.S.Hager and E.C.Se1tzer, Nucl. Data., Sec. A4, 1(1968). The con- version coefficients for the other transitions were small enough to be negligible. 210 mixtures of the J=4 and 2; and J=2 and 0 proton couplings, respectively. For the electric transitions, effective charges of ep - 1.5 and en = 0.5 were assumed, together with a harmonic oscillator radial dependence. Free nucleon g-factors and harmonic oscillator radial dependence were assumed for the M5 calculation. Table 5-6 contains the results of these calculations, both in terms of the photon partial half-lives and in terms of the reduced transition probability. The experimental values also are shown in the same units for easy comparison. In addition a retardation factor for the half-lives is given. 5.5.3 Discussion The Moszkowski single particle estimates, summarized in Table 5-5, are in remarkably good agreement with the experimental results. Moszkowski himself states that these theoretical values are "crude" and "not expected to represent accurately transitions in actual nuclei". (Mbs65). However, in this case, a single-particle description appears to be an adequate approximation. It is rather surprising that the decay of the three-particle isomeric state to various levels of different couplings can be described so well by a single particle model. The results of the shell model calculations of partial half- lives are presented in Table 5-6. The agreement with experimental values is not as good as in the case of the Moszkowski estimates. In addition, the formalism for calculating higher order magnetic transitions, such as the.M5 has not been checked completely. Therefore, the calcu- lated value for the M5 transition may be in error. The results for the 211 a m x O a m x O O x O x O O O I O 0 w MN moH N 0 NH «N mOH .K N m NN eoH H H K: om N Ho woo o om m one oqom HoHaLNmmOmemumv ..-- --- --- 1..- NHMH mm H 046 ammm a f x O a f x O x O x O O O I O | O m mm 53 N n w mu HOH mo m CHH NOH co H e0H NH H H can H n: m 0+0 NH: --- 1... I- -3 1-: .13 Hm H.o...H.m~2 1.... --- n... -..- 1- - 98m Hm 298.23 a o x . a o x . . x . x . I I. . 1 . w mu moH m s m mm N0H mm o m NH HOH 2 H NOH mm H OOH" cm H o+H H2. .on0 .uaxm .ono\.umxo .onu .unxm huHmsousH suHumHon A>oxv A: :va soHumeumuom N\H Toomv souonm ..HuHsz >m a :39; 13qu .QMHHIMHmm HmHuumm How mmsHm> Homo: HHonm nuwa nuHammm Hmusmafiuonxm mo somwumgaoo elm oHan 212 E4 and E6 are more reliable, and indicate that the experimental values are retarded by factors of 12 and 22, respectively. The method of cal- culation was described earlier and will not be detailed here. The apparent difference between the calculated and measured values could be attributed to the following: 1) The effective charges of the proton and neutron may be smaller than expected in this case. This is a reasonable possibility, and is sufficient to account for most of the observed differences. 2) Configuration mixing may be taking place in the 7/2_ and 11/2- states, with contributions from a Qp3/2)2 configuration. Transi- tions from the pure f7/2, 19/2- state to these configuration-mixed states are sufficient to explain the differences between the experimental values and those we calculated. This last possibility is quite intriguing, since it offers a way to demonstrate the concept of configuration mixing. The three-particle isomeric state is, of course, a pure f7/2 configuration. 0n the other hand, it is quite possible that the other states are configuration mixed -most likely with a (193/2)2 component. This rather unusual situation provides a rare opportunity to check the configuration-mixing theory directly. We are now preparing to carry out a series of shell model calculations in which we will determine the transition probability of decays going to such configuration-mixed states. If these calculations reproduce the observed values, a significant step 111 demonstrating the concept of configuration mixing will have been made. CHAPTER VI THE DECAY OF “03c 6.1 Introduction The y-ray spectrum associated with the decay of ”08c was first studied by Class and Richardson in 1955 (Gla55). “08c was produced by the “0Ca(p,n)“°Sc reaction using 20-MeV protons on a natural calcium foil. Only one y ray, of energy 3.75:0.04 MeV, was attributed to the decay of “08c. Since this first investigation, many studies have been performed in order to determine the levels in “OCa populated by 1”SC. The fact that “08c is a doubly-closed shell nucleus (N=20, Z=20), has motivated much of the interest in this isotope. The bulk of the available in- formation on the levels in ”OCa has been obtained through scattering experiments (Bra56), (End67), (Ers66), (Gra65), (Spr65). Although some earlier y-ray work has been performed on the “08c decay (And66), Arm68), (Kas68), the rather short half-life of this isotope and the high energy of its y rays have hindered precise y-ray investigations of the levels in ”003 populated by its disintegration. However, with the advent of improved "slow"-pulsing techniques for the MSU Cyclotron and good on-line detection systems, it has now been possible to study the y decay of ”08c with a relatively high degree of accuracy. 213 214 6.2 Target Preparation For these on-line, pulsed-beam experiments, several kinds of targets were tried in attempts to reduce the background of unwanted y rays. Early targets consisted of slurries of CaCO3 (both natural and isotopically enriched) prepared in polystyrene or Duco cement binders on thin mylar foils. Later experiments utilized natural calcium metal targets. However, good results were not obtained until a 2-mg/cm2, 99.9732 isotopically-enriched “OCa foil, prepared at the Oak Ridge National Laboratory, became available from Dr. C. R. Gruhn. Originally the target was mounted in an Argon atmosphere and since has been maintained in a target storage chamber which is evacuated to a vacuum of the order of 5x10’5mm by an absorption pumping system. Transfer of the target to various experimental setups was accomplished by a vacuum-transfer lock assembly designed by K. Thompson (Tho69) and C. Maggiore (Mag70) (see section 2.3.3). Thus, the target has not been exposed to air. The amounts of contamination in the target due to oxidation and condensation of pump oil were obtained from elastic scattering data by T. Kuo (Kuo70). It was found that the thickness of oxygen was about 0.019:0.002 mg/cmz; carbon, 0.0026:0.003 mg/cmz; and hydrogen, 0.0017+0.0002 mg/cmz. A small amount of fluorine was also observed but not measured. The isotopic and Spectrographic analysis supplied by ORNL is listed in Table 6-1. The ”08c activity was produced by the 1+0Ca(p,n)'*°Sc reaction, using a 24-MeV proton beam from the MSU cyclotron. Typically, the 215 Table 6-1 Isotopic and Spectrographic Analysis* of 1”Ca Target Used in This Study Isotopic Analysis Spectrographic Analysis 40Ca 42Ca “3C3 cha ”6C3 “8C3 99.9732 0.008 0.001 0.018 <0.001 0.001 A1 Ba Co Cr Cu Fe Li M8 <0. <0 <0. <0. <0. <0. <0. <0. <0. <0. <0. <0. 02% .05 01 02 05 05 05 02 01 01 05 02 Mo Na Ni Pb Pt Rb Si Sn Sr Ti V Zr <0.05% 0. <0. <0. <0. <0. <0. <0. 0. <0. <0. <0. 01 05 05 05 02 05 05 02 02 02 l *Supplied by Oak Ridge National Laboratory. 216 foil was bombarded with a 10-nA beam for 20.4 sec per pulsed interval. For an experiment utilizing the helium-jet thermalizer, an evaporated, self-supporting foil (:1 mg/cmz) of natural calcium was prepared. The recoils were produced by a 200-nA beam of 24-MeV protons over a period of 15 hours. Severe deterioration of the foil was noted at the end of the thermalizer experiment, with almost complete oxidation of the foil having taken place. 217 6.3 y-Ray Spectra The most valuable experiments performed in this investigation utilized pulsed-beam, routing techniques accomplished with the aid of the routing timer module described in section 2.2.1A. Although various Ge(Li) detectors were used throughout the study, the best results were obtained with a 2.52 detector, having a resolution of 2.2 keV and a peak-to-Compton ratio of 16.5:1. The activations were carried out in the vacuum-transfer chamber, with the target plane inclined 45° to the beam. The detector viewed the target through a 1/2-mil Kapton window at 90° to the beam. The target-to-detector distance was about two inches. The resulting y-ray pulses were amplified and then sorted in a 50-MHz, 13 bit analog-to-digital converter (ADC) connected on line to the Laboratory's XDS Sigma 7 computer. Usually, one 4096- channel Spectrum containing the beam-on data and four successive 4096- channel spectra from the beam-off period were routed into the computer under program HYDRA. Four beam-off routed spectra from this study are shown in Figure 6-1. These resulted from a 32-hour accumulation of data in the slow-pulsing mode. In this particular experiment, a beam-on time of 0.40 sec and a beam-off period of 0.60 sec per pulse were used. The beam-off period was divided into four equal counting intervals of 0.15 sec each. No inhibition period was used between the end of a beam burst and the beginning of the first routed spectrum. Consequently, the first spectrum shown in Figure 6-1 shows the "washed- out" effect resulting from some beam-on spillover. Based on the half—lives of the transitions and comparison with scattering data, at least seven y rays were found to belong to the decay of ”08c. The energies and 218 I 000w H 00mm H _ 1 .omo: mo scoop osu scum muuoomm >muu> vousou .muouamom 50232 $224.10 coon 88 88 con. 3 _ _ H .H-s ..awwa 000. 0380-900 oommv.0-0m.0u 0 03000 - 9.0... m 8m 90.00.03. 000 H Him H. 1H I, 61. I I . ...; m as a . I 96 b .c_.9 P. 2 1 as C. .v c. ”v .V r .1? H _ _ 01 L H 1 L 1 9 09 83:! SlNflOf) "’2 'BNNVHO 219 intensities of these y rays are given in Table 6-2. The relatively thin natural calcium target and its rapid deteriora- tion in impure helium severely limited the l‘OSc thermalizer experi- ment. Because of the success with pulsed-beam techniques, no further thermalizer runs were performed in the “08c study. 220 Table 6-2 y-Ray Energies and Intensities from the Decay of 1+OSc Energy (keV) Relative Intensity 754.4:0.2 4813 1121.4iO.6 13:2 1875.5:0.5 25:2 2043.6:0.3 27:3 3166.4:0.6 14:2 3736.9:0.7 3100 3919.511.0 10:2 221 6.4 Proposed Decay Scheme The seven y rays attributed to the decay of “08c were fitted into a consistent decay scheme, as shown in Figure 6-2. The transition intensities, level energies and B+-feeding information were obtained from this study. The 1+0Sc half-life was taken from the work of Armini, et al. (Arm68). The number of y transitions observed in this study and their placement in the decay scheme coincides with previous results (And66), (Arm68), (Kas68). However, the energy assignments of the observed Y rays are different from earlier work by as much as 8 keV, leading to somewhat different energy assignments for the level spacings. The measured intensities are generally in agreement with previous experiments. The results of this study are listed along with those from previous investigations in Table 6-3. 222 4°80 2| l9 4- In'OUB3s. BO 3 Q :1: E 4- 5.66 51% (3.48) 'Z7T) H95 «[74) 4- E183 2T% GL7?) 56'” ass 17% (4.75) 4491.3 8%: 37365? " 0 0’ 4°00 20 Figure 6-2. Proposed decay scheme for l+OSc. 2223 Amemaxvu Hmeaaava Hoseaavm NHOH o.HHn.mHom nJOHH.H~mm HHHH H.Num.n~mm m.~uo.NH noo.uon.m ooH n.0nm.omum n.0um.omnm HuooH H.~nn.chm 0.00H coo.uomn.m mneH o.oue.och «.0Ho.non man H.~uH.H~Hm o.~no.mH so.“ mH.m manm m.ouo.mvo~ n.oHa.cao~ mwam N.mun.wao~ o.Nno.- No.“ No.N Nwmm m.oHn.man n.0no.nan mumm m.~u~.ommH o.Num.¢~ No.“ mw.H NHMH o.owe.H~HH n.ou~.H~HH NNNH m.~n~.mNHH o.~uo.n no.“ HH.H name ~.0ne.emu c.0no.emn «nee m.~uo.mm~ o.owo.He Ho.“ mn.o AuvsuauaouaH >6: .H»Vm >6; .H»Vm HRVHUHmaaueH >63 .H»Vm HNVsuHmcuuaH >6: .H>vm xuos usomoum oo>ouwHosmmhsmmM n.Hm um HsHau< m.Hm no comuovs< xuoz msoH>mum Boom muHsmom mic oHQMH onu :uHs moumaaoo cOHummHumo>sH mHAH Eouu moHuHmswusH was monumcm >mmn> omo: 224 6.5 Discussion Although this investigation did not reveal additional Y rays associated with the decay of 1+0Sc, it did provide a basis for narrowing down the exact energies and intensities of these transitions. For example, the excitation energy of the first T=1 analog state of “OCa has been reported recently in the range of 7669.1 keV (Arm68) to 7658.9 keV (Kas68). Our measurements indicate that the lower value is the true one. Likewise, other level assignments in ”OCa decay scheme were assigned more positively as a result of this study. Many types of model calculations have been performed in attempts to describe the 1+0Ca nucleus. One of the more successful of these is the rather extensive intermediate-coupling shell-model calculation performed by Kunz (Kun66). The results of this calculation are compared with current experimental values in Table 6-4. The agreement is reasonably good, although the predicted 4- level at 6.5 MeV is presumably the observed 5612.7-keV level. A spin and parity of 4- have been reported for this level (Gra66). 225 Table 6-4 Comparison of the Experimental Results of “08c with Intermediate430upling Shelldflodel Calculationsa B Decay " “OCa Energy Level log ft Branching Ratio I Expt.(keV) Theory(MeV) Expt. Theory Expt. Theory 4‘ 7656.3 7.62(4’) 3.48:0.15 3.27 5111 52 6.9 3’) 4.49 6 4‘ 5612.7 6.58(4“) 4.74:0.12 4.44 1111 10 5' 4491.3 4.13(5") 4.77:0.10 4.59 21:1 21 3‘ 3736.9 3.80(3’) 4.75:0.08 5.14 17:1 8 a(K6666) CHAPTER VII THE DECAY OF 53mCo 7.1 Introduction The discovery of a high-spin, three-quasiparticle metastable state in the 53Fe nucleus has prompted the search for analogous states in nuclei having similar configurations. One of the most promising cases for comparison with the 53Fe structure is the nucleus 53Co. However, until quite recently, no evidence was available to support the existence of this nuclide or its possible metastable state. Since the structure 0f 53(3o differs from 53Fe only in that it has a pair of neutron holes and a single proton hole outside the N=28, Z=28 doubly-closed shell inatead of a pair of proton holes and a single neutron hole, one would expect the level schemes of the two nuclei to be very similar. An early search by Eskola for the 53Co metastable state yielded negative results for possible states with half-lives greater than 15 sec (Esk67). Ho"Fever, one would expect a relatively short half-life for 53mCo since the 19/2‘ state can decay via a super-allowed 8+ transition to the isobaric analogue state in 53mFe. Therefore, a search was initiated to look for Y I‘ays that could be attributed to the decay of 53mCo. This effort Utilized various pulsed-beam and helium-jet thermalizer techniques developed for examining short-lived species. 226 227 7.2 Target Preparation All of our attempts to produce 53mCo were made using the 51+Fe (p,2n)53Co reaction induced by 30-40-MeV protons from the MSU cyclotron. Early pulsed-beam experiments were performed with isotopically separated 51+Fe in the form of Fe203. The oxide was mixed in a polystyrene binder and mounted on l/4-mil mylar backings in target frames. Later in-beam and thermalizer runs utilized a 1.02 mg/cmz, 97.42 enriched self-supporting 5“Fe foil. The major isotopic contaminant in this foil was 56Fe which was present in the amount of 2.21 atomic percent. The Q-value for the 5L‘Fe(p,2n)53Co reaction was calculated to be -22.8 MeV. The threshold for the next higher reaction, i.e., (p,3n) was also calculated and found to be -39.2 MeV (Mye65). In a separate study of possible proton radioactivity from 53’"Co, Cerny et al. report an excitation function for producing S3mCo by the Sl*Fe(p,2n) reaction (Cer70). This graph is reproduced in Figure 7-1. All of our experiments were carried out at proton energies of 30 to 40 MeV -- coinciding well with the peak region reported in the excitation function shown in Figure 7~l. Typical beam currents for pulsed-beam experiments were 0.5-10.0 nA depending upon the target and detector used. The helium-jet thermalizer runs utilized a beam current of :1 0A on the l mg/cm2 foil to produce reasonable count rates from the transported recoils. IOOO IOO IO Relative cross section 228 " I I +— I I I _— i _ I i' O i 1 . . . 25 3O 35 4O 45 Born b0 rding energy (MeV) Figure 7-1. Excitation function for the 51*Fe(p,2n)53mCo reaction reported by Cerny, et al. (Cer70). 229 7.3 Experimental Results 7.3.1 Proton Decay Before proceeding with a description of the y-ray spectra obtained in this study, I would like to review briefly the results reported by Cerny et al. regarding the possible proton decay of 53’"Co (Jac70), (Cer70). In the course of searching for beta-delayed protons from 53Ni produced by the “OCa(150,3n) reaction, Jackson et a1. observed a 1.53:0.04- MeV proton activity with a 245:20-msec half—life which subsequently was attributed to the proton radioactivity of 53”’Co (Jac70). However, this experiment could not rule out the possibility that the isomer decayed by beta-delayed proton emission. Later experiments utilizing proton? induced reactions on St*Fe produced a proton activity with a threshold of 26.3:0.4 MeV which was assigned to 53"700 (Cer70). The direct proton radioactivity of the isomer was established by failure to detect positron- proton coincidences in the decay. The values for the proton energy and half-life were found to be 1.57:0.03 MeV and 242115 msec, respectively. The observed half-life implies that the dominant mode of decay is by positron emission to 53"'Fe, with the proton emission constituting only a weak branch in the decay of 53’"Co. The partial half-life for the Fermi component of the super-allowed 8+4decay was calculated to be 0.35 sec (Fre66). Inclusion of the Gamow—Teller matrix element (assuming pure (f7/2)-3 configurations), yields a predicted half-life of 0.2 sec (deS63b) -- in agreement with the observed value. 7.3.2 yrRay Spectra The primary objective of this investigation was to search for a y—ray branch in the decay of 53’"Co. Two techniques were employed in 230 this effort. First, pulsed-beam, routing methods were used to look for short-lived species and to assign relative half-lives to those observed. Second, a helium-jet thermalizer system was utilized to obtain good statistics in a low-background counting area in order to detect very weak, short-lived y rays. Since Eskola's work placed an upper limit of 15 sec on the half-life of 53”’Co, our early pulsed-beam experiments were aimed at quite short half-lives -- with routing intervals of 0.5-0.10 sec (Esk67). The subsequent report of a 53""Co proton activity attributed a half-life of 0.242:0.015 sec to the isomer (Cer70). Consequently, routing intervals of :0.17 sec each were used to optimize the possibility of detecting and verifying y-ray half-lives similar to that reported for 53”’Co. The most effective of the pulsed-beam experiments utilized the separated isotope 51+Fe foil described above and a 2.52-efficient Ge(Li) detector. A representative set of beam-off, routed spectra from this study are shown in Figure 7-2. These four spectra contain the data obtained in four consecutive 0.17-sec intervals following a beam-on period of 0.45 sec per cycle -- no inhibition period was used. The total accumulation time for this experiment was 3.0 hr. Most of the peaks in Figure 7-2 have been labeled with their approxi- mate energies. Some known contaminants and side-products also have been labeled. During this phase of the 53"’Co search, ten separate pulsed- beam experiments were carried out over a period of several months -- some of which contained better statistics and more peaks than those shown. However, based on the energies and approximate half-lives observed, no y ray could be assigned positively to the decay of 53’"Co. The 5“Fe foil again was utilized in the helium-jet thermalizer system. The foil was bombarded with 30-35-MeV protons and the resulting COUNTS PER CHRNNEL 231 .. 5”"‘Co SEARCH )5 . «'33 % Pulsed Beam FT)/£| A = 0.00-O.l7$ec. -. E; '2 8?; a: B = 0!? - 0.34sec N a; E; £1- 0 = 0.34 - O.5l sec. -. Q; a - e ,2 0 = 0.5: - 0.68sec 1;: 91%| 4': ~. + ' I T) e g N I l S 10 2 10” 4- 3m 1 C) q [3 102“ llilllllll III II 1 r*\\\\¢ 10 x C 100+ IIIIII I I III ‘ D . 1 11 .1 11,1 .4.— 1000 2000 3000 L+000 CHHNNEL NUMBER Figure 7-2. Four routed beam-off spectra from the 53”'Co search using the "slow-pulsing" technique. 232 recoils were thermalized in helium and piped up to a fixed collector on the roof of the cyclotron vault. Under these relatively low background conditions, a 10.42 Ge(Li) detector was used to observe the y rays associated with the recoils. Since the mechanism for moving the collecting surface was not operational when these spectra were taken, some peaks due to the buildup of long-lived species were present. An example of such a spectrum is shown in Figure 7-3. This spectrum represents a total accumulation time of 11.5 hr. Note the greatly improved statistics as compared with the pulsed-beam runs. Although significant amounts of 53”H'gFe are present in this spectrum, one cannot conclude merely from the observation of 53”MgFe gamma rays that he has produced its S3”HgCo analogue since the threshold for the 5“Fe(p,pn)m+gFe reaction (13.6 MeV) is lower than the threshold for the 5l‘Fe(p,2n)53Ca reaction (22.8 MeV). The situation also is hampered by the fact that the thermalizer beam entrance window is constructed of thin Havar -- containing natural iron and thus contributing recoil contamination. Although the 53mCo thermalizer spectra contain several unidentified y rays, it has not been possible to attribute them definitely to the decay of 53'"Co or establish any sort of decay scheme. 2533 .asvuanaou uaNHHasuonu unnusaHHan asu ucha sauna. 00:5m onu scum suuuoaao uoHuaHu aqua» .muh ”Lamas mwmzaz JmZZQIQ coo: oobm opom opal .r 1 1 1 OH: 1.. OH H 1. DH N m .. OH 1.. m mm. __8 L F... -1 OH 1 m mm mm 1. a m. a .- H: ...—W Wm. "am HF ./ - .... memes _ m M15211 we ... _.Ww .mmm WWW .w mu _nr “w flu #H ngccomk 67m: m 4. we. mm an ace: 862m W 1 .. 6 1:50 H Ismamm 8.... VSLI WENNUHCJ 83d 81N003 234 7.4 Discussion The facts currently known about the modes of decay of 5377Co are illustrated in Figure 7-4. The values for the half-life and proton decay are from the work of Cerny et al. (Cer70). The calculated ground state and predicted levels which could be populated by a y-decay branch also are indicated. If one assumes that the structure of 53"'Co is exactly analogous to the 53"Fe case including a 2.5~m y-decay half-life, and further assumes that .242 sec is the correct overall half—life, then a y/B+ branching ratio of only about 1:500 would be expected for the 53"7C0 decay. If these conditions prevailed, the discovery of a y-decay branch in 53’"Co by the present techniques would be most unlikely, since the lower limit of detection for the 8+/y ratio is about 1:10 using these methods. However, any enhancement of the y decay de-exciting the isomeric level would bring the y-ray portion of the branching ratio closer to the limits of detection. For example, if the 15/2' level were to occur below the 19/2' level in 53"'Co, the E2 y ray de-exciting the isomeric level would compete very favorably with 8+ decay. Thus, one cannot rule out the possibility of observing a y—decay branch in the 53”’Co decay. One somewhat anomalous feature was noted in several pulsed-beam experiments. Although over 99% of the 53mCo is presumed to 8+ decay to 53"’Fe, several cases were found in which no significant amount of 53mFe activity was recorded. These were all cases in which the target, beam energy, beam alignment, etc. were chosen carefully to optimize the production of 53”’Co. On the other hand, all experiments revealed relatively large amounts of S3gFe and 52Fe. Since S3mFe was not present in the 235 53n1 27C026 9/2-) "'46 {0:242:15ms (' ___________ 10.75 2+ 9.\_ , ____________ 90 52F O + 26 e26 p (8.30) (7/2') 539 270026 3m 26Fez7 3.04 2.6m 19/2- 2.540 Iva- I328 9/2- 0 ’ 7/2- 539% 8.5m 26 27 ’3 '6 Figure7-4. Proposed decay scheme for 53mCo showing the known modes of decay for the isomer. 236 expected amounts, it would appear as if either 53mCo was not being produced in large amounts, or other decay modes were dominant. Although this study could not provide positive assignment of y rays to a y-decay branch in 53mCo, it did provide a number of unidentified possibilities. For the benefit of those who also may wish to investigate the 53'"Co structure, I have provided a comprehensive listing of all the y rays observed in this investigation in Appendix C. CHAPTER VIII THE SEARCH FOR 3-PARTICLE ISOMERIC STATES IN “3T1 AND L‘33c 8.1 Introduction High-spin, three-particle metastable states analogous to that discovered in 53Fe also may exist in 1+3T1 and l+38c. “3T1 is of course the particle conjugate of the 53Fe nucleus, and l‘3Sc is the particle conjugate of 53Co. The large decay energy of 1+3Ti and the possibility of the decay of its l9/2' state by a super-allowed 8+ transition to the 19/2' state of l‘3Sc implies that the half-life of the state is shorter than 1 sec. 0n the other hand, the 19/2- state of ”38c should be similar to the 53Fe case. Preliminary experiments were performed on both ”3T1 and 1+3Sc, but were limited to y-ray activities with half-lives greater than 15 sec (Esk67). This study was undertaken in an attempt to establish possible y-ray activities associated with the decay of 1”Ti or “33c. 237 238 8.2 Target Preparation Because of the availability of target material, most of the experi- ments in this search have utilized the 1+53c(p,3n)‘*3Ti reaction using 35-MeV protons from the MSU cyclotron. Since scandium is monoisotopic, the preparation of a suitable target was quite straightforward. Small pellets of purified scandium metal from A.D.MacKay, Inc., were hydraulically pressed into disks approximately 1 cm in diameter and 1 mm thick. Each disk was suspended in a target frame by thin mylar strips and used in the standard irradiation chambers. Typical beam currents were 0.5 - 10.0 nA for most on-line experiments. The above reaction affords both the possibility of observing y rays from the de-excitation of 1+3”’Ti directly or from the de-excitation resulting after a super-allowed 8+ transition to the analogous level in 1+3"78c. Since the cross section for the ”58c(p,2np)”3Sc reaction is expected to be quite significant, one would also anticipate the formation of “3mSc directly by this route. Another type of experiment was performed in which a helium-jet thermalizer was employed to look for “3mSc. The target for this experiment was a thin (20.5 mg/cmz) layer of isotopically separated “”Ca evaporated onto a tantalum backing (the target was mounted with the tantalum side facing the beam -- thus allowing the tantalum produced recoils to be trapped in the calcium, while the calcium produced recoils left the target and were thermalized.). A beam of 24-MeV protons was used to produce the “38c by the “”Ca(p,2n)“38c reaction. A beam current of :1 uA was utilized to produce the recoils. After being thermalized in helium, the recoils 'were transported through a polyethylene capillary to a collector and counting facility on the roof of the cyclotron vault. Due to the transit 239 time in the capillary, this method was limited to detecting activities with half-lives greater than a few tens of msec. 240 8.3 yrRay Spectra Most of the experiments performed in this study made use of the "slow-pulsing" technique to look for half-lives in the 10-1000 msec range. In these experiments, the cyclotron was pulsed by RF modulation, such that the activity was produced by beam bursts of about 1-2 sec duration and then counted in 4 successive, routed, beam—off spectra of about 100-600 msec each. A spectrum of the beam-on period also was obtained. A typical set of beam-off spectra from this type of experiment is shown in Figure 8-1. Peaks which have been reported as belonging to l"38c are labeled where appropriate. Since beam pulsing in the usec range was unavailable, an attempt was made to examine possible transitions in the nsec range -- thus bracketing the usec region. This was achieved by routing y spectra in the time intervals between the microscopic structure of the cyclotron beam. This period is about 50-60 nsec, depending on the beam energy. The spectra shown in Figure 8-2 are from such an experiment. Spectrum A is the beam-on data, representing the 19.8 nsec per pulse during which the beam was on target. (This period is dependent on the phase width.) Spectra B through E are the 4-8.5-nsec beam-off intervals following each RF bunch. These spectra contain many more peaks than found with the "slow-pulsing" technique, but are very useful in establishing lower limits for possible half-lives. A few representative scandium lines have been labeled for reference in Figure 8-2. The helium-jet thermalizer experiment utilizing the ““Ca target [did not reveal significant amounts of known scandium y rays. Because of the successful acquisition of data with pulsed-beam techniques, additional COUNTS PER CHRNNEL 241 43"‘Ti ,‘3"‘Sc SEARCH fimwflkniflwmdSmmm Four beam-off routed spectra from the “’“r1, 7?. '3: 5;; £16“ 3‘ HE”. ~ 5 A . W £ 7 B 8 EA =° ...? C ‘ 9‘82; as D . 3:: {\M ' l T s 10-- q 10~ 3 10~~ 2 10 .4. 1 10* o 10 v 1000 2000 Figure 8-1. l’3’7’Sc search using the "slow-pulsing" technique. 0.00 - O.|7 sec. O.l7 - 0.345ec. 0.34 - 0.5! sec. 0.5l - 0.685ec. 8 MIL .31.. NW 3000 ‘ iMlM #000 COUNTS PER CHRNNEL 242 Id Id Id 10%- ' J M A a 4 .Is 3,; ”11.3% SEARCH '53.. '3 A = BEAM-ON. use nsec. ‘3 3 {L A B= O-85mm. / «'3 .7, 8 38‘ .. z . c . 8.5-I7.0 nsec. a n . L L , 5 § 8 o = I7.0-25.5nsec. k I _ 9 I . E = 25.5-34.0nsec. “N E , , ' IMIIHIIIIIIII “III I I 10:00 2600 3000 l+000 CHRNNEL NUMBER Figure 8—2. Routed spectra from the “mTi, l‘3'”8c search utilizing the microscopic structure of the cyclotron beam for timing. 1 fi 243 thermalizer experiments were discontinued. All of the methods described above utilized large high-resolution Ge(Li) detectors having efficiencies of 2.5-10.4% compared with a 3X3-in. NaI crystal at 25 cm. The isomeric level in ”38c has been tentatively identified by other workers. Iordahescu reported the existence of two short-lived species in this region when performing a survey of a particles of 17.2-20.0 MeV on a number of thick natural targets (Ior68). With a potassium target, a y activity with an energy of 154 keV and a half-life of 456 usec was reported. With a calcium target, a Y ray with an energy of 163 keV and a half-life of 450 usec was found. More recently Sawa and Bergstrfim have reported a y-decay scheme for “3mSc (Ann70). This level scheme is shown in Figure 8-3. The isomeric transition they report is an E2 with an energy of 136 keV and a half-life of 0.5 usec. It appears that the 15/2- state has crossed below the 19/2- level, resulting in a much 5 37771?8 shorter half-life than one would expect from comparison with the conjugate configuration. 244 43mS 2| C22 T =o5: ows 3.23 ———r"2 I9/2- 2.987 T I5/2- |.83O I T— Il/2" 0 2 7/2' 439 ZISCZZ Figure 8-3. Proposed decay scheme for ”MISC reported by Sawa and Bergstrbm (Ann70). 245 8.4 Discussion In our present study, we have observed all the y rays reported by Sawa and Bergstrbm, including the 136-keV transition. However, the assignment of these y rays to a decay scheme for l‘3"Sc has not been attempted, since a number of problems exist which are difficult to reconcile with our data. If the isomeric transition decays with a half-life of about 0.5 usec, then one would expect the y rays in the resultant cascade to follow a similar half-life. However, our pulsed-beam measurements indicate a much longer (>2 sec) half-life for the 1157-keV (15/2 + ll/2) transition. Indeed, the assignment of this y ray to the ”3"Sc decay scheme is ambiguous, since the reactions used to produce “33c also make ““Sc, the decay of which contains a strong y ray at almost the same energy (1156 keV). Using our method of bracketing the usec half-life range, we have found several y rays which fall into the correct lifetime range. However, because of the lack of energy sums and crossovers, it is not obvious that one can construct a completely unambiguous decay scheme for “y"Sc. The rather extensive study of the low-lying states in 1+38c by Ball, et a1. provides a few states which could belong to the isomer decay cascade. Nevertheless, the positive assignment of y rays and the establishment of a decay scheme for ”3mSc is extremely tedious based on the currently available data. The relatively large number of side products from unwanted reactions and contaminants, coupled with the rather weak y-rays expected from de- excitation of possible isomeric states makes the detection and assignment of these unknown y rays very difficult. By comparison with the 53"’7Co — ‘53"Fe case, one would expect any possible y-decay branch in ”3mTi to be quite weak with the dominant mode of decay being the super-allowed 8+ decay to “3'"Sc . 246 Although no definite decay schemes for ”3mTi and ”3mSc could be established as a result of this study, several unidentified y rays were observed which might be associated with the decay of the isomers. At the present time there is no definite evidence to support the existence of ”3mm. A comprehensive table of all y rays observed in the ”3mTi, “y"Sc search is given in Appendix D. Ill-l7 ill“ 247 IX. SUMMARY AND CONCLUSIONS Viewed in retrospect the rather diverse series of studies which constitute this thesis presents many interesting facets -- both from an experimental and a theoretical standpoint. Although they do not contain a "wealth" of information in the sense of establishing dozens of new levels, each segment of the study provides some insight into the nuclear problem. The establishment of new levels in 53Mn populated by the 8+ decay of 53Fe provides not only additional knowledge of these states, but allows further testing of the simple shell model. deShalit has pointed out that the N=28 closed shell is particularly stable and therefore much less subject to configuration mixing than N=20 (de863a). Thus, the 53Mn nucleus with 28 neutrons and 25 protons provides an excellent example for the study of the (lf7/2)-3 proton configuration. Likewise, the elucidation of a metastable state in 53Fe has provoked considerable interest -- both experimental and theoretical. Experimentally, the direct observation of y—ray transitions having multi— polarities of E6 and M5, the highest ever observed, was most exciting. Since the metastable state has a spin of 19/2, the highest that can result from the three-quasiparticle configuration [(nf7/2)—2]6+(vf7/2)_1, its character is expected to be almost pure ffi/z. Therefore, transitions from this state and their measured rates have profound implications for testing concepts of the shell model theory. For example, since decays from this relatively pure state lead to states which may be highly configuration mixed, a rare opportunity is provided for direct testing Of the concept of configuration mixing. Results obtained from this study also have suggested that perhaps the proton and neutron effective charges 248 are smaller than expected in this region. Switching to the “OCa double-closed shell region, a comprehensive study was made to determine the levels populated by the decay of “08c. Although no new levels were established as a result of this effort, significant improvement was realized in the exact energy of the “OCa levels. Experimentally, this study was used to develop and utilize on-line,pulsed- beam techniques for studying short-lived species. Since both the levels in “OCa and the 8+ decay to them are well characterized, a good opportunity exists to backtrack and describe the “08c structure and wavefunction in some detail. The unexpected discovery of an isomeric state in 53Fe turned the course of this investigation toward a search for similar states in nuclei having analogous configurations. 53Co and the particle conjugates “3T1 and l*3Sc were chosen as the most likely candidates for having similar three-particle isomeric states. A comprehensive search for y-ray activity from possible metastable states in these nuclei was carried out using various experimental techniques developed for short-lived species. After an exhaustive search, very little evidence was found to support the existence of such states. However, since other modes of decay have been demonstrated for at least one of these (Cer70), their existence is not ruled out. There is some evidence that in 1+38c the level structure has shifted so that the half-life is very short with an E2 transition de-exciting the metastable level (Ann70). Although the goal of revealing isomeric states in these nuclei was not achieved, this facet of the investigation should not be deemed as unworthwhile. Having eliminated this avenue of inquiry narrows down the choice of approaches to the problem. Also, the results found here may be quite useful in criticizing or confirming other data. 249 In addition to the nuclei actually investigated, this study has suggested several other species which would be natural extensions of this work. The nucleus 39Sc is not known, although it is quite interesting from both a theoretical and an experimental viewpoint. The use of on-line, pulsed-beam techniques should be very helpful in establishing its existence and possibly a level scheme. Another very interesting case is 51Fe which also is not known. Knowledge of this structure would be very helpful for comparison with the 53Fe data. A survey of other nuclei in this region to search for additional metastable states would be relatively simple and is certainly worth considering. Extension of on-line, pulsed-beam techniques to short-lived species in other regions of interest presents many pos- sibilities for meaningful research. Although the data presented in this thesis do not by themselves provide an answer to fundamental questions in the nuclear problem, it is hoped that they constitute a small, but significant addition to the total body of knowledge regarding nuclear structure. BIBLIOGRAPHY (Abr67) (And66) (Ann70) (Arm68) (Arn64) (Aub66) (Aub67) (Aue64) (Aue64a) (Aue67) (Bal70) (BalJB) 250 BIBLIOGRAPHY M. Abramowitz and I. 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APPENDICES 260 APPENDIX A FERMPLOT FORTRAN Listigg asuon+~cu+muz x 30.nmde.~< .wsa-‘.H.m4»~».~m0a wzumd znzu>.oom anaa .uwmz./3mz.zaxuz.>>v cameo Jn> 2m4a .mz~<\m2\zozzou >~x~> zonmzmzao ~x zouwuuuad wmmnoo ween» wsn> muouhz~ eonazmmu zw4~an~ OMa co 7 ) rm mm0m>.u»aum..~.mma {\330..«ozss.\.H333033v.uhmommonn ZDu mz.oas? m.unxm...ozx doozx.» ozx<0ox n\320N .ac73¢33.u»momuu >03033 omfl am 6'. r4 0 Ch maa 00 me so no «0 00 mm um um om mm am mm mm om me w: n: o: m: s: n: N: «a 0: mm on an mm :m mm 262 ax<.m.axuo\a><+.x<+fi.¢.x<+ae.u ooze 2\>.>< 2xxux< «.2 .xs»m~.axmo¢.>s>+xsxvuo oomnmanm..m. emN >.x.<.x<.m.ooma..x zonmnumea unmnoo omoauzma .. m . o .0 ...mx» ..ofiH..m4mzz< unocu~o+nzammozam .n.wmeu.n.unm4 7u~Iu~ooz~>uJH . z.<7.z~ . . .m.o<.n<.qhnmo.<2z<\mzxzozzmu m x o u .am0a.unau..:mo«.wua zoawzuzuu mxommqaxusx>msvxu.o..>m4v10.u+m..>m4 .zm flexed-..>m4v1u fi+>mna>m4 oom o» co oozx.<»mm.fi<.>mo. a” ..~+uz.<7.\>uo.n»aomu>uo >mn+u~osu~ou>mo .1.mmm..w.unmo o.m4a .mz.<\mzxzozzou .onczu..om.zu..sm0a.mma...~o«eus(u zoamzuzao «000010 mzaeooamam com If; 0 (U mom 00m «mnemonwm 265 APPENDIX B _Inpu; Instructions for the 0ak_§igg§ Shell Model dies .The following comments and format instructions pertain to the use of the Oak Ridge Shell Mbdel Codes as adapted for the XDS Sigma 7 computer at the Michigan State University Cyclotron Laboratory. These instructions were provided by Dr. B. H. Wildenthal. I have included them here both because of their benefit in helping one understand the shell model calculations and because of their practical value to others planning to perform such calculations. The basic input cards for the codes are distinguished by index numbers in columns 1-3. The different logical sections of the input are referred to by these index numbers, as well as by "description-of- function" names. Punch columns are indicated by bracketed superscript numbers. —+ 0(3) This is the Title card for a job. __, 1(3) usms (10) 010009) NSHELS is the number of active orbits in a calculation, e.g., if one uses the 1d5/2’ 231/2, and 1d3/2 orbits in a calculation, NSHELS - 3. _, 2(3) mac) “(20) :100) 1(40) (Etc.) There must be NSHELS 2-cards. ID is a 2-character nmemonic for a shell, e.g. D5 for 1d 2j is 2-times the angular momentum of a 5/2' particle in orbit ID. Enter +1 for an even-parity orbit, -1 for an odd- parity orbit. The order in which the 2-cards appear defines the shell 266 index order number, ISHEL, by which the program treats the various shells. These shells will henceforth be referenced as shell #1, shell #2, etc. This ordering of shells is sometimes important, because the available coefficient of fractional parentage tables are not always symmetric in particle coupling. The j - 5/2 shell should generally be shell #1. _.. 12(3) 2j(ISHEL)(6) ISHELU'O) nus) 2J (2°) 2T(25)...etc. i i i (Etc.) 12(3) -1(10) terminates section There must be a block (21) of 12-cards for each 2-card, occurring in the same order as the 2-cards. Each individual lZ-card describes a "single-shell wave function", that is, a proper antisymmetric combina- tion of n1 particles (each of angular momentum j) in shell ISHEL, coupled to total angular momentum, J1, total i-spin Ti’ etc. as needed to completely specify a unique state. The multi-shell, multiparticle, wave functions will be constructed by using the single-shell wave functions (SSWF) from the input as building blocks. Unless one specifically intends to truncate the model space by omitting lZ-cards, he should take care to use a complete set. These are available as library decks. If some single-shell combinations are missing, the program assumes that one wishes to truncate, and hence will proceed. 0n the other hand, it is inefficient to include many l2-cards which will not be used, e.g. if one has only 4 active particles, it is unnecessary to include j -.5/2 12-cards with ni > 4. -. 125(3) mm This card informs the program that you wish to construct a state (or states) with N active particles. 267 3) (20) (30) (10) ( ‘7 13 n(ISHEL-1) In(ISHEMZ) n(ISHEL'NSHELS) (Etc.) 13(3) 0(20) C(30) etc. terminates The l3-cards list the configurations (particle partitions over the NSHELS active orbits) that one wishes to include in (or by which he wishes to define) the space S. The limit on n can (ISHEL) either be Pauli-imposed or limited more strictly by the user. The 13- cards must be ordered so that the multiple-digit numbers n1n2°"nNSHELS increase in magnitude: (so-called "odometer" ordering) i.e., the first 13-cards should call for as many particles as possible in the last shell, as many as possible of the remainder in the next to last shell, etc. The individual cards of a given 13-card block must all have the same parity, that is, all cards must either have an even number of particles in odd-parity orbits (and hence have even parity) or all must have an odd number in odd-parity orbits (and hence have odd parity). The parity of an Neparticle state is thus defined implicitly. Different parity states of the same number of active particles require two separate 125-13-card sets. _. 14(3) 2.1(20) 21*(30) (Etc.) One then stacks as many 14-cards after the 13-cards as there are J-T combinations to be calculated for this number N of active particles. -+ 125(3) N'(20) loops back into a new 125-13—14 sequence. —+ 14(3) (-1)(20) terminates After a 125-13-14 set, one can either loop back to a new set 268 of 125-13-14 cards or terminate this section of the program input. After passing from the 125-13-14 section, the program proceeds to construct the multiparticle, multishell basis vectors for the states of NJT1r as requested. This process uses a combination of the information inputted by the 12-cards and via the 125-13 cards. Up to this point, all applications or versions of the shell model codes have identical input. Now, however, one must consider the operator, and depending on the form of the operator, there are different inputs. The eigenvalue-eigenvector problem will be treated first. (20) (30) .4. 21(3) N2bme NSHELS This card announces the number of two-body matrix elements (N2bme) which will follow and inputs a redundant (but very necessary) value of NSHELS. The number of two-body matrix elements is usually the maximum that can be constructed in the model space S, although in some cases, a subset of cards can be omitted. 28(3) ISHEL(a)(15) ISHEL(b)(20) ISHEL(c)(25) ISHEL(d)(30) 2J(35) 2T(“°) 2bme(65) There must be N2bme of these 28-cards. The ISHEL indices denote which set of orbits are used for this 2bme, <(papb)JT|H|(pcpd)JT>asym and J and T are the spin and i-spin of the coupled pairs. The value of the matrix element is entered as "2bme". The cards must be ordered such that the multiple-digit numbers ISHEL(a) ISHEL(b) ISHEL(c) ISHEL(d) 2J 2T occur in increasing magnitude. (10) (20) PFIL (SHELL#1)(15) SSMEFILE (30) -—+ 32(3) NSHELS PFIL (SHELLf2)(25) SSMEFILE PFIL SHELL#3)(35) SSMEFILE<40> etc. Card 32 informs the program where the NSHELS different coefficients of fractional parentage tables that will be needed to do the problem 269 are located. These are stored either on tape or disk and are all under one file number (SSMEFILE). Recent use has been with SSMEFILE - 8, but this is arbitrary. The SSMEFILE is multiple-filed. The PFIL (K) are the Pfil numbers needed to reach the desired SSME blocks (for shell K) from the start of the whole file, (i.e., the file is rewound after each "read"). The sequence of files is noted in the file name or on the tape label. The present order is 5/2, 1/2, 3/2, 7/2 max.T, 5/2 max.T. If shell #1 is 3/2, then PFIL (shell #1) 8 2, etc. __+ 33(3) Present instructions call for including this card, but leaving it blank. 34(3) .1 There should be NSHELS 34-cards, which should be left blank. _. 51‘” 1‘10) 522mm) 322mm) SPE(3)(‘°) etc. and/or —+ 52 These cards are for the input of one (use 52 if one) or more sets of single particle energies. For example: 1 - (1d SPE(1) a -4.15 5/2’ 2 - (291/2) SPE(Z) - -3.28 3 . (1d3/2) SPE(3) 8 +0.93 -9- 999(3) End of input Present files are used as follows: 8 - SSME 9 - Intermediate storage of H-matrix elements. 14 - Eigenvector output 15 - Storage of basis vector list 270 If the SMIT-tape option is used, File 14 will receive G- coefficients prior to eigenvectors. Other Qperators: All versions of the shell model code generate a list of N, J. T cases. This ordered list iS'always part of the output, such that in calling for the construction of operator matrices connecting different states in the list, one makes use of the order-number of the state concerned, i.e. he calls for a matrix connecting the "5th" state and the "9th" state. For Siggle Nucleon §ffactor: the Follow the "14" - "-1" card one needs to have: 21(3) ISHEL(IO) The 21-card indicates in which orbit a nucleon is to be created. program treats one j-transfer at a time. 1(3) (10) (5+lOXISHEL) (10+10XISHEL) 32(3) NSHELS PFIL(ISHEL)‘ SSMEFILE This is just like the Hamiltonian operator version, except that numbers for the specific orbit in question are to be listed. 33(3) blank card 0(3) blank card 40(3) N(left;final)(lo) N(right;initia1)(20) NCASES(2)(3°) NCASES(r)(4°) NSKIP(£)(50) NSKIP(r)(6o) “L(7O) nR<80) ETC. 40(3) (_1)(10) terminates The N (left and right) refer to the numbers of active particles in the left and right-hand (final and initial) states. The NCASES refer to the number of states in a left-hand or right-hand block. 271 For example, for a given state one might want to connect to several final states, or vice versa, or both. The NSKIP refer to how many states in the NJT list must be skipped in order to arrive at the desired state, left or right. The position after a 40-card is the sum of NCASES and NSKIP -- valid for "left" and "right" independently of each other. The various 40-cards are cumulative. The «'3 (:1) are the parities of the states. 52.5 61.7 72.0 83.5 90.3 99.1 122.3 129.9 138.4 147.2 153.2 159.7 168.9 173.5 183.6 196.6 203.3 217.4 241.6 276.5 320.5 356.2 368.3 272 APPENDIX C Energies 6£_y Rays Observed 16_the 53mCo Searchl' NA 377.9 L 396.1 B 411.7 NA 415.0 440.0 447.8 454.1 477.6 511.0 539.6 583.0 595.6 601.0 645.7 661.8 681.8 693.7 701.1 717.7 730.2 741.3 754.1 783.9 811.3 832.8 B B NA NA (keV) 835.3 843.9 846.4 852.3 866.6 870.1 888.5 909.8 922.4 931.1 934.9 954.5 961.5 984.0 990.0 1009.7 1011.5 1019.7 1026-0 1039.5 1074.6 1096.7 1112.1 1116.0 1125.3 1130.2 1157.0 1238.7 1246.8 1249.6 1275.0 1280.6 1312.8 1317.7 1328.2 1334.9 1362.7 1368.4 1377.8 1407.9 1433.7 1441.4 1461.0 1530.6 1607.9 1619.9 1633.6 1679.3 B NA L L L B L B NA NA NA NA NA 1712.8 L 1727.1 1731.5 1757.4 1779.6 1791.2 1807.0 1810.4 1820.0 1829.4 1880.6 1919.6 1944.8 1954.0 1992.9 2140.0 2167.8 2177.8 2209.8 2220.6 2243.5 2274.6 2313.5 2318.9 L L L L NA B NA NA NA NA L L NA NA NA NA NA NA 273 APPENDIX C - Continued 2339.7 L 2369.4 2540.2 2597.9 2603.5 2614.1 2750.7 3054.6 3098.9 3375.6 3404.0 3414.4 3447.1 4079.2 4214.6 4242.2 NA 1Each y-ray energy is accompanied by a symbol denoting its approximate half-life based on the experiments performed in this study. The meanings of these are as follows: S - short, t1/2 t1/2 > 0.1 sec long, t1/2 >10.0 sec not available, i.e., the experiment in which the y ray was seen did not include time discrimination. beam on, i.e., this y ray was observed only during beam-on intervals. The reader is cautioned not to interpret the beam-on designation as implying a short half-life. In most experiments the beam-on counting period was at least four times as long as each individual beamroff routed spectrum. 50.9 63.9 72.8 84.1 91.2 107.7 115.6 127.2 135.4 139.1 142.5 151.0 153.9 166.7 178.5 189.2 196.0 205.5 219.8 221.6 234.0 245.9 270.5 274.3 M 280.5 8 292.0 8 296.0 S 303.6 321.5 335.7 347.9 349.2 356.3 363.6 373.2 395.8 398.4 403.6 414.9 424.2 431.3 438.5 456.2 461.0 472.2 478.6 482.7 500.9 NA L 274 (keV) 511.0 530.5 542.7 566.1 571.5 593.2 607.8 610.8 618.1 628.7 657.6 663.0 667.8 671.1 683.8 696.5 699.4 723.2 727.0 745.6 758.4 761.4 769.2 772.3 APPENDIX D L NA NA S 812.2 816.7 827.3 830.4 836.8 841.9 844.8 ~ Energies of 1 Rays Observed in the “3’"Ti and “mSc Searches2 L B NA B L B L 846.4 L 850.3 857.6 869.6 872.3 878.9 884.4 890.4 911.5 926.5 932.1 936.1 960.0 975.0 984.6 990.4 1002.3 S S 1014.0 1022.3 1038.5 1050.8 1056.8 1069.9 1074.0 1083.1 1116.6 1125.6 1146.2 1157.9 1174.5 1183.3 1186.0 1209.8 1212.2 1228.8 1236.1 1239.3 1246.5 1259.7 1263.5 NA NA 1275.6 L Appendix D - Continued 1285.6 (M) 1291.9 B 1296.8 L 1313.2 L 1317.3 L 1325.3 B 1327.5 B 1333.6 L 1337.4 B 1362.6 NA 1369.8 L 1372.3 L 1378.3 L 1409.3 L 1413.6 NA 1435.7 L 1461.7 L 1468.6 B 1484.6 B 1493.4 NA 1500.1 L 1525.0 1: 1560.6 B 1575.8 NA 1591.6 L 1611.5 B 1642.7 B 1651.9 B 1657.7 NA 1662.1 B 1668.5 L 1676.3 B 1700.1 B 1729.8 L 1733.9 L 1758.4 L 1765.7 L 1771.8 L 1780.7 L 1791.7 NA 1803.0 B 1807.8 B 1828.6 B 1861.9 NA 1875.1 NA 1879.4 NA 1883.3 NA 1887.4 B 1902.3 B 1919.91» 275 1934.1.NA 1944.6 NA 1980.3 B 2034.0 NA 2093.8 B 2101.9 NA 2168.0NA 2178.9 B 2208.7 B 2222.6 B 2241.71: 2245.81. 2247.2 B 2313.2 L 2316.3 NA 2396.9 NA 2599.9 L 2615.0 L 2657.0 L 2741.6 B 2744.2 NA 2753.2 L 2756.3 L 3001.2 B 3124.5 NA 3194.8 NA 3254. 3 NA 3271.2 NA 3538.7 NA 4156.2 B 276 Appendix D - Continued 2Each y-ray energy is accompanied by a symbol denoting its approximate half-life based on the experiments performed in this study. The meanings of these are as follows: S 8 short, t1/2 <0.1 sec. M L NA medium, 10.0 sec > t1/2 >0.l sec. not available, i.e., the experiment in which the y ray was seen did not include time discrimination. beam on, i.e., this y ray was observed only during beam-on intervals. The reader is cautioned not to interpret the beam— on designation as implying a short half-life. In most experiments the beam-on counting period was at least four times as long as each individual beam-off routed spectrum. 277 APPENDIX E Energies of-L Rays Observed in the 53W Fe Investigation (keV) 74.1 751.1 1288.0 1826.7 3100.7 85.6 777.2 1310.8 1971.5 3122.1 123.8 788.7 1315.4 2018.3 3160.1 154.2 817.8 1318.8 2083.9 3248.0 184.9 834.5 1328.1 2102.3 3274.5 210.1 842.9 1367.7 2111.8 3282.9 224.6 846.8 1398.4 2166.7 3365.4 249.2 853.6 1407.0 2242.1 3425.0 319.1 896.1 1434.3 2273.5 3487.1 377.9 906.0 1461.8 2308.5 3783.1 415.4 935.9 1505.3 2316.5 4015.3 438.0 962.4 1538.6 2330.0 4153.3 457.4 983.8 1589.4 2339.6 4184.9 469.0 1011.5 1597.6 2613.2 4291.9 477.0 1039.3 1619.9 2685.6 497.4 1077.5 1712.6 2722.1 511.0 1095.8 1730.6 2746.5 608.0 1124.3 1757.5 2750.7 660.9 1169.5 1763.7 2756.4 669.7 1217.8 1777.8 2754.6 701.1 1230.5 1790.4 2852.4 715.7 1247.5 1798.7 2944.6 744.1 1274.3 1810.3 3040.6