..H: ”V 2. . . .,-1 14:.“ .. $4~.\I. Mn "‘1”. i .1” MI. v.’:.'l‘ _ ...“... '1...:.»u.' ...-11.3.3.1. . .1‘. .‘Cfn. 3...... . “ .4_J . u .‘LJ. .i.. "H. - (.43Nu....\.-7'u . x. .-.-. ".1: j.,‘.;._~,.. . L3 ..‘u r- n .4 a . '.l-I! pf? . .. . 1:52, ‘_.. :v- >»-v I IL 4 3.. 4r .. .4. ,v. 11".. .. .. J . .WLu ',:,,- ......,..\,...., ’ . _ ,5; 1:133...“ ._ Date MS U is an Affirmative Action/Equal Opportunity Institution MICHIGAN STATEI flfl'nilflfilml i’lflmlfllflml 3 1293 01038 0768 LIBRARY Mlchlgan State Unlverslty This is to certify that the dissertation entitled "Beta-decay Branching Ratios of the Neutron-Rich Nucleus BoronlS" presented by Richard Harkewicz has been accepted towards fulfillment of the requirements for Ph.D. . Chemical Physics degree in @flfifiegm, Jan. 16, 1992 0-12771 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE ] ,___l u | || - m . gugl __:l_ll—l: 3" If MSU Is An Affinnetive Action/Equal Opportunity Institution czbiMMuHS-DJ THE fl-DECAY BRANCHING RATIOS OF THE NEUTRON-RICH NUCLEUS 15B By Richard Harkewicz A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1992 672.36% ABSTRACT THE fi-DECAY BRANCHING RATIOS OF THE N EUTRON-RICH NUCLEUS 153 By Richard Harkewicz Detailed experimental information on the fl-decay properties of nuclei far from stability can provide crucial tests of the validity of shell-model Hamiltonians which have been constructed from data associated with stable and near stable nuclei. Such tests can lead to refinement of shell-model interactions. The neutron-rich boron isotopes are particularly interesting in that the ratio of neutrons to protons lies in a range of two to almost three. While progress in establishing the limits of particle stability for the boron isotopes has been quite good, suprisingly up to now much remains unknown about the decay of 158. In the present study 15B nuclei were produced at the National Superconducting Cyclotron Laboratory at Michigan State University through fragmentation of an E/ A = 80 MeV 18O beam from the K1200 cyclotron in a thick 9Be target. The products of this reaction were then separated using the momentum-loss achromat mode of the NSCL A1200 separator. This technique provided a nearly pure beam of 15B ions (> 93%) which was transported to a low background experimental vault with an overall yield of approximately 600 15B ions per second. The 15B ions were implanted in the center of the NSCL neutron detector array, a device designed to study the decay of fl-delayed neutron emitting nuclei. The array consists of 16 proton-recoil plastic scintillation neutron detectors which covers a total solid angle of approximately 1.9 steradians that can measure neutron energies by the time-of-flight method. In the present work, the first fl-delayed neutron spectroscopy of 15B was performed, and in addition, a remeasurement of the 15B half-life was made. As a result of these measurements, the 15B ,B-decay branching ratios have been established. The experimentally determined 15B B-decay properties from the present work are compared to shell-model calculations carried out in the complete psd model space us- ing the Millener-Kurath-Wildenthal interaction. Future work at the N SCL using the neutron detector array to study other ,B-delayed neutron emitting nuclei is suggested. Ideas concerning how the array may be improved are also provided. Make voyages. Attempt them. There is nothing else. — Tennessie Williams to God (for his creations) to Gena (for being his greatest One) iv ACKNOWLEDGEMENTS It has been an honestly dynamic, eye opening, “part of me dying - part of me being born” time at the cyclotron lab (or I should more bluntly say the great Midwest) since I ventured out here four and a half years ago, coming by way of the mean, backstreets of Newark, New Jersey (my home town). First off, I must thank Dave Morrissey for his guidance and belief in me during my graduate career. Dave, thanks for your patience and understanding and thank you for being an active, “always there” advisor. Thank you for your encouragement when it would have been easiest just to quit — I owe more than words can express to you Dave. The entire staff at the lab has been true family to me and I don’t know where to start in expressing my appreciation to each and everyone. Well, special thanks go out to Dennis and Anne Swan for their genuine friendship. Thanks Dennis and Anne for keeping my car running and keeping my stomach full during some cold, dark Michigan winters — I hope, one day, your garage is complete. Thank you Jerry Nolen for all your guidance and support and thanks for letting me do what I do best - you’re a natural mentor. Thank you Brad Sherrill for your exhaustive efforts in making it all work. Thanks go out to so many more friends. Dick Blue, Walt Benenson, Ed Kashy, Arron Galonsky, Harold Hilbert (thanks for letting me burn so much solder), Steve Hickson, Steve Bricker, Bob Young, Jan Mooney, Phil Fighter and the guys in the shop (where I always felt most at home), all my 15B collaborators (Dave, Alex, Jerry, Brad, Nigel, John and Jeff), Renan Fontus and Tom Jones (for the electronic diagrams), Don Lawton and Rick Swanson, Al Zeller and Tim Antaya (for getting me into ultra-marathons in the 90’s), Doug Harris (for teaching me to bend conduit), and all my fellow grad students (especially Don Sackett, Raman V Pfaff and Mike Lisa). I know I’ve left out names but you’re all in my heart — I’m going to miss you wonderful people; I really mean that. I’d like to thank my Mom, Alice, for raising the four kids and still having time for the somewhat odd last one when he came along. Thanks go out to my sister Janet, her husband Tony and my swell nephew Anthony (also my Godson); thanks for the support. I’d also like to thank my brother Ken (mi compadre) and my brother Ed. I just have to say the past is behind us, we all survived (with a few scars) and I truly love you all. Last, and certainly not least (perhaps just saving the best for last) thank you Gena from the bottom of my heart for your understanding and just for being who you are. It’s been a real journey with you and there’s a place deep within me that is there for only beautiful you. Thanks Josh for being the fun kid you are and being so honest. The two of you mean a real lot to me. vi Contents LIST or TABLES ix LIST or FIGURES "" 1 Introduction 1.1 A Brief Overview of fl~Decay ....................... 1.2 ”B and the Other Neutron-Rich Boron Isotopes ............ 11 2 Experimental Details 16 2.1 The NSCL A1200 Radioactive Beam Facility .............. 16 2.2 The Neutron Detector Array ....................... 21 2.3 Neutron detector eficiency ........................ 29 2.4 Comparison of the Measured (PuBe) Efficiency to a Monte Carlo Cal- culated Eficiency for an Array Detector ................ 35 2.5 Exploring Position Sensitivity with the Neutron Detector Array . . . 41 2.6 Cyclotron Beam On/ Beam Off Cycles for Decay Studies ....... 46 3 Results and Analysis 49 3.1 33mm of the Experimental Runs Made to Measure the Decay of 50 3.1.1 Group One Experimental Runs ................. 50 3.1.2 Group Two Experimental Runs ................. 56 3.1.3 Group Three Experimental Runs ................ 56 3.2 A Measurement of the Half-life of "B .................. 60 3.3 ”B fl-Decay to “C Bound States .................... 66 3.3.1 "‘0 fl-Decay Following the Implantation of “"8 ......... 66 3.3.2 The Implantation Detector’s B-Detection Eficiency ...... 70 3.3.3 Determination of the ,B-Decay Branch to “C Bound States . . 78 3.4 “B B-Decay to "C Unbound States - ,B-Delayed Neutron Emission . 81 vii 3.4.1 158 fl-Delayed Neutron Time-of—F light Measurements ..... 81 3.4.2 Other Decay Channels for ”’B ,B-Delayed Neutron Emission . 96 3.5 The 15B ,B-Decay Branching Ratios ................... 101 4 Discussion — Comparison to Theoretical Predictions 110 4.1 The Nuclear Shell-Model ......................... 110 4.2 Shell-Model Calculations for 15B ..................... 116 5 Conclusions 121 LIST OF REFERENCES 125 viii List of Tables 1.1 2.1 2.2 2.3 2.4 2.5 3.1 Summary of the half-life measurements made for the decay of 153. Listed is the reasercher and date the measurement was published, the reaction used to produce the 153, and the reported 153 half-life. Summary of the A1200 beam purity for the implantation of the 15B secondary beam. ............................. Summary of the measured neutron detection efliciencies (using the PuBe source) for the Sixteen array detectors. Listed are the mea- sured efficiencies, including the estimated error associated with each measurement, for the detection of 1.8 MeV, 3.0 MeV and 4.5 MeV neutrons. Also included is the mean and standard deviation of the Sixteen measurements for the three energy bins. ............ Comparison of measured (PuBe) and calculated (Monte-Carlo) effi- ciencies for neutron array detector # 1 as a function of neutron energy (not including solid angle) ......................... Summary of the N SCL neutron detector array specifications ...... Beam On / beam Off 60Co 7-ray source measurements used to calibrate exact times of On/Off cycles. Listed are the time cycles, number of 7 events recorded during On/Ofl' cycle, time calibration of real time clock, last channel of Off cycle time spectrum, and calculated exact times of beam On/ beam Off cycles. ................... Summary of part of the experimental runs (Group One) involved with measuring the decay of 15B. These runs were used to obtain a 15B half- life measurement and fl-delayed neutron time-of-flight spectra. Listed are the run number and corresponding on/off cycle, the time of each run, the total number of 15 B ions deposited in the implantation detector (per run), the A1200 15B production rate, and the total number of 15B atoms (per run) remaining at the end of the implantation period (see text for explanation) ............................ ix 14 27 34 40 45 48 55 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Summary of part of the experimental runs (Group Two) involved with measuring the decay of “B. These runs were used to measure the 15B fl-decay branch to 15C bound states. Listed are the run number and on/off cycle (only 5 S / 6 S cycle was used for these runs), the time of each run, the total number of 15B ions deposited in the implantation detector (per run), the A1200 15B production rate, and the total number of 15C atoms (per run) remaining at the end of the implantation period assuming a 100% 5B fl-decay branch to 15C bound states (see text). Summary of part of the experimental runs (Group Three) involved with measuring the decay of ”B. This run was used to determine the implantation detector’s B-decay detection efficiency for 15C. Listed is the run number and on/off cycle (only 5 s/7 S cycle was used), the time of the run, the total number of ions deposited in the implantation detector (per run), the A1200 production rate, and the total number of atoms (per run) remaining at the end of the implantation period. . Summary of the half-life, t1 ,2, and true activity present at the end of the implantation period, AWN” obtained from the decay of 15B inclusive fl-emission for the Group One experimental runs (one through ten). Also included is the background component for each run and the reduced chi-square for the least-square fitting procedure. ....... Summary of the Group Two experimental runs in which “B ions were deposited into the implantation detector during a 5 S beam on period and decays were monitored during a 6 s beam off period. The de- cay curves from these runs were fit with a least-square procedure in which each component’s decay constant was a fixed parameter and its activity was a free parameter. The components of each fit and the cor- responding activity, A0, are Shown in the fourth column. The adjusted activities, AWN”, account for the 0.375 s that elapsed between the end of implantation period and the beginning of the fit and are shown in the fifth column. The last column lists the reduced chi-square for the least-square fitting procedure. ...................... Summary of the implantation detector’s fl-detection efficiency for the fl-decay of ”B from the Group One experimental runs. ........ Summary of the implantation detector’s fl-detection efficiency from the Group Three run. The AWN, values were obtained from the fitted decay curve shown in Figure 3.4; also listed is the reduced chi-square value for the least-square fitting procedure used to obtain these values. The efficiencies were deduced from these AW,” values and the number of atoms present at the end of the implantation period. ........ Summary of the implantation detector’s fl-detection measured effi- ciency for implantated ions from Groups One, Two and Three runs. Also listed is the “actual” average fl-particle energy from the decay (see text for explanation) and the depth of implantation into the 10 mm thick implantation detector. ....................... 58 59 63 68 74 76 77 3.9 3.10 3.11 3.12 3.13 4.1 Summary of the determined 15B fl-decay branching ratios to ”C bound states determined individually from the three experimental runs of Group Two. Also listed is the decay branch determined from the decay curve generated from the summation of these runs. .......... Summary of the calculated neutron energies from the fitted Spectra of the Sixteen neutron detectors. The flight path was calibrated using the lowest energy neutron peak in the fitted Spectra as a standard; this peak represents a 1.759 MeV neutron and corresponds to the known 3.103 MeV state in 15C. The other neutron energies shown below were calculated using this calibrated flight path and their associated peak centroid supplied by the fitting procedure. All neutron energies are in MeV ..................................... Summary of the relative fl-delayed neutron branching ratios for the populated states in 15C determined from the results of the sixteen ar- ray detector time-of-flight measurements. Listed is the mean and stan- dard deviation for the branching ratio percentages; first, to include the detector # 7 values, and second, to exclude them. All branching ratios are in percent. Errors associated with each detector measurement are dealt with later ............................... Summary of the relative fl-delayed neutron branching ratios for the populated states in 15C with their corresponding uncertainties. Also listed is the “weighted” mean and uncertainty for each branching ratio percentage. The details concerning the method used to determine the uncertainties and weighted values are explained in the text. All values are in percentage. Note that the detector # 7 values are not included. Neutron energies, measured 15C states (this work), known 15C states 80 92 93 94 a), ,6 branching and log ft values in 15B decay. All energies are in MeV. 106 Measured and predicted Gamow-Teller fl—decay strengths to the lowest {3 g”, 3-, %— and g‘ “) states in mass 15; also included are the mea- sured and predicted energy levels of ”C populated. The 3.103 MeV 15C level was adjusted in the Shell-model calculations to match the experimental value. (BR) denotes branching ratio. All energies are in MeV ..................................... xi List of Figures 1.1 1.2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Experimental log f t values and associated types of fl-decays. From K. Krane, Introductory Nuclear Physics (New York: John Wiley and Sons, 1988). ................................... Energy level scheme of 15C. From F. Ajzenberg-Selove, Nucl. Phys. A523, 1 (1991) ............................... Schematic drawing of the NSCL A1200 radioactive beam facility and the K1200 cyclotron. ........................... Schematic view of the NSCL experimental floor layout.The 15B sec- ondary beam was produced and separated at the A1200 and then trans- ported to a low background experimental vault, some 60 meters away from the primary 180 reaction ....................... Schematic drawing of the N SCL neutron detector array and the exper- imental setup. The numbering of each neutron detector is consecutive going from # 1 to # 16. ......................... A close-up view of the detectors (implantation and the two silicon surface barrier) and associated hardware located at the center of the neutron detector array ........................... Energy spectra obtained from the AE detector and the veto detector (located at the center of the neutron detector array) for the implanta- tion of the ”B secondary beam ...................... Schematic drawing of the electronic setup used in the ”B decay study. This setup could remain essentially the same for other fl-delayed neu- tron decay experiments. ......................... Time-of-flight spectra obtained from an array detector and the small, standard detector using the PuBe neutron source. These spectra were used, in part, in determining the neutron detector array neutron de- tection efficiency. The peaks labeled “flag” and “cosmic” are explained in the text. ................................ Energy “bins” selected from the PuBe neutron source time-of-flight spectra. .................................. Compton edges obtained in the pulse height spectrum of the standard detector using 60Co and 134Cs 7-ray sources. Note that the location of the Compton edge was taken to be the half-height of the edge. . . . . xii 15 19 20 24 25 26 28 32 33 37 2.10 2.11 2.12 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Array detector showing the five positions a 60C0 source was placed in order to determine the detector’s neutron threshold setting and its dependence on position. The source was collimated and placed flush against the detector. ........................... Compton edges obtained, using a 60C0 source, from the left and right sides of array detector # 1 for the five positions shown in Figure 2.10. Results of placing a collimated 60Co source at the five array detector locations Shown in Figure 2.10 and using the “position through timing” function (Equation 2.6). ......................... Experimental decay curve for “B inclusive fl-emission obtained by summing all the 20/40 cycle runs (4 through 10). The solid line corre- sponds to a single-component fit plus a constant background ...... Experimental decay curve for 15 B requiring fi-neutron coincidence. The solid line corresponds to a single-component fit plus a constant back- ground. .................................. Experimental decay curve generated by summing the three individual runs of Group Two. During these runs 15B ions were deposited into the implantation detector during the 5 S beam on period and decays were monitored during the 6 s beam off period. The solid line corresponds to a three-fit component (6He, 9Li, 15C) plus a constant background. The error bars are statistical. ...................... Experimental decay curve for the Group Three experimental run. Dur- ing run # 14, 15C and "N ions from the A1200 were deposited into the implantation detector during a 5 s implantation period and decays were monitored during the 7 s beam off period. The solid line corresponds to a two component-fit plus a constant background. .......... Top figure is the raw, unfitted fl-delayed neutron time-of-flight spec- trum obtained from detector # 6. The x-axis corresponds to time, with the lowest energy neutrons in the highest channel number peak. Shown is the “fast” fl-peak and the “cosmic” peak; these are explained in the text. Bottom figure is the above spectrum which has been fit- ted. The five unfolded ,B-delayed neutron peaks, with their energies, are Shown. The Spectrum is not corrected for neutron efficiency. The fits to individual peaks are indicated with solid lines, the background by long dashes, and the sum of all contributions by the short dashes. The fitting procedure is described in the text. ............. Fitted fl-delayed neutron time-of-flight spectra obtained from the neu- tron array detectors # 1 through 8 .................... Fitted fl-delayed neutron time-of-fiight Spectra obtained from the neu- tron array detectors # 9 through 16. .................. The B-delayed neutron decay branching ratios obtained from the dif- ferent array detectors. The solid lines and values on the right are the weighted averages obtained for each of the five percentages from the detector measurements; note that the detector # 7 values are shown here but its values were not used in calculating the weighted averages. xiii 38 39 44 64 75 89 90 91 95 3.9 3.10 3.11 3.12 3.13 4.1 4.2 Neutron energy spectrum generated from the sixteen neutron detector time-of-flight measurements. Top figure is the energy spectrum with a linear y-axis, bottom figure is the same spectrum with a log y—axiS. Note the evidence of only five fl-delayed neutron peaks ......... Two dimensional Spectra Showing the neutron time-of-flight measure- ment for detector #6 (x-axis) vs. the neutron time-of-flight measure- ment for the fifteen other detectors (y-axis, and numbered for detector number). These spectra were used to look for two neutron coincidence events and evidence of 15B fl-delayed two neutron emission via the ground state of 13C ............................. Efficiency curve for the polyethylene-moderated neutron detection sys- tem used by Reeder et al. [Re91] in their recent measurement of the 15B PM. Calculated Monte-Carlo efficiencies are represented by the solid circles and experimentally determined efficiencies by the open circles. See text for a detailed explanation. ................... Experimental decay curve for ”N inclusive fl-emission; 190 was an im- purity. The solid line corresponds to a two-component fit, the reduced chi-square for this fit was 0.5. ...................... Time-of-flight ,B-delayed spectrum obtained for the decay of ”N from neutron array detector number # 6. Shown are the “fast” ,B-peak and the 1.702 MeV and 1.172 MeV neutron peaks. Note that the detector was not able to detect the 0.383 MeV neutrons from the decay of "N, 99 100 107 108 however the spectrum location where they would be expected is shown. 109 At the left are the energy levels calculated using the Woods-Saxon po- tential (Eq. 4.1) alone (Intermediate form). At the right are the energy levels calculated when the spin-orbit potential is included (Intermedi- ate form with Spin orbit); notice the spin-orbit interaction splits the levels with I > 0 into two new levels. To the right of each energy level is, first the individual nucleon capacity of that level and, second the cumulative number of nucleons up to that level. The inclusion of the spin-orbit potential results in the magic numbers (shown in the cir- cles) being exactly reproduced. From K. Krane, Introductory Nuclear Physics (New York: John Wiley and Sons, 1987). ........... Graphical comparison of the experimentally determined Gamow-Teller fl-decay strengths for “B and those predicted by the theoretical shell- model for mass 15. The y-axiS represents the energy levels (13;) in 15C. Refer to Table 4.1 for the actual B(GT) and E: values. ........ xiv 115 120 Chapter 1 Introduction fl-decay is the process through which a nucleus that has an imbalance in its num- ber of protons and neutrons can become more stable by converting a proton into a neutron or a neutron into a proton. In this process, the mass number of the nu- cleus, A, remains unchanged but the atomic number, Z, changes by one unit; this transformation is accompanied by the emission from the nucleus of an electron and an anti-neutrino (for neutron excessive nuclei, where a neutron is converted into a proton) or a positron and a neutrino (for proton excessive nuclei, where a proton is converted into a neutron)‘. ,B-decay was one of the first forms of radioactivity to be observed, and it still provides new valuable insight into the internal structure of the nucleus. An important nuclear model, the shell model, was formulated nearly fifty years ago, and is able to successfully explain and predict various nuclear properties, including details of fl-decay. Two important assumptions of the Shell-model are (1) the nucleons within the nucleus move in a potential that they themselves create, and (2) the motion of a single nucleon is governed by a potential caused by all of the other nucleons. Detailed experimental information on the ,B-decay properties of nuclei far from stability are particularly important because they can provide crucial tests of the 130th the electron and positron can be referred to as “fi-particles”, and both the neutrino and anti-neutrino can be referred to as “neutrinos” in these decays. validity of the assumptions used to construct Shell-model Hamiltonians which have been based on data associated with stable and near-stable nuclei. These tests can lead to refinement of the knowledge of shell-model interactions. With such refinements, the shell-model extrapolations for the properties of even more exotic nuclei become, of course, more reliable. The further nuclei are from stability, the more energy they have available for de- cay processes and the more exotic these processes become. One such decay process is that of fi-delayed nucleon emission. With the increased decay energy, the decay may populate highly excited states in the daughter nucleus and these states may subsequently decay by prompt nucleon emission2 . The emitted nucleon may actu- ally provide more information than the fl-particle because, while the energy of the fl-particle is continuous due to the decay energy being Shared among three bodies, the nucleon has a definite energy determined by the energy of the populated excited state in the daughter nucleus, as this is a two body decay. By observing the emitted nucleons’ energies and emission probabilities, the populations of the excited states of the daughter from the ,B-decay can be determined. This experimentally deter- mined information can then be related to theoretically predicted quantities; as will be expanded upon Shortly. It should also be noted that with the advancements in accelerator technology, the ability to produce nuclei further and further from stability at unprecedented rates will continue to yield new experimental data from which the shell-model can be “put to the test”. The goal of the present work was to establish the previously unknown 15B fl-decay branching ratios; ”B already known to be a fl-delayed neutron emitter. A large part of the present work involved designing, constructing and testing the NSCL neutron 2The emission of the nucleon occurs typically in 10-20 seconds after the excited state has been populated through the fi-decay, so essentially the [i—particle and nucleon are emitted from the nucleus simultaneously. detector array, a detector array designed to study ,B-delayed neutron emitting nuclei. In this opening chapter, (1) some discussion of the types of fl-decays will be presented (allowed and forbidden) along with an explanation of some experimentally derived quantities which bridge the gap between theory and experiment, and (2) the neutron- rich boron isotopes will be examined (with an emphasis on 15B). Chapter II describes the production and separation of 15B using the MSU N SCL A1200 radioactive beam device, the experimental setup, and detailed information on the neutron detector array. In Chapter III, the experimental results and analysis are presented, and the ”B fi-decay branching ratios established. Lastly, Chapter IV compares the experimental results to shell-model calculations carried out in the psd model space. 1.1 A Brief Overview of fi-Decay An entire derivation of the Fermi theory of ,B-decay is not the purpose of this section; the steps of this derivation can be found in almost any introdutory nuclear physics text (such as “Introductory Nuclear Physics” by K. Krane [Kr88] or “Nuclear and Radiochemistry” by Friedlander, Kennedy, Macias, and Miller [Fr81]). What will be presented here are a few tenets of Fermi’s theory of ,B—decay explicated by K. Krane [Kr88] and D. Mikolas [Mi89] and how they relate to experimentally determined quantities. This will aid in some of the discussions which follow latter. Fermi treated the fl-decay causing interaction as a weak pertubation. Through Fermi’s Golden Rule, be related the transition probability for fl-decay, A, to the interaction that causes the transition between an initial and final quasi-stationary state, V, and also a density of final states that is accessible during the decay, p(Ef): 271' 2 A = 71%.: pus» (1.1) where V}.- is the integral of the interaction that causes the transition between the initial and final states of the system: V,. = / ¢}V1/2,-dv (1.2) The density of final states term in the above equation has the obvious effect that a given transition is more likely to occur if there is a large number of accessible final states. Different mathematical forms of V are available which discribe its transformation properties and its behavior under rotation and Space inversion. These include, but are not limited to, the vector operator (W), and the axial vector operator (VA) which will be addressed later; for now. V will be used to represent either of these operators. For fl-decay, the wave functions of the fl-particle and the neutrino must also be considered, where it; only refers to the final nuclear wave function, so the more complete interaction matrix element should have the form: Vf°=g/(¢;505<,0,,)V1,b;dv (1.3) where 9 represents the ,B-decay strength constant and determines the strength of the transformation interaction. The ,B-particle and neutrino wave functions are usually assumed to have plane wave forms 903(17) 0( eff-”fl” and 90,,(5) o< ei‘I'F/I‘, where [2' is the fi-particle momentum and (I the neutrino momentum. Expanding the exponential forms of these functions gives: iii-F 1 i132; um: _ 2 e 1+ h +2[h]+ (1.4) Wu: ”I” 1L7}? e 1 72 +2[ 711+ (1.5) Notice that in these expressions, the ,B-particle and neutrino wave functions de- pend on 1", the location in the nucleus where the two particles are created. If the particles are created at the nuclear origin (r = 0), then they cannot carry off any orbital angular momentum (l = 0) and the wave functions both reduce to a value of 1. This limit is known as the allowed approximation and the only factors that depend on the ,B-particle and neutrino energy come from the density of final states. Eq. 1.3 can then reduce to: Mfi = g / wade) (1.6) where M f; is the nuclear matrix element and accounts for the overlap of initial and final nuclear states. Two types of allowed fl-decay exist, called Fermi and Gamow-Teller decay and can be distinguished by the spins of the particles. In allowed Fermi decay, the ,6- particle and neutrino are emitted such that their intrinsic Spins of 1/2 (S = 1/2) are anti-parallel and couple to zero. With 1 = 0, in Fermi decay there is no change in the Spin of the nucleus. Using the standard quark-model of the nucleons, only the identity of one of the three quarks within the nucleon changes, ([udd] —+ [uud] for example, neutron —+ proton), while the Spin of the nucleon, and hence the spin of the entire nucleus, remains unchanged [Mi89]. The only thing that does change is the charge of the nucleus which has been labeled the total isospin vector, T2 3; the isospin, T (to be described shortly), remains unchanged in pure Fermi ,B-decay and, as a result this quantity can be thought of as conserved during the decay and connects two states of identical nuclear wave functions“. All the Fermi decay strength should go into this single daughter state known as the analog state. In allowed Fermi decay, the transition operator is of the vector form, W. The charge independence of the nuclear force allows the neutron and proton to be treated as two different states of the same particle, the nucleon. In the absence of an electromagnetic field the proton and 3The total isospin vector, T,, has the value §(N — Z). The isospin of a nucleus, T, can have values ranging from |T,| to |A/2|. 4In the first order, the strong or nuclear force is not effected by the charge of a nucleon (an electromagnetic force). The daughter state connected by pure Fermi decay, the analog state, has an identical nuclear wave function to that of the parent. neutron are degenerate. The nucleon is thus assigned a “quasi” spin vector, called the “isospin”, with the isospin quantum number being +% or isospin-up for the neutron and —% or isospin—down for the proton. fl-decay can also occur in the Gamow-Teller mode in which the B-particle and neutrino are emitted parallel and their spins couple to a Spin of S = 1. In a more microsc0pic picture the spin of a quark must flip, and this allows both the Spin and isospin of the nucleus to change by one unit. Gamow-Teller decay populates many more states in the daughter than does Fermi decay; recall that Fermi decay iS limited to feed only the analog state, where as Gamow-Teller decay can also feed the analog state but is not limited exclusively to it. In allowed Gamow-Teller decay, the transition operator is of the axial vector form, VA. Also note that in either Fermi or Gamow- Teller allowed fl-decay the parity of the initial and final states is not permitted to change. fl-decay selection rules can be written in terms of these permitted Spin and parity changes. For allowed Fermi decay, AT = 0, AJ = 0, and An = no. Examples of allowed pure Fermi decay are the 0* —) 0+ decays of “O -> ”N“ and 3‘C1 —> 34S; these decays cannot occur through a Gamow—Teller transition. For allowed Gamow- Teller decay, AT: 0 or 1; AJ = 0 or 1; and An = no. Decays such as 6He —-> 6Li (0+ —> 1+) and 13B —-> 13C (g- -—) {) are pure Gamow-Teller transitions and contain no Fermi component. A decay such as n —-+ p (%+ —> %+) can satisfy both the Fermi and Gamow-Teller selection rules and is an example of a “mixed” Fermi/Gamow-Teller transition. In both the allowed Fermi and Gamow-Teller transitions the fl-particle and the neutrino are emitted with zero orbital angular momentum. In cases where the two particles must carry off one or more units of orbital angular momentum, these decays are called forbidden decays — the degree of “forbiddeness” ( lst, 2nd, etc.) correspond- ing to the number of units of orbital angular momentum carried off (1 h, 2 it, etc.). The assumption in Eqs. 1.4 and 1.5 that the ,B-particle and neutrino wave functions reduce to the value of one is obviously not valid here; each succeeding term in the expansion of the exponential form of the plane wave function gives a higher order of forbiddeness. Generally, forbidden fl-decay is a much more difficult process to cal- culate accurately than allowed decay. Since a difference in the parity of the initial and final states of a nucleus requires an odd number of orbital angular momentum units to be emitted, this represents the most frequent occurrence of forbidden decays. Selection rules for first-forbidden decays are AJ = 0, 1, or 2 and An = yes; examples being 17N -—) "O @— -—> %+) and 15B —> ”G (g- -—i y). Selection rules for second- forbidden decays are AJ = 2 or 3 and A11- : no; an example being 22Na —) 22Ne (3+ —» 0+). There are also third-forbidden decays (four cases known) and fourth-forbidden decays (two cases known). As expected, the higher the order of forbiddeness, the less likely is the probability for the B-transition. If the opportunity permits, a nucleus will decay via an allowed or lowest order transition possible. Only when no other decay channel is possible, do the higher-order decays occur. In his formulation of allowed fl-decay theory, one of Fermi’s goals was to be able to predict the momentum and energy distributions for Specific fl-decays and have these agree with actual experimental results. Using the relationships established in Eqs. 1.1 through 1.6, and others, Fermi was able to successfully predict the Shape of B—decays by including three factors. These are (1) a statistical term which accounts for the number of final states accessible to the emitted particles; (2) a term which accounts for the influence of the nuclear Coulomb field; and (3) a term which includes the nuclear matrix element |M 1,12 to account for the overlap of initial and final nuclear states. The first and second terms can be combined into one term known as the Fermi integral, f (Z, E'o), where Z is the atomic number of the daughter nucleus and E0 is the “state-specific” fl-endpoint energy (Q3 — E3); this integral can be calculated knowing the Z and E0. Using a calculated quantity known as the comparative half-life, ft, Z113 t oa ft = f( (fig/2,“ t l) (17) experimentally determined values such as the total half-life (the actual half-life which is measured) and fl-decay branching ratios (BR) can be used to indicate how well ini- tial and final nuclear state wave functions overlap. Comparative half-lives (expressed in the units of seconds) allow uS to put all B-decays on equal footing (“normalized” for the number of final accessible states and the nuclear Coulomb field), and therefore differences in ft values indicate differences in the matching of the initial and final nuclear states. As an example, consider the fl-decay of 15B (.l’r = 3‘ [Aj91]) to the 3.103 MeV, %_ state in 15C (this is the lowest energy negative parity state in 15C). In the present work, a total half-life of 10.3 ms was measured for 15B, as was a 62.8% decay branch to the 3.103 MeV state. Using the method of Wilkinson and Macefield [Wi74] to calculate the Fermi integral, and taking the maximum fl-endpoint energy, Q3, to be 19.1 MeV [Aj91], the comparative half-life is determined as follows: Z: E =1 MV 0.0103 ft=f( 6’ 0 0:286 ). S=21,878s (1.8) Typically, the log of the ft values are reported, so for the above example the log f t value is 4.34. The log ft value can be related to the order of forbiddeness of a decay; Figure 1.1 summarizes experimental log f t values for many different decays. It is clear from this figure that there is a correlation between the log f t value and the order of forbiddeness. Each additional degree of forbiddeness increases the log ft value by approximately 3.5, representing a reduction in the transition probability of about 3x10“. Most allowed decays have log f t values in the range of 3.5 to 6.5, and first- forbidden decays have values in the range of 6.5 to 9.0. Second-forbidden decays have log ft values in the range of 10 to 13, third-forbidden decays 14 to 20, and fourth- forbidden decays have log ft values of near 23. The utility of log f t values lies in their predictive ability. For example, given the ,B-decay of 15B, if a log ft value of 5.4 was deduced for the decay to an unknown state in 15C, it would be reasonable to assume that this was an allowed decay, and the 15C state’s J’r would be limited to if, 3', or $1 since the J’r of 15B is g-. Now, with some of the basics of fl-decay having been reviewed, the neutron-rich boron isotopes will be discussed next. Number of cases A O [IIIIIII|lllllllllllllllllllIll w o 2 O m Superalfowed D Allowed a First forbidden Second forbidden Third forbidden é Fourth forbidden 9 10 ll 12 13 l4 15 16 17 18 19 20 21 22 low Figure 1.1: Experimental log ft values and associated types of fl-decays. From K. Krane, Introductory Nuclear Physics (New York: John Wiley and Sons, 1988). 11 1.2 15B and the Other Neutron-Rich Boron Iso- topes The stable boron isotopes include 10B and “B (20% and 80% atom percent abun- dance, respectively). Although it may be proper to refer to any boron isotope with mass greater than eleven as being “neutron-rich”, in the present work the neutron- rich boron isotopes will be taken to be those with a mass of fifteen or more. Such neutron-rich boron isotopes have been studied over a long period of time, and they are particularly interesting in that the ratio of neutrons to protons is very large, be- ing in the range of two to almost three. 158 was first observed to be stable against prompt particle emission in 1966 [P066]. In 1974 the particle stability of 17B and the particle instability of 163 were Shown [B074]. Recently, in 1984, 19B was Shown to be the most neutron-rich stable boron isotope; in that same experiment 18B was shown to be unstable to prompt neutron emission [Mu84]. Thus progress in establishing the limits of particle stability for the neutron-rich boron isotopes has been quite good. Suprisingly though, up till now nearly twenty-five years after it was first observed to be particle stable, much remains unknown about the decay of 15B. The half-life of 15B has been measured by a number of different research groups most of which are in good agreement. Table 1.1 gives a summary of these half-life measurements. If the particularly low value of 8.8 ms observed by Curtin et al. [Cu86] is excluded, the weighted average obtained from the remaining half-life measurements is 10.3:l:0.2 ms. The value of 10.5:l:0.3 ms for the ”B half-life has been adopted by A jzenberg-Selove [Aj91]. However, not much is known about the fl-delayed neutron decay of 15B, other than that it is dominated mostly by single fl-delayed neutron emission. In 1984 Dufour et al. [Du84] established the limits of P0,, < 5% and P2,, < 1.5% for 15B decay (implying 12 therefore P1,, > 93.5%), and more recently Reeder et al. observed P1,, > 77.3% and P2,, = 0.4:l:0.2% [Re91, Re90]. However, no measurement of the fl-delayed neutron energies has been made, hence the fl-decay branching ratios of ”B to states in 15C is not known. Referring to Figure 1.2 (the energy level scheme for 15C), the ”B fi-decays that populate the ground state (Ex = 0.00 MeV, J’r = %+) and first excited state (E,7 = 0.74 MeV, J’r = %+) of 15C would be (1) particle bound due to the 1.218 MeV neutron separation energy, and (2) first-forbidden decays due to the positive parity of these states. The observed low P0,, is consistent with the fact that these are first-forbidden decays. Decays to the low-level, negative parity states in 15C would be allowed (due to the Spins and negative parity of these states) and additionally favored by the large phase space available; since these states have energies above the 1.218 MeV neutron separation energy (neutron emission via the ground state of “C), neutrons with kinetic energies in the range of 1.8 to 5 MeV will be emitted as a result of their feeding — this is consistent with the observed large P1“. If the higher level states in 15C are populated by the fl-decay, it is possible they can decay by emitting one neutron via the first excited state of ”C (”C level must be at least 7.31 MeV) or even decay by emitting two neutrons via the ground state of 13C (”C level must be at least 9.39 MeV). It would be expected though that decays occurring via these two channels would be severely restricted due to the smaller amount of available phase space and this is partially supported by the observed low P2". The importance of establishing the ”B fl-decay branching ratios to test the va- lidity of shell-model calculations for nuclei far from stability was pointed out in the first section of this chapter. It Should also be noted that 15B has been used as a cali- bration standard for other fl-delayed neutron experiments, and that such calibrations depend on the assumed neutron energy distribution [Mu88, Le89]. A measurement of the neutron energy Spectrum for ”B is important for establishing the utility of 13 ”B as such a standard. Lastly, the decay study of ”B in the present work was partially undertaken as the “ground breaking” in the technical development of the hardware which would hopefully be used in the future studies of many other, more exotic, ,B-delayed neutron emitting nuclei at the NSCL using the newly designed and constructed neutron detector array. 14 Table 1.1: Summary of the half-life measurements made for the decay of 15B. Listed is the reasercher and date the measurement was published, the reaction used to produce the 15B, and the reported 153 half-life. Researcher Reaction Half-life (ms) (year) Dufour et al. [Du84] 18O fragmentation 11:1:1 (1984) Curtin et al. [Cu86] 180 fragmentation 8.8:l:0.6 (1986) Mueller et al. [Mu88] 86Kr fragmentation 10.4:l:0.3 (1988) Samuel et al. [Sa88] 22Ne fragmentation 10.821205 (1988) Lewitowicz et al. [Le89] 48Ca fragmentation 10.3:l:O.6 (1989) Reeder et al. [Re91] proton spallation 10.1:t0.2 (1991) 15 F. AJZENBERG-SELOVE J” = 3/2- l9.|O / 158 fi-/// ”-83- -- ---- 10.25 9.395 MeV 1 C + 2n 9.0 7.31 MeV ”C" + 11 1.218 MeV Figure 1.2: Energy level scheme of 15C. From F. Ajzenberg-Selove, N ucl. Phys. A523, 1 (1991). Chapter 2 Experimental Details This chapter describes the experimental details involved with measuring the decay of 15B. The information provided, however, could also be used as a guide in the future decay studies of other neutron-rich exotic nuclei using the NSCL neutron detector array. The production and separation of ”B using the NSCL A1200 radioactive beam facility is briefly described, along with the transportation of the 15B secondary beam to a low background experimental vault. The recently constructed neutron detector array, a device designed for the study of fl-delayed neutron emitting nuclei, is introduced and its performance and specifications are described in detail. The method used to determine the neutron efficiency of the array is also outlined. Lastly, because it is necessary for decay studies to pulse the primary cyclotron beam on and off, the different cycles employed in this experiment, and the technique used, are described. 2.1 The N SCL A1200 Radioactive Beam Facility The 15B nuclei observed in this work were produced at the National Superconduct- ing Cyclotron Laboratory at Michigan State University with an E/A = 80 MeV 1806"” beam, with an intensity of 12 pnA, from the K1200 cyclotron. A 9Be tar- 16 17 get, 790 mg/cm2 thick, was used and the reaction products were separated using the momentum-loss achromat mode of the A1200. A limited description of the A1200 separator is presented below and a full description of the device has been provided by Sherrill et al. [Sh91] A schematic view of the A1200 radioactive beam facility is shown in Figure 2.1. The device consists of a series of fourteen superconducting quadrupole and four su- perconducting dipole magnets. It can be operated as a fragment separator with an angular acceptance of 0.8 msr, a 3% momentum acceptance, and a maximum rigidity of 5.4 Tm. The 9Be target was placed at the “object” position of Figure 2.1 and heavy-ion reaction products resulting from the projectile fragmentation of the 18O beam moved in the forward direction with essentially the beam velocity. Initial se- lection of reaction products with a specific m/q is accomplished with the first two dipole magnets; in the present experiment the dipole magnets were tuned (3.535 Tm) for an m/ q = 3. Reaction products having a different m / q are filtered out or dumped at these first two dipole magnets. For example, the primary 180 beam with an m/ q of 2.25, after passing through the Be target (1808+), was dumped on a catcher bar inside the first dipole magnet and did not continue forward through the remainder of the A1200 device. A thin (7.84 mg/cm'z) plastic scintillation detector, placed at Image # 1 of F ig- ure 2.1, was used to make a time-of-flight measurement of reaction products. The forward moving reaction products with the same m / q then travel through an achro- matic wedge placed at Image # 2. The wedge introduces a Z dependent momentum shift due to the Z and velocity dependent energy-loss in the wedge given for example by the Bethe formula: —dE/d:1co 93%) beam of 1585"" ions at the its final image; impurities were 12Be“, 9Li3+, 6He2+ and 3H1+ (described in more detail be— low). The 15B secondary beam was then transported through a beamline to a low background experimental vault, some 60 meters away (including a total of 3 meters of concrete shielding) from the Site of the primary 180 reaction (see Figure 2.2), with an overall yield of approximately 600 particles per second. 19 \ recoveries nun ror -' K48“ GYGLO‘I’IOI Figure 2.1: Schematic drawing of the NSCL A1200 radioactive beam facility and the K1200 cyclotron. 20 ~ 0‘ r mmm \. f h \'.’i I b E "-3.- - ---- ‘8. ”fix. : e-l - gh. \. g - PD : 1:1 ,1, : E 0].. """:"""'o 1 - I, j 8 s i l \' ' § ’ 1 1 - , < ' I L .......... . | | ' ' Li...“- .- 1 - a, I .' :Ellafiqlo : l-HL--- '4" LI: ' C0313 ..... ll: ==\\\\\\\\\V\. . a E E s D Figure 2.2: Schematic view of the N SCL experimental floor layout.The "’B secondary beam was produced and separated at the A1200 and then transported to a low back- ground experimental vault, some 60 meters away from the primary 180 reaction. 21 2.2 The Neutron Detector Array The 15B ions were stopped in an active detector in the center of an array of neutron detectors. A schematic view of the NSCL neutron detector array is shown in Fig- ure 2.3. The 15B beam (E/A = 59.8 MeV) passed through a thin kapton window (0.25 mm thick) that separated the vacuum of the beamline from the air, approxi- mately one meter of air, 6.8 mm of aluminum degrader (exiting with E/ A z 25 MeV), a silicon surface barrier AE detector (0.2 mm thick, 300 mm2 area) and came to rest at a depth of 5.2:l:1.2 mm (the 1.2 mm is a limit, not 10‘) in a 10 mm thick plastic scintillator, referred to as the implantation detector (30412, 2.0 cm by 2.5 cm by 1 cm deep). A close-up view of the detectors and associated hardware located at the center of the array is Shown in Figure 2.4. The energy-loss of the ”B ions in air and Silicon, and the amount of aluminum degrader needed to stop the ions in the center of the implantation detector was determined using the N SCL program INTENSITY [Wi91]. This program uses the energy-loss parameters explicated by Hubert et al. [Hu90]. Energy loss in the AE detector, in addition to a time-of-flight measurement, al- lowed on-line monitoring of the purity of the ”B secondary beam. The time—of-flight measurement was started by a Signal from the start detector at Image # 1 of the A1200 (refer to Figure 2.1) and stopped by a signal from the AE detector at the center of the neutron detector array (refer to Figure 2.3). This arrangement also allowed us to determine the exact number of 15B ions deposited in the implantation detector. A thick Silicon surface barrier veto detector (1 mm thick, 300 mm2 area) was placed behind the implantation detector in order to verify that the 15B ions were indeed stopped in the plastic material. Figure 2.5 shows the energy spectra obtained from the AE detector and the veto detector for the implantation of the ”B sec- 22 ondary beam. The ions and their relative percentages that entered the AE detector were 3H” (2.7%), 6He2+ (1.7%), ”Lia+ (1.3%), ”Be” (0.8%), and 1535+ (93.5%). By comparing the number of ions that entered the AE detector to thernumber that entered the veto detector, the relative percentages of ions that actually stopped in the implantation detector were 3H” (0.17%), 6He2+ (0.56%), 9Li3+ (0.83%), ”Be“ (0.62%), and 15B5+ (97.8%). Notice that, most of the 3H passed through the implan- tation detector and all the 15B stopped in it. The purity of the A1200 secondary beam for this experiment is summarized in Table 2.1. AS indicated in Figure 2.3, the implantation detector was partially surrounded by Sixteen large rectangular (157 cm by 7.6 cm by 2.54 cm thick, each) 80412 plastic neutron detectors bent in a one meter radius of curvature. The gap between adjacent neutron detectors had an area of approximately 800 cm2. Neutrons leaving the central implantation detector and interacting with any part of any one of the sixteen neutron detectors would have a uniform flight path of one meter. The Sixteen detectors covered a total solid angle of approximately 1.9 steradians. The production rate of 15B was sufficiently high that the cyclotron beam was cy- cled on and off, discussed below, and neutrons were observed during the beam-off period. The fl-decay of the 15B was detected by two photomultiplier tubes (1.9 cm diameter, HAMAMATSU H3167) attached to the implantation detector. The cal- culated mean-time of these signals served as the start for the neutron time-of-flight measurement. Each neutron detector also had two photomultiplier tubes (7.6 cm diameter, TH ORN EMI .9821 B) and the mean-time served as a neutron time-of-flight stop. Figure 2.6 is a schematic diagram of the electronic setup used for the 15B decay experiment. The electronic modules used for the secondary beam purity time-of-flight measurement are Shown (beam On period), as are the electronic modules used for 23 the fl-delayed neutron time-of-flight measurement (beam Off period). The electronic modules needed to pulse the primary cyclotron beam on and off, in addition to those necessary for obtaining a half-life measurement during the beam Off period, are Shown and details concerning their use are described later in this chapter. (This setup could remain essentially the same for other ,B-delayed neutron decay experiments). 24 Neutron Detectors Flight Path 100 cm . Implantation ‘ -~\ I , .. Detector D ./ ‘~“ 158 "’I "\-\ it “ lb Beamtine W “m Silicon ‘-~.\ Detectors a'/." ' B : Aluminum Kapton Degrader ' Window 20 cm Figure 2.3: Schematic drawing of the N SCL neutron detector array and the experi- mental setup. The numbering of each neutron detector is consecutive going from # 1 to #16. s 2 an 00. .‘g VEl'O \ cm W?!” *‘ss‘? 2‘“ 5cm 3.8M 7501! Figure 2.4: A close-up view of the detectors (implantation and the two silicon surface barrier) and associated hardware located at the center of the neutron detector array. 26 COUNTS/CHANNEL l-rl-l.l.. ‘200 A i 300‘ 400 CHANNEL N0. 10° “UL COUNTS/ CHANN EL CHANNEL NO. Figure 2.5: Energy spectra obtained from the AE detector and the veto detector (located at the center of the neutron detector array) for the implantation of the “B secondary beam. 27 Table 2.1: Summary of the A1200 beam purity for the implantation of the 158 sec- ondary beam. 0 15B beam purity monitored by time-of-flight measurement (start from start detector at “Image 1” of A1200, stop from AE detector signal) and energy loss in AB detector. 0 A1200 secondary beam purity from AR detector: - 3H” 2.7% — 6He2+ 1.7% - 9Li3+ 1.3% - ”Be“ 0.8% — 1535+ 93.5% o A1200 secondary beam purity that actually stopped in implantation detector (determined from AE and veto detectors): - 3H” 0.17% — 6He2+ 0.56% - 9L13+ 0.83% - ”Be” 0.62% — 15B“ 97.8% 28 a ' - 1 [shaft—'1 15° I 01558- 9 rue 5739 9 scars on E 9 we 1' etc so —— W or me > scare me as: f\ E-vero M! l a soc are to —— m I“ sror > sense not. W_ > one ornc'. “ > o __ m _> scares 9 5109 an: Ohio l 9 nesnm arc E—9 CYCLOTRON °ULSE m ‘01 > SCKER more"?! D (ON) r > an -2 no ';0 33CALER (HG'OM [- ' l 9 an -1 -/ cro (OFF) . l- m a scare (no-rout; 11m. scare: , DETECT. (HO-TOYAL.L..v51 RIGHT) 931T REES“! >roc con sum ~>conmrea sum ADC GATE >ooc SAVE ,1 coo 1—91'0: can STOP (2901" ‘5) —E >Toc can srcr (1000s F51 w— >OCC l NEUT. 1 ITECT. roc srcr > SCALER > em-a 714300614 0:31 > SCALE! ./ ADC - Analog to digital converter CDC — Gate delay generator AMP - Shapmg amplifier MG - Master 5‘“ C PD - Constant fraction discnminator QDC - Charge to digital convene: DCC - Dual gate generator RTC - Real time clock FA - Fast amplifier TDC - Time to digital converter FO - Fanout w - Time delay Figure 2.6: Schematic drawing of the electronic setup used in the 15B decay study. This setup could remain essentially the same for other B-delayed neutron decay ex- periments. 29 2.3 Neutron detector efficiency The neutron detection efficiency of the neutron detector array was determined as a function of threshold setting using a plutonium-beryllium source (PuBe source) positioned at the center of the detector array. In addition, a small liquid scintillation detector which will be referred to as the standard detector (30501, 6.75 cm diameter by 3.60 cm deep), whose efficiency could be reliably determined to within 5% using a Monte-Carlo efficiency code [Ce79], was also placed a distance of one meter from the PuBe source to be used as a reference in our efficiency calibration. The PuBe source produces neutrons in coincidence with a 4.4 MeV 7-ray through the 9Be(“He,n)”C* reaction. The 4.4 MeV 7-ray produced in this reaction was detected in a 5 cm diameter by 10 cm deep BaFg detector and served as a time-of-flight start Signal. The Ban detector was used here because it had fast timing characteristics comparable to the implantation detector, but unlike the implantation detector, it also had superior stopping power to identify the full energy of the 4.4 MeV '7-ray. Neutron time-of—flight spectra were obtained for each of the Sixteen array detec- tors in addition to the standard detector (here the standard detector had a neutron threshold set at 0.2 MeV electron-equivalent energy). Figure 2.7 shows the time-of- flight spectrum obtained for one of the array detectors (each of the other fifteen were very similar) and the time-of-flight spectrum obtained for the standard detector. The “fast” 7—ray peak seen in each spectrum established “time-zero”; this peak is due to the PuBe source producing 7-rays (in addition to neutrons) in coincidence with the 4.4 MeV 7-ray. The peak labeled “cosmic” resulted from cosmic particles passing through a neutron detector first and then passing through the implantation detector and triggering the master gate of the data acquisition system; a peak appeared in this same channel location of the time-of-flight spectra when a 7-ray source was placed 30 on the outer side of a neutron detector. The peak labeled “flag” was a diagnostic marker written into software to indicate when a neutron detector did not have an event occurring within a selected time window. Having an accurate time calibration of each spectrum (obtained by using an ORTEC model # 462 time calibrator) and a fixed flight path of one meter, neutron energy “bites” were obtained from each time-of-flight spectrum (the sixteen array detectors and the standard detector) for neutrons with kinetic energies in the likely energy range for the decay of 15 B (1.8, 2.8, 3.2, 4.3 and 4.8 MeV; this deduced from the known states in "’C and the neutron separation energy of 14C [Aj91], and Shell-model predictions [Cu86]). For 1.8 MeV neutrons, an energy bin (bin # 1) of 1.6 MeV to 2.0 MeV was selected; the calculated Monte-Carlo neutron detection efficiency for the standard detector was 17.6% for 1.60 MeV neutrons and 22.9% for 2.0 MeV neutrons (hence, an average efficiency of 20.3% for this energy bin). For 2.8 MeV and 3.2 MeV neutrons, an energy bin (bin # 2) of 2.4 MeV to 3.4 MeV was selected; the calculated Monte- Carlo neutron detection efficiency for the standard detector was 24.0% for 2.4 MeV neutrons and 23.9% for 3.4 MeV neutrons (hence, an average efficiency of 23.95% for this energy bin). Lastly, for 4.3 MeV and 4.8 MeV neutrons, an energy bin (bin # 3) of 4.0 MeV to 5.0 MeV was selected; the calculated Monte-Carlo neutron detection efficiency for the standard detector was 22.9% for 4.0 MeV neutrons and 21.9% for 5.0 MeV neutrons (hence, an average efficiency of 22.4% for this energy bin). Figure 2.8 shows these three energy bins for the PuBe time-of-flight spectra. The efficiency of each array detector was then determined by (1) taking the ratio of number of neutrons detected in an array detector and the standard detector as a function of energy (number of neutrons in the specific energy bin), (2) normaliz- ing for the solid angle of the array detector (119.5 msr) and the standard detector (3.585 msr), and (3) normalizing according to the calculated Monte-Carlo neutron 31 detection efficiency for the standard detector for the Specific energy bin (using the average efficiency specified in the previous paragraph). For purpose of example, the neutron detection efficiency of array detector # 1 for 1.8 MeV neutrons was deter- mined as follows: _7735 3.858 —-2—09 x—1195x0.203X100=22.5% (2.2) The estimated error associated with this measured efficiency accounted for the number of neutrons available for the measurement, the 5% uncertainty in the Monte-Carlo calculation, and an additional term to account for uncertainties related to the PuBe energy bin (this estimated to be 5% for bin # 1, 1% for bin # 2, and 2% for bin #3), and was determined as follows (for bin # 1, det # 1): ¥5v[./20m 7735 209 (7735 ) + (0.05)2 + (0.05)2 = 0.100 (2.3) As such, array detector # 1 had a detection efficiency of 22.5:1:2.25% for 1.8 MeV neutrons. Table 2.2 summarizes the neutron detection efficiency measurements for the sixteen array detectors; included is the estimated error associated with each measure- ment in addition to the mean and standard deviation of the efficiency measurements. 32 toooo-vfifivv...-.-,.- 21‘ 7peak : 8000 t: / Array 1 .) Detector COUNTS/ CHANNEL CHANNEL NO. ‘00"*'l""r"'rrr . i . a 7peak , ...1 ’ 3 ‘j ‘ {a 30°F 5 Standard ‘ g : Detector 1 Q zooL J E * .2 a r t o 100: E - o 100 zoo 300 Figure 2.7: Time-of-flight spectra obtained from an array detector and the small, standard detector using the PuBe neutron source. These spectra were used, in part, in determining the neutron detector array neutron detection efficiency. The peaks labeled “flag” and “cosmic” are explained in the text. 33 6000 Array Detector 4000 8000 2000 COUNTS/CHANNEL 1000 o as 150 175 200 225 250 ' CHANNEL NO. 250 Standard ' Detector 200 150 100 COUNTS/CHANNEL no no 150 200 220 240 CHANNEL N0. Figure 2.8: Energy “bins” selected from the PuBe neutron source time-of-flight spec- tra. 34 Table 2.2: Summary of the measured neutron detection efficiencies (using the PuBe source) for the Sixteen array detectors. Listed are the measured efficiencies, including the estimated error associated with each measurement, for the detection of 1.8 MeV, 3.0 MeV and 4.5 MeV neutrons. Also included is the mean and standard deviation of the sixteen measurements for the three energy bins. [ Detector ]] 1.8 MeV [ 3.0 MeV I 4.5 MeV II # l 22.5i2.25% 21.8:‘l:l.27% 18.0:l:1.11% # 2 20.7i2.07% 20.6:1:l.20% l7.5:i:l.08% # 3 23.3:l:2.33% 21.8il.27% l7.8:l:l.10% # 4 23.2:l:2.32% 22.4:i:l.30% l7.0:l:1.05% # 5 21.742.17% 21.441.24.170 16.611.03‘711 # 6 22.542.25% 224413070 17.1:l:1.06% # 7 22.3:122.23% 22.1:i:l.28% l7.4:l:l.08% # 8 21.7:lz2.17% 21.3il.24% l7.6:f:l.09% # 9 21.9:fz2.19% 22.7:l:l.32% 17.9:l:1.11% # 10 2104210170 240414096 17.1:t1.06% # 11 22.0i2.20% 21.7:l:l.26% l7.9:i:1.ll% #1 l2 20.7:1:2.07% 21.2:t1.23% l7.1:i:l.06% # 13 22.342.23% 22.0:l:l.28% 17.4:t1.08% # 14 23.4:l:2.34% 22.3:1:1.30% l5.9:l:0.98% # 15 24.042.40% 22.141.29% 17.4:1:1.08% # 16 23.2:t2.32% 21.8:1:1.27% l5.6:l:0.96% a,” 22.3 22.0 17.2 Jeff II 1.02 0.78 0.71 35 2.4 Comparison of the Measured (PuBe) Efficiency to a Monte-Carlo Calculated Efficiency for an Array Detector The measured neutron detection efficiency of an array detector (det # 1), which was obtained using the PuBe source, was compared to a Monte-Carlo [Ce79] calculated efficiency. The neutron detection efficiency of a detector is a strong function of the detector’s threshold setting. Typically, the threshold setting of a neutron detector is determined using 7-ray sources which, in their interaction with the scintillation material, produce Compton edges of specific energies. For example, a Compton edge obtained using a 60C0 source (which yields a Compton edge of approximately 1.0 MeV) with the standard detector used in the PuBe efficiency measurement appeared at channel 103 of the detector’s pulse height (energy) Spectruml. Using a ‘34Cs source (which produces two Compton edges, one at 0.42 MeV and one at 0.61 MeV) two Compton edges appeared in the pulse height Spectrum at channel 42 and channel 60. These are Shown in Figure 2.9. A threshold set at channel 20 of the detector’s pulse height spectrum, therefore, would correspond to a 0.2 MeV electron-equivalent neutron energy threshold (equivalent to approximately a 1.0 MeV neutron energy cut-off). For an array detector, establishing the known threshold setting was more compli- cated because the pulse height channel a Compton edge appeared at was dependent on the location along the detector 0a 7-ray source was placed (varying distances from the right and left photomultiplier tubes). Figure 2.10 Shows the five positions a colli- mated 60Co source was placed at in order to determine the detector’s threshold setting and its dependence on position. Figure 2.11 Shows the Compton edges obtained from 1The position of half-height was used to denote the Compton edge of all appropriate measure- ments in this work. 36 the left and right Sides of array detector # 1 for these five positions. Referring to the electronics diagram (Figure 2.6), a logical “and” was required between the left and right Sides of an array detector for an event to be valid. For this reason, the validity of an event occurring on the left half of the detector would be determined by the Signal detected in the right photomultiplier tube and its associated threshold setting (Since, for such an event, the right signal is smaller then the left signal and hence the limiting factor), while the validity of an event occurring on the right half of the detector would be determined by the detector’s left Side. Referring to Figure 2.11 and observing the Compton edge obtained from the detector’s right Side for positions # 1, 2 and 3 in addition to observing the Compton edge obtained from the detector’s left side for positions # 3, 4 and 5, an average threshold of 0.12 MeV electron-equivalent energy was estimated (equivalent to approximately a 0.8 MeV neutron energy cut-off). A Monte-Carlo efficiency calculation [Ce79] was performed for array detector # 1 using the 0.12 MeV electron-equivalent threshold setting. The results of the measured (PuBe) and Monte-Carlo calculated efficiencies are shown in Table 2.3 (not including solid angle). The overall agreement is quite good. 37 3000, ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' 2500:” °°Co 1 ..J . a : 1 3 2°“? 1.0 MeV 1 o . ,/ : E 1500*:- 1 a : « :3 1000:” 1 O > . 0 ; I 500: j a J 1 o L - . l - . . A L r —L . l . . .. . 0 so 100 150 200 250 CHANNEL N0. 2500r"''I“*'r"v'lf'*'l"*4 L 1 . 134 , ..1 3°“? CS ‘1 I 0.43 MeV I 1500- p/ 1 o » 1 19 1000: '2 E . 0.61 MeV . s : ‘ 500' / - p 1 I I o A - A l a . l . . AmLmA . . 14 L . A 0 so 100 150 zoo zoo CHANNEL NO. Figure 2.9: Compton edges obtained in the pulse height Spectrum of the standard detector using “Co and 13‘Cs 7-ray sources. Note that the location of the Compton edge was taken to be the half-height of the edge. 38 Pos. Figure 2.10: Array detector showing the five positions a 6"C0 source was placed in order to determine the detector’s neutron threshold setting and its dependence on position. The source was collimated and placed flush against the detector. 39 LEFT RIGHT 100 --., vvvvvvvvvvvv I“': WW1, so POS. 1 ~; 1:: P08. 1 —; so : 75 _ 20 1 25 '3 0 -- - - --L-- ”nu-A1 0 - 1----m---1----1 0 100 200 300 400 500 0 100 200 300 400 500 100 '1"'I‘**'1'rr so POS. 2 '2 00 -I 40 -I 20_ ~I .4 0 . --_--1----1---- m 0 100 200 300 400 500 300 400 500 z 1'50 "'I'Ififrfifi'fi" “1 "f; ' "I""I'rfi1"‘ 2 P08. 3 P08. 3 i U -: -§ \ lleL hri-L-J --1rn--1--L3 U) zoo 300 400 500 300 we 500 E 1"fir'r” IF" I '3 :3 P08. 4 ‘ P08. 4 -3 O f _i U '- _s [Alhxmnh 11......14---: 300 400500 "r**"r‘ ": "T"'l "', POS.5 4 P08. 5 ' 3 '. d - I 1 - d l .. L1---LL._--ALL A ‘ AAAL11122L- L- 100 200 300 400 500 100 200 300 400 500 CHANNEL NO. Figure 2.11: Compton edges obtained, using a 60Co source, from the left and right Sides of array detector # 1 for the five positions Shown in Figure 2.10. 40 Table 2.3: Comparison of measured (PuBe) and calculated (Monte-Carlo) efficiencies for neutron array detector # 1 as a function of neutron energy (not including solid angle). Energy Measured Calculated (MeV) (PuBe) (Monte-Carlo) 1.8 22.5:l:2.25% 22.0% 3.0 21.8:l:l.27% 20.8% 4.5 18.0:l:1.11% 18.8% 41 2.5 Exploring Position Sensitivity with the Neu- tron Detector Array While a technique which would identify and confine a neutron interaction to a specific location on an individual array detector was not needed for the 15B decay experiment (since the neutrons were emitted isotropically from the implantation detector), the ability to achieve position sensitivity with individual array detectors was explored. It is already possible to determine events occurring in different array detectors simulta- neously; for example, in the 153 experiment it would have been possible to identify that events had occurred in detectors # 1, 4 and 14, or any combination, from a single decay. Going a step further and being able to associate an event with a specific sector of a single detector could expand the usefulness of the neutron detector array in angular correlation experiments. To determine if position sensitivity was possible with an array detector, a colli- mated 60Co source was placed at positions one through five of an array detector (refer to Figure 2.10). Two techniques were then investigated. One technique used the pulse height (energy) signal measured at each end of the detector, the other technique used the timing signal measured at each detector end. The technique using pulse height signals to determine position is based on the principle of light attenuation through the plastic. When the 60Co source is placed at array detector position # 3 (center), the pulse height measured from the left and right sides of the detector should be the same; this of course if the two sides are gain matched. When the source is placed at position # 1, the pulse height measured at the detector’s left side is larger than that measured at its right side. Simply, the more plastic the light must travel through before reaching a photomultiplier tube, the more the light is attenuated, hence the smaller its measured pulse height signal. Two 42 functions were used to obtain position information from pulse height measurements. The first assumed linear attenuation of light through the plastic scintillator: L ulschei ht POnga, = 0 set + 310 e x p g 2.4 I ff p Lpulseheight ‘l' Rpulacheight ( ) The second assumed exponential attenuation of light through the plastic: L u so ci POScxpommgaz = offset + slope x (MAM) (2.5) Rpulaeheight The technique using timing signals to determine position information is based on the fact that light traveling through the plastic scintillator travels at a finite and measurable velocity (roughly 15 cm/ns). When the 60Co source is placed at position # 3 (center) of the array detector, light reaches the left and right photomultiplier tubes at nearly the same time, about 5.2 ns after being created. When the 60Co source is placed at position # 1, light will reach the left photomultiplier tube in about 1.7 us, while it will take about 8.7 us to reach the right tube. The function used to obtain position information from the timing signals was: Rtime "’ Ltime t g Offse + S 0pc x Rtimc 'l' Ltimc ( ) The method employing pulse height signals supplied position sensitivity with a res- olution of approximately 25 cm (FWHM) using the linear function and approximately 20 cm (FWHM) using the exponential function. The method employing timing sig- nals proved superior, supplying position sensitivity with a resolution of approximately 13 cm (FWHM). Figure 2.12 shows the results of placing the 60Co source at the five detector locations and using the “position through timing” function (Equation 2.6); those shown in the figure are the results obtained with detector # 6. By taking the centroid of the five position peaks shown in Figure 2.12 and their associated array positions in 0 (-30°for pos # 1, —15°for pos # 2, 0°for pos # 43 3, 15 ° for pos #4 and 30 ° for pos # 5), a linear function was generated that would identify an event to a detector position in 9. It should be noted that the position resolution of 13 cm corresponds to approximately 7 ° in 0. Table 2.4 summarizes the specifications of the N SCL neutron detector array de- scribed throughout this chapter. 44 2500....r....,....,....,....r H 1 ' r/i ...] 20001" V o _ 1:: Q ‘ a. a .. 2 2 . m J <1 1500» g 9* . N _ i3: " Q. m - 4 0 ~ 0 V1 . \ l“ ‘1. O 00 E CL 5" 1000 ' _. z 1 D . 8 . . 500d - 0b 1 111 1 1 1 l 1 1 1 111 1 1 1 L 1 ...- . 0 25 50 75 100 125 CHANNEL NO. Figure 2.12: Results of placing a collimated 60Co source at the five array detector locations shown in Figure 2.10 and using the “position through timing” function (Equation 2.6). 45 Table 2.4: Summary of the N SCL neutron detector array specifications. . Implantation detector constructed from 30412 plastic scintillator (2 cm square by 1 cm deep) and HAMAMATSU H3167 (1.9 cm diameter) photomultiplier tubes. . Neutron detectors constructed from 30412 plastic scintillator and TH ORN EMI 98218 (7.6 cm diameter) photomultiplier tubes. . Sixteen individual neutron detector elements in total array. . Total array active area covers a solid angle of approximately 1.9 steradians. . Each neutron detector element (157 cm by 7.6 cm by 2.54 cm thick) has an active area which covers a solid angle of approximately 120 msr (0.076 rad in angle 0, 1.57 rad in angle 45). . Gap between adjacent detectors measures approximately 800 cm2 or approxi- mately 0.05 rad in angle 0 (approximately 70% area of one detector element). . Neutron energy determined by time-of-flight method with flight path equal to 1 meter. Time-of-flight start from calculated meantime of implantation detector, time-of-flight stop from calculated meantime of neutron detector. . Total timing resolution of detectors determined by combination of electronics contribution (approximately 1 ns) and neutron-energy dependent time-uncertainty owing to a flight path uncertainty (for a typical detector, flight path uncertainty is approximately 4 cm). As such, total time resolution (FWHM) for detector is 2.4 ns for 1.8 MeV neutron, 1.9 us for 3.2 MeV neutron, and 1.7 ns for 4.8 MeV neutron. . Position information (in angle 0) for each neutron detector determined by timing comparison of left vs. right side of detector ($33.21.). This results in a position resolution of approximately 13 cm (FWHM) or 7 in angle 6. 46 2.6 Cyclotron Beam On/ Beam Off Cycles for De- cay Studies In order to study the decay of 15B it was necessary to pulse the primary cyclotron beam on and off for fixed intervals of time. Since the production rate of 15B was relatively high considering its 10.5 ms half-life (one 15B ion produced per 1.9 ms), it was most efficient to pulse the beam at fixed intervals. In decay studies for very exotic species, the half-lives tend to be very short (large A) and the times between implantation of these nuclei tend to be long (many times l/A). In these cases, it is most efficient to shut off the primary beam after each arrival, and the decay of the single atom is observed; this technique is explained in detail by Mikolas [Mi89]. The pulsing of the primary beam was accomplished with a gate module that periodically sent a logic signal to a fast phase shifter in the rf transmitter of one of the “dees” of the K1200 cyclotron. The cyclotron beam was interrupted within approximately 40 us [Mi89]. To measure the decay branches of 158 to neutron- unbound states in 15 C a 50 ms On / 50 ms Off cycle was used for part of the experiment and later changed to a 20 ms On/40 ms Off cycle. 15B ions were deposited in the implantation detector during the beam on time and decays were monitored during the subsequent beam off time. A real time clock module started at the beginning of each beam off interval (zeroed at the beginning of each subsequent beam on interval) was used to measure the time of each event relative to the end of the beam on period. The total beam off period was easily measured with the real time clock. The beam on period was calibrated by recording events from a 60C0 7-ray source positioned near the implantation detector (during these runs there was no cyclotron beam) for the different time cycles. By ratio of the number of sprays observed during the two periods and knowing the beam off time period exactly, the exact times of the cycles 47 turned out to be 49.23 ms On/49.80 ms Off and 20.33 rns On/39.55 ms Off. For purpose of example, the 50 ms/ 50 ms cycle was calculated in the following manner. In order to determine the exact time of the Off cycle, the last channel of the time spectrum from the real time clock was simply multiplied by the time per channel which was controlled by a crystal oscillator: 102ch. x 0.4883? = 49.80ms. (2.7) To determine the exact time of the On cycle, the exact time of the Off cycle was multiplied by the ratio of 7 events recorded for the On / Off cycles: 7129 49.80ms x 72—1—2- _ 49.23ms. (2.8) It should be noted that the computer dead time and sampling efficiency was the same for the On and Off cycle. To determine the number of 15B decays that led to bound states in 15C (tl/g = 2.449:l:0.005 s, [Aj91]), the cyclotron beam cycle was later changed to 4.847 3 On/ 5.719 s Off. Here, 15B ions were deposited in the implantation detector during the beam on period and 15C decays (,B-emission) were counted during the beam off period. To determine the efficiency of the implantation detector for 15C fl-particles, the A1200 was used to produce 15C and 17N and these ions were deposited in the implan- tation detector using a 4.762 3 On/ 7.063 3 Off cycle. The results of this implantation are discussed later. Table 2.5 lists the measurements recorded in order to determine the exact times of the different time cycles. 48 Table 2.5: Beam On/beam Off 60Co 7-ray source measurements used to calibrate exact times of On/ Off cycles. Listed are the time cycles, number of 7 events recorded during On/ Off cycle, time calibration of real time clock, last channel of Off cycle time spectrum, and calculated exact times of beam On/ beam Off cycles. time cycle 7 events time/ channel last channel exact time (On/Off) (On/Off) (Off cycle) (On/Off) 50 ms/50 ms 7129/7212 0.4883 ms 102 49.23 ms/49.80 ms 20 ms/40 ms 8270/16088 0.4883 ms 81 20.33 ms/39.55 ms 5 s/6 5 7764/9161 0.03125 5 183 4.847 s/5.719 s 5 s/7 3 3165/4694 0.03125 8 226 4.762 s/7.063 s L Chapter 3 Results and Analysis This chapter presents the experimental results and analysis involved with measuring the decay of 15B. The opening section gives a summary of the different experimental runs used to accomplish this measurement. The information provided not only gives the reader a concise overview of the entire experiment, but it also contains valuable information about A1200 exotic nuclei production rates and systematics which can be helpful in other decay studies. In the second section, the 15B half-life obtained from this work is compared to the published values of earlier studies. The third section presents the results of depositing 15B ions into the implantation detector and observing the fl-decay of 1"’C to determine the 15B B-decay branch to 15C bound states. The fourth section concentrates on the 15 B fl-decay branch to unbound states in 15C, and includes the results of the 15B fi-delayed neutron time-of-flight measurements. In the final section the ,B-decay branching ratios of 15B are presented and discussed. 49 50 3.1 A Summary of the Experimental Runs Made to Measure the Decay of 15B The experimental runs involved with the present work can be divided into three basic groupsl. The runs in Group One involved the deposition of 15B ions into the implantation detector during the beam on period and then monitoring their decays during the beam off period. These runs were used to obtain a half-life and fl-delayed neutron time-of-flight measurements of 15B; this group included runs (which will be referred to as) # 1, 2 and 3 (50 ms/50ms — on/off cycle) and runs # 4 through 10 (20 ms / 40 ms - on/off cycle). The runs in Group Two involved the deposition of 15B ions into the implantation detector during the beam on period and then monitoring 150 decays during the beam off period in order to determine the 15’B fl-decay branch to 150 bound states; this group included runs # 11, 12 and 13 (5 s/6 s — on/off cycle). Lastly, a run in Group Three involved the deposition of 15C and 17N ions from the A1200 radioactive beam device into the implantation detector during the beam on period and then monitoring their decays during the beam off period. This run was used to determine the detector’s fl-decay detection efliciency for nuclei other than 15B (specifically 15C); this will be described in more detail below. The third group included run # 14 (5 s/7 s — on/of'f cycle). 3.1.1 Group One Experimental Runs Two different beam on/ beam off cycles were used for the Group One experimental runs, the 50 ms/50 ms and the 20 ms/40 ms. Although either cycle alone could have provided the half-life and fl-delayed neutron time-of-flight measurements of 15B, the 20/40 was found to be more efficient (described below). In addition, using the 1Note that these do not include the PuBe source efficiency runs or the short duty cycle runs used to determine the exact times of the beam on/ off cycles. 51 different cycle times provided a test to see if similar results would be obtained under different conditions; for example, the implantation detector’s B-detection efficiency. Table 3.1 provides a summary of specific quantities related to the Group One runs. The total time of each run (to the nearest 0.01 s) was written to magnetic tape by the data acquisition program. The total number of 15B ions deposited in the implantation detector for each run was determined event by event from the particle identification in the AE detector/time-of-flight measurement and then normalizing this measurement to account for the beam on computer dead time”. Once the actual number of implanted 15B ions was known, the A1200 production rates were easily determined by using the total time of each run and the exact times of the beam on/off cycle (Table 2.5). It should be noted that the A1200 15B production rates (ions per ms) for runs 1 through 10 were, overall, fairly uniform with a high of 0.647, a low of 0.418, the mean value was 0.532 with standard deviation of 0.081. This variation can be accounted for by variations of the K1200 cyclotron primary beam current. For purposes of discussion, “beam on period” and “implantation period” can be considered synonymous, as can “end of the implantation period” and “beginning of the beam off period”. The last column of values in Table 3.1 is the sum of the number of 15B ions that existed at the end of each implantation period for the entire run. Consider the following example: it was determined (described below) that for run #1, 9.34 15B atoms were present in the implantation detector at the end of each implantation period. With a total of 32,445 implantation periods for run #1, the total number of 15B atoms present at the end of all the implantation periods for run # 1 was 3.03E5; this is the number listed in Table 3.1. This number is smaller than 2The computer dead time was determined by the ratio of two scaler values that were read for all measurements every time an event occurred, one scaler value being read uninhibited and the other read only when the computer was not busy. 52 the number of 15B ions implanted (third column in Table 3.1) because some of the 15B atoms decayed while the implantation was still in progress. It is the number of atoms present at the end of the implantation period (when decays are able to be observed) that comprise the sample population from which decay-related observables, like half- life, are determined. Decays that occur while the implantation is still in progress contribute nothing to these determinations. The number, N, of atoms present at any time, t, during the implantation period increases in proportion to the production rate, R, and decreases due to decay: dN = Rdt — /\th. This simple differential equation can be solved for N: dN _ dt R-AN dN m - / d‘ R — AN = 06"“ R— Ce‘“ N: /\ Knowing that at time zero, N equals zero and at time infinity N equals R/A gives: N = —(1 - e‘“) (3.1) This expression assumes that the rate of production, R, is constant throughout the run. If this rate fluctuates considerably during the run, the implantation should be divided into time intervals, t.-, during which time the rate, R,, is steady and then N can be determined as a summation of many short runs. In the present work, the production rate during each run was assumed to be constant. The validity of this assumption will be shown later in the section on the implantation detector’s fl-detection efficiency. 53 The number of 15B atoms that existed at the end of each implantation period, referred to as No 3, is determined by knowing the A1200 production rate in ions per ms, R153, the 15B decay constant A155 = (6.60:1:0.07)E-2 rns'1 [Aj91], and the exact time of the implantation period, ton: R153 N _ 0 Aug (1 - e“*“B‘°") (3.2) To account for 15B atoms that were “left over” (hadn’t decayed) from the previous im- plantation period, referred to as N (e ”we", the exponential decay of No is determined for the time of one implantation period, ton, and one beam off period, to”: Nlcftovcrs = Noe-A(ton+tou) (3'3) Nlcftovcr, is only (1.8 x 10‘2)No for the 20/40 cycle and (1.4 x 10‘3)No for the 50/50 cycle. Left overs from two cycles ago would result in (1.8 x 10’2)2No for the 20/40 cycle and (1.4 x 10‘3)2No for the 50/50 cycle. It is clear that left overs from even earlier implantation periods become insignificant. It was assumed therefore, that the number of 15B atoms present at the end of each implantation period, No+1cftou¢r,, is well approximated by the expression: NO-Heftovera = N0(1 + e-A(ton+tojj)) (3.4) The values in the last column of Table 3.1 were determined by multiply this quantity by the total number of implantation periods during an entire run. When the total number of implanted 15B ions is compared to the number of 15B atoms still remaining at the end of all the implantation periods, it is observed that the 20/40 cycle is nearly twice as efficient as the 50/50 cycle. Almost 55% of the implanted 15B ions remained to be studied at the end of the implantation period for the 20 / 40 runs, where as this quantity was less than 30% for the 50/ 50 runs. From Eq. 3N0 does not account for 1"’3 atoms “left over” from previous implantation periods. 54 3.1, it can be shown that when the implantation period, tan, is very long compared to the half-life of the species being implanted, a limit of R//\ is reached. When this is the case, new activity is being formed at the same rate at which the older activity decays; this is referred to as secular equilibrium. If the implantation period is twice the half-life, 75% of the maximum activity is produced and when the implantation period is three half-lives long, this will give 88% of the maximum activity. By keeping the implantation period between two and three half-lives, the accelerator is being used most efficiently. 55 Table 3.1: Summary of part of the experimental runs (Group One) involved with measuring the decay of 15B. These runs were used to obtain a 15B half-life measure- ment and fl-delayed neutron time-of-flight spectra. Listed are the run number and corresponding on/off cycle, the time of each run, the total number of 15B ions de- posited in the implantation detector (per run), the A1200 15B production rate, and the total number of 15B atoms (per run) remaining at the end of the implantation period (see text for explanation). Run # Run time 15B ions A1200 “3 15B atoms (On/ Off) (sec) implanted production remaining at end (per run) rate (ions/ ms) of implan. period (per run) 1 (50/50) 3,213 1.033136 0.647 3.03E5 2 (50/50) 4,560 1.194136 0.527 3.50E5 3 (50/50) 7,440 1.547E6 0.418 4.54135 4 (20/40) 10,183 1.566136 0.453 8.58135 5 (20/40) 7,894 1.186E6 0.442 6.49E5 6 (20/40) 7,163 1.378E6 0.566 7.54135 7 (20/40) 10,797 2.036E6 0.555 11.2E5 8 (20/40) 14,175 2.341136 0.486 12.8E5 9 (20/40) 14,188 2.826136 0.587 15.5E5 10(20/40) 4,880 1.064E6 0.642 5.83E5 E = 84,493 E = 16.11E6 E = 0.532 E = 7.90E6 (23hr,30min) (50/50 = 3.774136) 0' = 0.081 (50/50 = 1.11E6) (20/40 = 12.34136) (20/40 = 6.79E6) 56 3.1.2 Group Two Experimental Runs The second group of experimental runs (# 11, 12, and 13) involved the deposition of 15B ions into the implantation detector and then monitoring 15C decays (fl-emission, t1); = 2.449:l:0.005 s [Aj91]) in order to determine the 15B fl-decay branch to 15C bound states. Table 3.2 provides a summary of the Group Two runs. The three runs in this group all used the same on/off cycle (5 s/ 6 s). The runs are listed separately to demonstrate the consistency among the runs. The values in the last column of Table 3.2 are the number of 15C atoms remaining at the end of the implantation period and were determined using the same technique employed in the previous section (Eq. 3.4). It was assumed here that 100% of the 15B atoms ,B-decay to ”C bound states; this assumption, is of course, not true and is made only to demonstrate the implantation efficiency4 (approximately 55%). Since the half-life of 15B is so short (10.5 ms, [Aj91]) compared to the implantation period of 4.847 s for these runs, it is fair to assume that nearly all (99.7%) of the implanted 15B ions decay to some state of 15C by the end of each implantation period. It is almost as though a 15C ion beam of mixed energy states was being deposited into the implantation detector. 3.1.3 Group Three Experimental Runs The third and final group of experimental runs (# 14) involved depositing beams of 15C and 17N into the implantation detector in order to determine the detector’s ,B-decay detection efficiency for 15C decays. This efficiency is important to determine the ”’B fl-decay branch to 15C bound states from the Group Two runs. Table 3.3 contains the information for this run. 4Not to be confused with the implantation detector’s fl-detection efficiency ! 57 In run # 14 the A1200 was tuned such that both 15C and "N ions were present at the focal plane of the device and transported to the implantation detector. From the projectile fragmentation of the primary 180 beam, the production cross section for ”N is much greater than it is for 15C. While the A1200 was tuned for maximum transmission of 15C, the “tail” of the ”N momentum distribution appeared as a sizeable contaminant. The production rates of 15C and 17N for run 14, 0.43 ions/ms and 0.59 ions / ms respectively, confirm this. It was actually beneficial to have the "N ions, in addition to the 15C, in understanding the implantation detector’s fl-detection efficiency; this will be explained later. 58 Table 3.2: Summary of part of the experimental runs (Group Two) involved with measuring the decay of 15B. These runs were used to measure the ”B B-decay branch to 15C bound states. Listed are the run number and on/ off cycle (only 5 s/ 6 8 cycle was used for these runs), the time of each run, the total number of 15B ions deposited in the implantation detector (per run), the A1200 15B production rate, and the total number of 15C atoms (per run) remaining at the end of the implantation period assuming a 100% 158 fl-decay branch to 15C bound states (see text). Run # Run time 15B ions A1200 15B ”C atoms (On/ Off) (sec) implanted production remaining at end (per run) rate (ions/ ms) of implan. period (per run) 11 (5/6) 32,442 7.390E6 0.497 4.02E6 12 (5/6) 20,017 4.301E6 0.468 2.34E6 13 (5/6) 11,322 2.861E6 0.551 1.56E6 J__—_—_J__.__—_—___—____ 2 = 63,781 E = 14.55E6 5 = 0.505 2 = 7.92E6 (17hr,4§r_r1in) 0’ = 0.042 59 Table 3.3: Summary of part of the experimental runs (Group Three) involved with measuring the decay of 15B. This run was used to determine the implantation detec- tor’s fi-decay detection efficiency for 15C. Listed is the run number and on/off cycle (only 5 s / 7 s cycle was used), the time of the run, the total number of ions deposited in the implantation detector (per run), the A1200 production rate, and the total number of atoms (per run) remaining at the end of the implantation period. Run # Run time Ions A1200 Atoms (On/ Off) (sec) implanted production remaining at end (per run) rate (ions/ ms) of implan. period (per run) 14 (5/7) 1,825 3.187135 (‘50) 0.434 (150) 1.74135 (‘50) 4.327135 (1"N) 0.589 ("N) 2.99135 (17N) 60 3.2 A Measurement of the Half-life of 15B In the present work, decay curves for 15B inclusive fl-emission were obtained for the Group One runs (one through ten). A least-square fitting procedure which assumed a single exponential decay component and a constant background was used to deduce the half-life of 15B, and in addition, the activity present at time-zero, A0 5. The least- square fitting procedure could be applied to the data between specified beginning and end channels (these channels correspond to time). Since the decay is exponential, the half-life should be independent as to where the fit is begun and ended. For example, the same half-life should be obtained for a fit between channels # 5 to # 80 (2.44 ms to 39.06 ms) or channels # 10 to # 75 (4.88 ms to 36.62 ms) where the 2.44 ms and 4.88 ms correspond to time after the end of the implantation period (calibration of 0.48828 ms/ ch). Indeed, using these two different “fitting limits”, half-life values of 10.3:l:0.2 ms and 10.2:l:0.3 ms were obtained for 15B. The A0 value obtained, however, will depend on where the fit is begun and must be corrected for the exponential decay that occurs between the actual end of the implantation period and start of the data fit in order to obtain the true activity, AWN” present at the end of the implantation period. For runs one through ten, the fit to the data began at 2.44 ms after the end of the implantation period (ch. # 5) and AM,” was calculated as: A0 AWN“ = e—A158.(2.44ms) (3'5) Channel # 5 was choosen because this gave good fitting results for all ten runs. Other fitting limits were tried, giving very similar A0,,”e values once the appropriate compensation was made to account for the exponential decay. Table 3.4 is a summary 5A similar fitting procedure was tried in which the components’ decay constants could be fixed to include a ”Be component, in addition to the 153 component. The ”Be appeared to make no noticeable contribution to these decay curves. Calculations made by estimating the amount of 1"'Be that should decay along with 1"‘8 (determined from the A1200 beam purity and on/off cycle time) indicate the 12Be A0 should at most be 0.35% that of the ”B A0. 61 of half-life and AW”, values obtained from the decay of 15B during these runs. Referring to Table 3.4, there is good agreement among the different runs for the half-life measurement of “B. Figure 3.1 is the decay curve obtained by summing all the 20/40 cycle runs (4 through 10). The same fitting procedure used to fit the individual runs was used here, giving a half-life of 10.3i0.2 ms and AM,” of (3.56:1:0.02)E5 cts./ms (the error in this value represents both the statistical error from the fitting procedure and the error in the 15B decay constant needed to deter- mined it). The background component was 3.53E3 cts./ms (bkgdzl5B z 1:100); the reduced chi-square for this fit was 0.4. This half-life is in good agreement with the adopted value of 10.5:l:0.3 ms for ”B from the literature [Aj91]. It should be noted that the decay curve shown in Figure 3.1 is the result of having a total of almost 5 million 15B atoms in the sample population. The 5 million is determined by knowing the number of 158 atoms at the end of all implantation periods and then determining the actual number that decayed during the beam off period, to” (39.55 ms): Decoys = M0 — e‘mfitm) (3.6) 3153 Earlier studies were conducted at the Michigan State University National Super- conducting Cyclotron Laboratory of the ”B half-life by Curtin, et al. in 1986 [Cu86] and Samuel, et al. in 1988 [Sa88]; refer to Table 1.1. These groups used the N SCL Reaction Products Mass Separator (RPMS) [Ha81] to separate out the 15B nuclei produced in projectile fragmentation reactions. In each of these earlier experiments, a total of approximately 3000 “B decays were measured from which the half-life was determined. Comparing this number to the nearly 5 million of the present work, it is quite clear that the A1200 radioactive beam device can provide impressive production rates of exotic nuclei for decay studies. 62 In the present work, an additional decay curve was obtained for 15B by requiring B-neutron coincidences from which a half-life of 10.5:l:0.5 ms was obtained. Here, the 15B A0,"uc was 6.01E3 cts. / ms and the background component was 1.37 cts./ms (bkgd215B z 1:4400); the reduced chi—square for this fit was 1.08. This decay curve is shown in Figure 3.2. This measurement was obtained by requiring an event to occur in any one of the sixteen neutron detectors of the array in coincidence with a fl-decay in the implantation detector (this was done entirely in software). When compared to the decay for inclusive fl-emission, the ,B-neutron coincidence measurement had about a 44-fold decrease in background, as should be expected. 63 Table 3.4: Summary of the half-life, t1 ,2, and true activity present at the end of the implantation period, AOJWC, obtained from the decay of ”B inclusive ,B-emission for the Group One experimental runs (one through ten). Also included is the back- ground component for each run and the reduced chi-square for the least-square fitting procedure. |7Run # t1); A0,"ue Bkgd. RX2 (On/Off) (ms) (cts./ms) (cts./ms) 1 (50/50) 10.540.38 1.54134 1.29132 1.19 2 (50/50) 10.3:l:0.36 1.79E4 2.68E2 1.10 3 (50/50) 10.2i0.34 2.32E4 4.12E2 0.83 4 (20/40) 10.240.30 4.41134 6.99132 1.05 5 (20/40) 10,240.31 3.37134 6.25132 0.97 6 (20/40) 10.4:l:0.30 3.92E4 3.82132 0.78 7 (20/40) 10.3:1:0.29 5.83134 6.28E2 0.90 8 (20/40) 10.340.28 6.74E4 8.07132 0.86 9 (20/40) 10.4:h0.3l 8.23134 6.79132 0.74 10 (20/40) 10.440.32 3.07134 1.86132 0.77 Ema-,1... = 10.3 2 = 41.22134 owegghtcd = 0.11 (50/50) = 5.65E4 (20/40) = 35.57134 64 106 ’ ' T ' ' l ' f f r I f ' f f l 4 t1/2 = 10340.2 ms ACTIVITY (cts/ms) 104' - - - - l - 1 L 1 l . A . 1 l 1 n 0 10 20 30 TIME (ms) Figure 3.1: Experimental decay curve for ”B inclusive fl-emission obtained by sum- ming all the 20/ 40 cycle runs (4 through 10). The solid line corresponds to a single- component fit plus a constant background. 65 10000 - . I ’ 153 decay ‘ - requiring fi-n coincidence 5000‘ .‘ « ‘v. _. t1/2 = 10540.5 ms 3 2000 ~ ‘1 « \ a \9/ ‘Ib . E r ‘3 1 a i 1 , o . - <1 500 - ' ' I; 200 - 7 100 - - - - l 1 - 1 - l - - - - l - O 10 20 30 TIME (ms) Figure 3.2: EXperimental decay curve for 15B requiring fl-neutron coincidence. The solid line corresponds to a single-component fit plus a constant background. 66 3.3 15B ,B-Decay to 15C Bound States This section addresses the 15B fl—decay branch to bound states in 15C. Recall, the Group Two runs involved the deposition of 15B ions into the implantation detector during a 4.847 s beam on period and then monitoring the ,B-decay of 15C during a 5.719 s beam off period, and the Group Three runs involved the deposition of 15C and 1',N ions from the A1200 into the implantation detector in order to determine the detector’s fl-detection efficiency. 3.3.1 15C fi-Decay Following the Implantation of 15B The decay curve obtained from each individual Group Two run was fit with a least- square fitting procedure in which each component’s6 decay constant was fixed and its activity (A0) was a free parameter; the decay curve generated from the sum of these individual runs was also fit with this procedure. These results are summarized in Table 3.5 and the fitted decay curve for the summation of the three runs is shown in Figure 3.3. The least-square fit for these decay curves started at 0.375 s (channel # 3, 0.125 s/ch.) after the end of the 15B implantation to insure that essentially all the implanted 153 ions decayed (more about the decay of ”B during these runs will be mentioned later). Notice that the measurements from the Group Two runs were more sensitive to the longer lived A1200 impurities 6He (t1/2 = 0.807 s [Aj88]) and 9Li (tug = 0.178 s [Aj88]). Referring to Table 2.1, the percentage of A1200 secondary beam that actually stopped in the implantation detector was 0.56% 6He, 0.83% 9Li, and 97.8% "’3. Accounting for the number of 6He and 9Li atoms that would be present along with the 14.55E6 15B atoms implanted during these runs, 8.34E4 and 12.4E4 6The components for these runs include 15C and the known impurities 9Li, 6He, and a constant background. 67 respectively, and then the number of 6He and 9Li atoms which would be present at the end of the implantation period using Eq. 3.4, 1.96E4 and 0.657E4 respectively, the measured initial count rate (AWNC) should be 17.0E3 cts/s for 6He and 25.6E3 cts/s for 9Li, if the implantation detector was 100% efficient for the fl-particle detection of decays from 6He and 9Li. Referring to the results in Table 3.5, the measured AWN“. value was (6.5:l:1.7)E3 cts/s for 6He and (7.3:l:4.3)E3 cts/s for 9Li. These values are in reasonable agreement with the calculated estimates considering the large uncertainties in the A0 values and also that the implantation detector does not have 100% fl-detection efficiency. This efficiency will be addressed in the following subsection. Before the 158 fl-decay branch to 15C bound states can be deduced, the implan- tation detector’s fl-detection efficiency for 15C decay must be determined. 68 Table 3.5: Summary of the Group Two experimental runs in which ”B ions were deposited into the implantation detector during a 5 s beam on period and decays were monitored during a 6 s beam off period. The decay curves from these runs were fit with a least-square procedure in which each component’s decay constant was a fixed parameter and its activity was a free parameter. The components of each fit and the corresponding activity, A0, are shown in the fourth column. The adjusted activities, AWN“, account for the 0.375 s that elapsed between the end of implantation period and the beginning of the fit and are shown in the fifth column. The last column lists the reduced chi-square for the least-square fitting procedure. Run # time of 15B ions A0 from fit AW,“ RX2 7 run (s) implanted (10E3 cts./s) (10E3 cts./s) 11 32,442 7.390E6 8.3740.52(Bkgd.) 8.374052 0.90 35040.93 (15(3) 38941.0 27641.0 (6He) 38141.4 05440.87 (911) 2843.7 12 20,017 4.301136 4.7840.45(Bkgd.) 47840.45 1.21 2.514081 (150) 27940.90 0.664088 (6He) 09141.2 0.934076 (9Li) 4.0438 13 11,322 2.861136 2.8140.39(Bkgd.) 28140.39 0.97 12240.71 (15(3) 18640.79 02840.77 (6114:) 17741.1 0.24:1:0.67 (9L1) 1.0i2.9 11,12,13 63,781 14.55E6 l6.0::i:0.61 (Bkgd.) l6.0i0.61 1.10 (sum) 7.26i1.1 (15C) 8.07:1:1.2 4.68412 (6He) 64541.7 17041.0 (9L1) 7.31448 69 * i 15C decay following 1 implantation of 15B 20000 - """"""""""" b EEk'éfofifid— ’ " ' - ' 1 ’07 10000 _- ‘ \ . m 1 4.3 3 " \ \ E7 \ E 5000 I \ \ \ * < \\ \ \ \ \ \ \ \ \ \ \ 6H8 \ \ \ \ \ 2000 — \ ‘ \ - 7 \\ \ \ \ 19Li \ \ \ ‘ \ \ 1000 I1 1 1 1 L 1 1 4 A 1 . 1 . 1 l L - 1 l - - n -_1 L 0 1 2 3 4 5 TIME (s) Figure 3.3: Experimental decay curve generated by summing the three individual runs of Group Two. During these runs 153 ions were deposited into the implantation detector during the 5 s beam on period and decays were monitored during the 6 s beam off period. The solid line corresponds to a three-fit component (6He, 9Li, 15C) plus a constant background. The error bars are statistical. 70 3.3.2 The Implantation Detector’s fi-Detection Efficiency The implantation detector’s fl-detection efficiency for observing 15C B-decay and its efficiency for 15B fl-decay must be determined. Recall it was shown in Section 2.2 of the previous chapter that the 60 MeV/ A “B ions that entered the experimental vault came to rest at a depth of 5.2:l:1.2 mm in the 10.0 mm thick implantation detector. It can be assumed that all the implanted 15B ions decayed by fl-emission with a total half-life of 10.3i0.2 ms (half-life determined from the present work), without knowledge of what percentage of the decays populated bound states in 15C. Using the number of 15B atoms that remained at the end of the implantation period (listed in Table 3.1) and the measured activity as a result of these implantations, A0,truc (listed in Table 3.4), the efficiency of the implantation detector for ”B fl-emission was determined for the Group One runs; these data are summarized in Table 3.6. Referring to Table 3.6, there is good agreement among the efficiencies determined for the ten individual runs of Group One. It should also be noted such consistency between runs also supports the assumption that, for individual runs, the production rates were constant. The adopted value for the fl-detection efficiency of the implan- tation detector for 15B fl-emission is taken to be 80.6:l:2.3% (uncertainty taken to be 21:20). Now that the fl-detection efficiency of the implantation detector for ”B decay has been established, the Group Three run (# 14) can be addressed. Recall that during the Group Three run 15C (t1); = 2.449 s [Aj91]) and ”N (tl/z = 4.173 s [Aj86]) ions from the A1200 radioactive beam device were deposited into the implantation detector during a 4.762 s implantation period and decays monitored during a 7.063 s beam off period (refer to Table 3.3). The decay curveiobtained from this run is shown in Figure 3.4. The same least-square fitting procedure used to fit the runs of Group Two 71 was used here (decay constants are fixed and activities are free parameters). Table 3.7 presents a summary of the measured activities from this run and the calculated ,6- detection efficiency of the implantation detector for the 15C and ”N decays. The summary of the implantation detector’s fl-detection efficiency is thus 80.6:lz2.3%, 47.8:l:4% and 55.9:1:4% for the decay of ”B, 15C and 17N, respectively. Recall, that 6.8 mm of aluminum degrader was used during the implantation of 15B ions (Group One runs) and from the calculated energy-loss [Hu90], it was determined that the 15B ions came to rest at a depth of 5.2:1:1.2 mm in the 10 mm thick detector. Us- ing the same energy-loss calculation and technique as above, it is determined that 2.5 mm of aluminum degrader should have been used for the 54.3 MeV/ A 15C ions from the Group Three run in order that they come to rest in the center (depth of 5 mm) of the implantation detector. By having the ”B and 15C ions come to rest at the same depth of the implantation detector, a fair comparison of their efficien- cies could be made; differences in the efficiencies could then be attributed solely to differences in the nature of the fl-particles of the decays7. During the experiment 2.3 mm instead of 2.5 mm of aluminum degrader was used for the implantation of 15C and 17N. The 15C ions actually came to rest at a depth of 6.4i0.8 mm and the "N ions at 5.421207 mm in the 10 mm thick implantation detector. The efficiency of the implantation detector depends on the amount of energy a ,B-particle deposits in the detector (the more energy deposited, the more likely it will be detected). The amount of energy deposited by the ,B-particle is dependent on the amount of material it travels through and its kinetic energy (maximum energy deposited by low energy fl-particles traveling through the maximum distance of material, in this case when it originates at the center of the detector). Before attempting any comparisons of the efficiencies, it is helpful to compare the implantation depth, the “actual” average ,3- 7Since the stopped ion, or properly termed atom, produces the fl-particle, it can be assumed that the fl-particle’s origin in the implantation detector is where its parent ion came to rest. 72 particle energy from the decays, and the calculated implantation detector fl-detection efficiency. Table 3.8 summarizes this comparison for ”‘B, 15C, "N, and also for the 6He and 9Li impurities of the Group Two runs. Reiterating that the implantation detector’s ,B-detection efficiency is dependent on the implantation depth and energy of the ,B-particle, and referring to the informa- tion contained in Table 3.8, several conclusions can be made. First, the efficiencies obtained for the 6He and 9Li impurities of the Group Two runs are too uncertain to serve in establishing what is needed to determine the 15B decay branch to 15C bound states (the primary goal here). While it is certain that some of the 6He and 9Li came to rest in the implantation detector, some passed through it without stopping (verified by these ions appearing in the veto detector), and it is fair to say that these ions most probably came to rest at various depths in the implantation detector. In addition, due to the uncertainity in the least-square fit of the decay curve for these impurities (refer to Table 3.5) there are large uncertainties in their calculated efficiencies. For the 15B, 15C and 17N, the efficiencies and implantation depths could be cal- culated with reasonable accuracy. While the average energy of the fl-particle was greater from the decay of 15B (5.4 MeV) than it was from the decay of 15C (2.2 MeV) or ”N (1.3 MeV), the detector’s efficiency was highest for the 15B (80.6%). Since higher energy ,B-particles deposit less energy in their passage through matter (smaller —dE/d:c) than lower energy ones9, the higher efficiency for the fl-particles from the decay of 15B may have to be attributed to the implantation depth. The lower effi- ciency of the detector for 15C fl-decay from the Group Three run might be attributed 8This “actual” average energy is 0.35 of a weighted average. The weighted average is determined by the states and branching ratios populated in the daughter atom; the 0.35 accounts for part of the decay energy carried away by the neutrino. The 5.4 MeV listed for ”B is actually determined from information provided later in this chapter. 9Actually —dE/dz for B—particles of these three energies are very similar, they are of energies that would classify all of them as being minimum ionizing. 73 to its “over-depth implantation” (the 6.4 mm depth instead of 5 mm for the 15C)”; this however does not adequately explain the lower efficiency for 17N fl-decay, since the 17N atoms came to rest almost in the center of the implantation detector (5.4 mm). It may also be that the A1200 beam spot was not centered on the implantation detector during the Group Three run; this could diminish the detector’s efficiency. By considering that (1) the fl-decay of the 153 parent and the 15C daughter atoms took place at the same location inside the implantation detector, (2) the average energy of the fl-particles from the decays of "’B and 15C differ by only 5% in their —dE/da: in plastic [Pa72], and (3) the low energy threshold setting of the implantation detector (100 keV), it is concluded the implantation detector had the same B-detection efficiency for decays of ”’B and 15C as long as these decays occur at the same detector depth; since the 15C atoms are daughters of the 158 atoms, the decays do occur at the same depth. Having now established that the implantation detector’s fl-detection efficiency for the decay of 15C is 80.6%, the 15B fl-decay branch to 15C bound states can be addressed. ”When ions come to rest near the surface of the implantation detector, some fi-particles exit the detector without having traveled through enough material to be detected. 74 Table 3.6: Summary of the implantation detector’s fl-detection efficiency for the fi- decay of 158 from the Group One experimental runs. Run # Implantation detector’s (On / Off) fl-efficiency 1 (50/50) 79.7% 2 (50/50) 79.8% 3 (50/50) 79.3% 4 (20/40) 79.4% 5 (20/40) 80.3% 6 (20/40) 80.7% 7 (20/40) 81.1% 8 (20/40) 81.4% 9 (20/40) 82.6% 10 (20/40) 82.0% r = 80.6% 0' = 1.15 75 50000 ~ 4 . , - , ”N and 15C A1200 beam 20000 < \ I ‘ ‘ 73100001 ‘x “x 4 \ > \ \ - 4 4 3 ~ \ \ . 3 ‘ \ E 5000 ~ ‘ \ 4 \ 3 E L \ \ 1—1 \ \ o 4 <2 1 2000 r - background 1000 :7 -------------------- : 0 2 4 6 TIME (s) Figure 3.4: Experimental decay curve for the Group Three experimental run. During run # 14, 15C and "N ions from the A1200 were deposited into the implantation detector during a 5 s implantation period and decays were monitored during the 7 s beam off period. The solid line corresponds to a two component-fit plus a constant background. 76 Table 3.7: Summary of the implantation detector’s flvdetection efficiency from the Group Three run. The AWN, values were obtained from the fitted decay curve shown in Figure 3.4; also listed is the reduced chi-square value for the least-square fitting procedure used to obtain these values. The efficiencies were deduced from these AWN: values and the number of atoms present at the end of the implantation period. Run # AW"... Rx” Implantation detector’s (10E3 cts./s) ,B-efficiency 14 26.9:fz2.0 (”N) 0.833 55.9:l:4% 22841.9 (150) 478.44% 1.1:!:0.9 (Bkgd.) 77 Table 3.8: Summary of the implantation detector’s ,B-detection measured efficiency for implantated ions from Groups One, Two and Three runs. Also listed is the “actual” average B-particle energy from the decay (see text for explanation) and the depth of implantation into the 10 mm thick implantation detector. Ion Average B-particle Implantation Implantation detector’s implanted energy (MeV) depth (mm) fl-detection efficiency 15B 5.4 5.2:l:1.2 80.6i2.3% (Group One runs) ”N 1.3 5.4:l:0.7 55.9:h4% 15C 2.2 6.4i0.8 47.8:l:4% (Group Three run) 9Li 4.0 (disperse) 29:1:20% ”He 1.2 (disperse) 39:1:12% Group Two runs) 78 3.3.3 Determination of the fl-Decay Branch to 15C Bound States As discussed earlier in this chapter, since the half-life of 1”B is so short compared to the 4.847 s implantation period, virtually all the implanted 15B ions decayed to some state of 15C before the end of the implantation period (99.7% using Eq. 3.4). A total of 14.55E6 15B ions were deposited into the implantation detector during all the Group Two runs. This would result in 4.5E4 ”B ions still remaining at the end of the implantation period. Indeed, when the decay curve was generated from all the Group Two runs a sharp peak was observed in the first channel with 3.9E4 counts. Compensating for computer dead time and the fl-detection efficiency gives 4.7E4 counts, in good agreement. As such, it can be imagined that a ”C ion beam was deposited into the implantation detector. By determing the number of I” C atoms that remained at the end of the implantation period (Table 3.2), knowing the activity attributed to the decay of 15C (Table 3.5), and accounting for the implantation detector’s ,B-detection efficiency, the ”B fl-decay branch to 15C bound states can be determined; the summary of these findings are listed in Table 3.9. Referring to Table 3.9, there is reasonable agreement among the three individual Group Three runs for the 15B decay fl-decay branch to 15C bound states, and the value of 0.46:1:0.08% from the summed data will be adopted in the present work; the error in this value accounts for the statistical error in the least-square fitting procedure from which the 15C activity was determined and also the error in the ,6- detection efficiency of the implantation detector. This measurement is in agreement with, though significantly lower than, the limit of P0,, < 5% established by Dufour et al. [Du84]. A more recent measurement of the P1,, for ”B made by Reeder et al. [Re91] will be addressed in the next section of this chapter which supports the P0,, of 0.46% established here. 79 In the following section, the fl-delayed neutron time-of-flight spectra obtained for ”B will be examined and the decay branch to the unbound states in 15C will be established, leading to a determination of the 15B fl-decay branching ratios. 80 Table 3.9: Summary of the determined 15B fl-decay branching ratios to 15C bound states determined individually from the three experimental runs of Group Two. Also listed is the decay branch determined from the decay curve generated from the sum- mation of these runs. Run # 15B fl-decay branch to 15C bound states ll 0.43:1:0.10% l2 0.53:1:0.15% 13 0.39:1:0.22% Sum of runs 0.46i0.08% 11,12 and 13 81 3.4 15B fl-Decay to 150 Unbound States — ,B-Delayed Neutron Emission This section presents the results for the fl-delayed neutrons emitted in the decay of 15B. A review of the energy level scheme of 15C (Figure 1.2) shows that three neutron decay channels are possible. The majority of the neutron decays occur via the ground state of 14C and involve the populated low level (states below 7.31 MeV), negative parity states of 15C. These decays will be addressed first in this section. If the state populated in 15C is at least 7.31 MeV, single neutron decay via the first excited state of 14C is possible, and two neutron emission via the ground state of 13C is possible if the populated 15C state is at least 9.40 MeV. These decay channels will be addressed in the latter part of this section. 3.4.1 15B B-Delayed Neutron Time-of-Flight Measurements The Group One runs, in addition to supplying the data for the 15B half-life deter- mination, were used to obtain 158 fl-delayed neutron time-of—flight measurements. Each of the sixteen neutron detectors of the array provided a separate time-of-flight neutron spectrum. Figure 3.5 shows the results obtained from detector # 6; the top figure is the “raw” unfitted time-of-flight neutron spectrum, the bottom figure is the expanded, fitted spectrum showing five neutron peaks and their energies. The fitted time-of-flight spectra obtained from detectors # 1 through 8 are shown in Figure 3.6 (the bottom spectrum shown in Figure 3.5 is the same spectrum shown here for de- tector # 6, only larger), those obtained from detectors # 9 through 16 are shown in Figure 3.7. The details which will now be described concerning detector # 6 (raw spectrum and fitting procedure) pertain to and were observed in the other fifteen detectors, detector # 6 is used only as an of example. 82 Referring to Figure 3.5, the unfitted spectrum shows a peak centered at channel number 186.6 resulting from relativistic electrons that traveled from the implantation detector to the neutron detector (i.e. the fl-decay of 158). These electrons travel at a velocity very near the speed of light, c, (their average energy is 5.4 MeV, giving them a velocity of 0.996c or 29.88 cm/ns), taking 3.35 us to travel the 1 meter flight path, and are used to establish a time reference. An accurate time calibration of 0.3428 ns / ch was made using an electronic time calibrator. The small “cosmic” peak which was explained earlier in Section 3 of Chapter II, is seen here. The program PHAEDRUS [Sc83] was used to fit simultaneously the five fl-delayed neutron peaks. The low level, negative parity states of 15C have level widths on the order of 10 to 40 keV [Aj91]; these are small compared to the peak widths caused by instrumen- tation. The peak widths used in the PHAEDRUS fitting procedure were forced to be fixed parameters. Their widths were determined from the total time uncertainty, a 11, and a neutron-energy dependent time- combination of 1.0 us from the electronics uncertainty owing to a total flight path uncertainty, determined to be 4.25 cm]2 for detector # 6. This flight path uncertainty, and the subsequent width of the neutron peaks, were determined as follows. First, an estimate of the neutron velocity in ns/ cm corresponding to each peak was made using the centroid of the particular peak, C", the centroid of the ,B-peak, “The 1.0 ns time resolution owing to electronics was the FWHM of the 7-peak observed in the time-of-flight spectrum from a collimated ””Co source. Although this measurement is not totally independent of flight path uncertainty (the 7-ray may have interacted at the front or the back of the neutron detector, 3 difference of 2.54 cm or about 0.17 us in flight time), these uncertainties were minimized by placing the collimated source flush against one part of the detector thereby minimizing flight path uncertainty due to the detector’s curvature. ”This total flight path uncertainty is the result of three contributions. First, the thickness of the neutron detector (2.54 cm) and not being able to tell at what depth of the detector the neutron actually was detected. Second, the size of the 15B beam spot on the implantation detector; this could be as large as 2 cm (height dimension of the implantation detector). Third, the neutron detector’s deviation from a true 1 m radius of curvature; some parts of the 157 cm long detector were actually closer (or further) from the implantation detector than other parts and this adds an additional 2 cm to the uncertainty. 83 0,3, the time calibration, ns/ ch, the known flight path of 100 cm and accounting for the 3.35 ns it took the fl-particle to travel 100 cm: 100cm (Cu - Cg) x ns/ch + 3.35718 0,1: (3.7) For the lowest energy neutron peak in the raw spectrum ( top of Figure 3.5, peak furthest to right), this velocity turns out to be 1.84 cm / ns, corresponding to a neutron energy of about 1.77 MeV”. Since the lowest energy peak was not “riding on the shoulder” of any other peak but was well separated and Gaussian, its peak width could be very easily measured and was selected to be the standard from which the other peak widths would be determined. Its peak width was 7.35 channels or 2.52 ns (0.3428 ns/ch). This 2.52 ns is the total time uncertainty. Reiterating, the total time uncertainty, Attotal, is a combination of the time uncertainty from the electronics (1.0 ns), Atezcc, and the time uncertainty owing to the uncertainty in flight path, Atm: A”fatal = A”glee + Atfiz (3'8) As such, Atm for this peak is 2.31 ns. Knowing the velocity of the neutron, v", the flight path uncertainty, Al, can be determined: Al = Aim X 1),, (3'9) and is 4.25 cm; this value is reasonable considering the three sources of flight path uncertainty, and their amounts, discussed in footnote # 12. Now having established the flight path uncertainty, the widths of the four other neutron peaks can easily be determined by simply reversing the order of the above process. The total width of these peaks for detector # 6, going from the lowest to highest neutron energy, turns out to be 2.52 ns, 2.09 ns, 1.99 ns, 1.79 ns, and 1.73 ns. These are the widths that were ”For neutrons with energies much lower then the neutron’s rest mass (939.6 MeV), the neutron energy in MeV is approximately the square of the velocity (cm/n5) times 0.523. 84 used as fixed parameters in the PHADERUS fitting procedure resulting in the fitted spectrum shown at the bottom of Figure 3.5; notice the five unfolded neutron peaks. In addition, a smooth polynomial function was fit through the regions of the spectrum with no peaks for the background. The background consisted of (1) a constant level throughout the entire spectrum resulting from random coincidence events, and (2) a steadily increasing level toward the low energy end of the spectrum resulting from decay neutrons that did not travel directly from the implantation detector to the neutron detector. The fitted spectrum for each neutron detector resulted in a centroid for each peak from which an accurate measurement .of the neutron energies could be determined, and an area for each peak from which a relative population of states or branching ratios could be deduced. The determination of the neutron energies will be addressed first. For neutrons with kinetic energies much lower than the rest mass of the neutron (moo2 = 939.6 MeV), the energy of the neutron in MeV, En, can be determined as follows: ' 2 13., = %(939.6MeV):—;‘- = 0.522703; (3.10) where v,, is the neutron velocity in cm/ns and c is the speed of light in a vacuum, 29.979 cm/ns. Thus, the neutron energy is easily determined once the neutron velocity is known. Eq. 3.7 shows how to determine the neutron velocity from its centroid in the time-of-flight spectrum. Notice that this calculated velocity is a function of the flight path distance (100 cm in Eq. 3.7). It is clear that the large, lowest energy neutron peak in the time-of-flight spectra belongs to the lowest negative parity state in “C (refer to Figure 1.2). The energy of this state has been accurately measured to be 3.103:l:0.004 MeV [Aj91]. Accounting for the 1“C neutron binding energy of 1.2181 MeV [Aj91] and the recoil energy of 1"C during the neutron decay, the energy 85 of the emitted fl-delayed neutron associated with this state is 175910.004 MeV. Using the centroid corresponding to this state from the fitted time-of-flight spectra in Eq.‘ 3.7 and allowing the flight path to vary such that it results in a neutron energy of 1.759 MeV is a method of calibrating the exact flight path distance for the sixteen array detectors. Then, the energies associated with the four other neutron peaks can be determined using this calibrated flight path and their centroid. values from the fitted spectra. Table 3.10 shows these results for the sixteen array detectors. Referring to Table 3.10, the calibrated flight paths are all within one cm of the assumed one meter distance. Observing the neutron energies, there is good agreement among the sixteen detectors. The neutron energies adopted from the sixteen detector measurements are taken to be 2.81:1:0.02 MeV, 3.21i0.01 MeV, 4.32:1:0.03 MeV, and 4.75:1:0.07 MeV (mean value of the sixteen measurements, with error being :i: one o). It should be noted that these energies are determined from a “relative ” measurement. If instead a fixed flight path of 100.0 cm is choosen, the neutron energies are within 2% of the values obtained from the relative measurement. After correcting for the “C recoil energy and neutron separation energy, these correspond to 15C states of 4.23:1:0.02 MeV, 4.66:1:0.01 MeV, 5.85:1:0.03 MeV, and 6.31:1:0.07 MeV. These values agree with the known low level, negative parity states in 15C (refer to Figure 1.2); this will be discussed in more detail later. Next, a determination of the relative population of these 15C states can be made from the neutron peak areas and the neutron detector efficiencies established in the last chapter. The relative branching ratios for the five neutron emitting states were determined from each of the sixteen detector measurements in the following manner. The individual neutron peak areas, Am, Am, etc. were normalized with their cor- responding (specific neutron energy and specific detector) measured efficiencies, cm, 86 6N2, etc. from Table 2.2 to give the relative branching ratios”, BRN1,BRN2, etc. AN1/6N1 BR ‘7 = X 100 3.11 N1( 0) AN1/6N1 + AN2/6N2 + AN3/5N3 + AN4/6N4 + AN5/6N” ( ) These results are summarized in Table 3.11. Errors associated with these measure- ments will be discussed shortly. Referring to Table 3.11, there is reasonably good agreement for the branching ra- tios among all the separate detectors, except for the noticably low 3.10 MeV branch of 59.0% obtained from detector # 7. A Monte-Carlo simulation was performed [Ce79] to estimate the attenuation of neutrons in the implantation detector. Assuming the neutrons travelled an average 0.5 cm of plastic before exiting the implantation detec- tor, the probability of any interaction was about 10% for 1.77 MeV neutrons and this probability remained almost the same for the higher energy neutrons (9.6%, 9.1%, 9.0% and 7.0% for the 2.80 MeV, 3.21 MeV, 4.30 MeV and 4.80 MeV neutrons, re- spectively). Therefore, if attenuation (to the degree predicted) did occur it should effect all the neutrons in essentially the same manner and not noticably change the relative branching ratios. Detector # 7 was “straight above” the implantation detec- tor (at a right angle to the direction of the beam axis), so if the 15B beam spot was “low” the amount of plastic travelled before exiting the implantation detector could be a maximum of 1 cm. This would increase the probability for interaction with the detector, however the other energy neutrons should be effected in a similar manner. So, for the present it remains unresolved as to why the 3.10 MeV branch obtained from detector # 7 is this low and it will be interesting to see if this phenomenon is ob- served in future experiments using the array (this matter is actually addressed at the end of this chapter). Chauvenet’s criterion was applied to test the “reasonableness” of the 59.0% value and showed that about 110 measurements would have to be made 14Note that in these calculated branching ratios, it assumes 100% of the fl-delayed neutrons populate only these five 15C states; this assumption will be addressed in the next section. 87 before obtaining one as “bad” as 59%. For this reason, a decision not to include the detector # 7 measurements was made resulting in some noticeably smaller standard deviations, given at the bottom of Table 3.11. These standard deviations from the mean values can be regarded as a random component of the total uncertainty in the branching ratio measurements. Next, an estimation of error associated with each ar- ray detector measurement can be made which can be regarded as an instrumentation uncertainty. Referring to Eq. 3.11, each calculated branching ratio percentage is a function of the five neutron peak areas and, in addition, the five corresponding neutron detection efficiencies. As such, in order to determine the error associated with each percentage, ABRM, 3812,”, etc. the following expression is evaluated: 6812101 BBB ABRM = ( 8AM )AAM + ("—11- 861V] 6312,.“ 3€N5 )4 Mm. (3-12) CN1 where AAM, AA“, etc. is the error associated with the neutron peak area values and is obtained from the fitting procedure, and )4ch , etc. is the error associated with the measured neutron detection efficiency and obtained from Table 2.2. By taking the simple sum in the above expression rather than adding in quadrature, the estimation of A33”, is actually a conservative upper bound and does not require that errors in the neutron peak areas and detector efficiencies be random and independent (adding in quadrature does require this). These errors were evaluated for the branching ratio percentages listed in Table 3.11 and are listed in Table 3.12. Also listed in this table is the “weighted” mean and uncertainty determined as follows: 16 2 '= (Ci/0'" 1' 'ht d = -i—l—— (3.13) may C :21 1/0? 16 Uweighted = (Z 1/0?)-1/2 (3.14) i=1 88 where x.- and a; are the branching ratio percentage and associated uncertainty, re- spectively, for detector # i. It should be noted that the detector # 7 measurements are not included in these weighted values. Finally, an estimate of the total uncertainty associated with the branching ratio percentages was made by adding the random uncertainty (standard deviations at the bottom of Table 3.11) and the instrumental uncertainty (weighted uncertainties at the bottom of Table 3.12). Note again, that by taking the simple sum and not the sum in quadrature, these errors are rather conservative. This results then in the ,6- delayed neutron branching ratio percentages of 63.2:l:2.4%, 7.75:l:1.3%, 22.9i1.6%, 4.10i0.8%, and 1.82i0.5% to the 3.10 MeV, 4.23 MeV, 4.66 MeV, 5.85 MeV, and 6.31 MeV states, respectively, in 15C. Figure 3.8 shows the branching ratio percentage versus detector # obtained from the different detectors (refer to Figure 2.3 to see neutron detector’s orientation with respect to the implantation detector). 89 800 V l r v V l V v— V v l f ---,HHIY Detector-l6 fl-peak j 500 - L COUNTS/ CHANNEL 200 F <- cosmic peak o, . - l . . . . l . 150 200 250 300 350 CHANNEL N0. 1 r m l f ' ‘ : Detector I 600 - f a >o ., g : u-l . 6 - F. I g ‘00 '- > v-t .. D o 1 I 3 ‘ D o l U 300 - a; ‘ \ : a 'l 83 . > : , O ‘ E 3“ ' >3 3 1 8 a: 8, l N 1 $3 4 1" « sea son A i 350‘ CHANNEL N0. Figure 3.5: Top figure is the raw, unfitted fl-delayed neutron time-of-flight spectrum obtained from detector # 6. The x-axis corresponds to time, with the lowest energy neutrons in the highest channel number peak. Shown is the “fast” ,B-peak and the “cosmic” peak; these are explained in the text. Bottom figure is the above spectrum which has been fitted. The five unfolded ,B-delayed neutron peaks, with their energies, are shown. The spectrum is not corrected for neutron efficiency. The fits to individual peaks are indicated with solid lines, the background by long dashes, and the sum of all contributions by the short dashes. The fitting procedure is described in the text. 90 COUNTS/CHANNEL r 'l'ffli'"’Ir*'TT""lrr‘ : Ir'fi'l 'Infil ’rrlr F': 500, 1 600,- 1 —‘ 2 ; : 200: ‘ 200:- 1 . . _ \ 3 o o" "‘4‘“- --- 225 250 275 300 325 350 _"l""lfi*'l'*"I""T" 'T'fiTI""l""I"'TI" 1 GOOt- 1 600, 400:- Det # 3 € 400 200' «j 200. i 225 250 275 300 325 _l ' ‘ ' ' I rfi' * l ' ' ' ' 600:- 1 600 4003- -j 400 200: «j 200: 250 300 350 '*I'**‘r'*"l*"'r""Ff" ‘ ’ soo -: 600 P p 400»? Det # 7 400: 200 ' 200 I AAALLLALIA‘A 0‘ o , 250 275 300 325 350 375 225 250 2‘75 300 325 350 CHANNEL NO. Figure 3.6: Fitted fl-delayed neutron time-of-flight spectra obtained from the neutron array detectors # 1 through 8. COUNTS/CHANNEL 600_ 400 200 I o' > 225 250 275 300 325 600 E I 400 fi— 200 : Vflvvvv'vvffj—Yv’vvlvav" Det # 11 coo ' r p— b h b h 400:- h b b 200 r b D p 1 ALLA 14 LAAlAAAAJA 600 E- 400 :— 200 I 0 ’ - 225 250 275 300 325 350 .l. AAlLLAAJA‘A 91 600 I 200 ’ 400 I 200 I 600 400 I 600 , 400 I- 200 I 400 I— 800 200, o ’ ' 225 250 275 300 325 350 250 275 300 325 350 CHANNEL NO. Figure 3.7: Fitted ,B-delayed neutron time-of-flight spectra obtained from the neutron array detectors # 9 through 16. 92 Table 3.10: Summary of the calculated neutron energies from the fitted spectra of the sixteen neutron detectors. The flight path was calibrated using the lowest energy neutron peak in the fitted spectra as a standard; this peak represents a 1.759 MeV neutron and corresponds to the known 3.103 MeV state in 15C. The other neutron energies shown below were calculated using this calibrated flight path and their as- sociated peak centroid supplied by the fitting procedure. All neutron energies are in MeV. Det # Calibrated flight E, E, En En path (cm) # 2 # 3 # 4 # 5 1 100.9 2.81 3.20 4.30 4.84 2 100.9 2.79 3.21 4.30 4.70 3 100.4 2.80 3.18 4.33 4.77 4 100.9 2.83 3.22 4.30 4.74 5 100.8 2.79 3.20 4.31 4.77 6 100.7 2.80 3.20 4.32 4.79 7 100.8 2.83 3.21 4.34 4.73 8 100.2 2.82 3.21 4.32 4.76 9 100.4 2.80 3.20 4.27 4.66 10 100.7 2.80 3.22 4.30 4.57 11 100.7 2.81 3.20 4.33 4.77 12 100.5 2.81 3.22 4.36 4.75 13 100.7 2.83 3.22 4.27 4.77 14 100.5 2.82 3.22 4.35 4.75 15 100.9 2.83 3.24 4.32 4.87 16 100.8 2.84 3.22 4.33 4.81 5 100.7 2.81 3.21 4.32 4.75 0' 0.2 0.02 0.01 0.03 0.07 93 Table 3.11: Summary of the relative fi-delayed neutron branching ratios for the pop- ulated states in 15C determined from the results of the sixteen array detector time- of-flight measurements. Listed is the mean and standard deviation for the branching ratio percentages; first, to include the detector # 7 values, and second, to exclude them. All branching ratios are in percent. Errors associated with each detector measurement are dealt with later. Detector 3.10 MeV 4.23 MeV 4.66 MeV 5.85 MeV 6.31 MeV # state state state state state 1 61.4 8.41 23.7 4.80 1.71 2 63.1 9.03 22.2 4.21 1.41 3 63.2 7.76 22.4 4.72 1.93 4 62.2 8.42 23.2 4.29 1.86 5 63.8 7.37 22.9 3.99 1.92 6 64.9 6.30 23.3 3.59 1.97 7 59.0 8.43 25.5 5.14 1.96 8 61.4 9.05 23.4 4.25 1.87 9 64.4 6.34 23.7 3.42 2.16 10 64.0 7.81 21.8 4.14 2.28 11 63.7 7.97 23.1 3.44 1.87 12 63.5 7.63 23.6 3.52 1.68 13 63.7 8.36 22.8 3.62 1.56 14 62.7 8.23 22.4 4.64 2.07 15 63.8 7.29 22.8 4.57 1.50 16 61.5 8.29 23.3 4.82 2.08 Eincl.#7 62.9 7.92 23.1 4.20 186 Ugnc1,#7 1.48 0.80 0.84 0.56 0.24 fe,c(.#7 63.2 7.88 22.9 4.13 1.86 and,” 1.10 0.82 0.57 0.51 0.25 94 Table 3.12: Summary of the relative fl-delayed neutron branching ratios for the populated states in ”C with their corresponding uncertainties. Also listed is the “weighted” mean and uncertainty for each branching ratio percentage. The details concerning the method used to determine the uncertainties and weighted values are explained in the text. All values are in percentage. Note that the detector # 7 values are not included. Detector 3.10 MeV 4.23 MeV 4.66 MeV 5.85 MeV 6.31 MeV # state state state state state 1 61.4:lz5.2 8.41:i:1.7 23.7:t3.7 4.80:l:l.l 1.71:1:0.7 2 63.1:l:5.2 9.03:l:l.9 22.2:l:3.6 4.21:1:1.1 1.41:1:0.6 3 63.2:1:5.0 7.76:t1.7 22.4:l:3.3 4.72i1.0 1.93:1:0.7 4 62.2:1:5.4 8.42:1:1.8 23.2:t3.8 4.29:1:1.1 1.86:1:0.7 5 63.8:l:5.4 7.37:1:1.7 22.9i3.8 3.99:1:1.0 l.92i0.8 6 64.9:lz5.1 6.30:l:l.4 23.3:l:3.7 3.59:1:1.0 1.97:t0.7 8 61.4:l:5.5 9.05:1:2.0 23.4:1:3.9 4.25:1:1.1 1.87:1:0.6 9 64.4:l:5.5 6.34:l:l.5 23.7i4.0 3.42-1:1.0 2.16:1:0.8 10 64.0:1:5.6 7.81:1:1.8 21.8:l:3.8 4.14:1:12 2.28:1:0.9 11 63.7:l:5.4 7.97:l:l.8 23.1i3.9 3.44:1:09 1.87:1:0.8 12 63.5:l:5.2 7.63:1:1.7 23.6:t3.8 3.52:1:1.0 1.68:L-0.6 13 63.7:1:5.5 8.36:1:1.9 22.8i3.9 3.62i1.0 1.56:1:0.6 14 62.7:1:5.6 8.23i1.8 22.4:l:3.8 4.64:1:13 2.07:1:0.8 15 63.8:l:5.5 7.29i1.7 22.8:l:3.8 4.57:1:1.2 1.50:1:0.7 16 61.5:l:5.6 8.29i1.9 23.3i3.9 4.82:t1.3 2.08:1:0.8 [ swcighm [L63.2:1:1.4 l 77540.5 [ 22911.0 1 4.10i0.3T1.82:1:0.20 u. 95 l I _T— I I I l I I I T l 1 I I I 1 - - n A n U 0 J3 l n 41 1'1 - D u ... tr 0 — _ u 63.2:2473 ,\ 60" 0 D —‘ N .. . v . U} _ - O. - H '1 E .. 4O — — CD 2 F d m _ - a - ‘ g W x H 1‘ X—l-fi—m—H—JZZ 9:1 67 m 20 — x — o o O + + g A A ‘ -_t_—_+__§_.,_.—t+ + . . + H+—‘ 7.75:: 1.3% .. .. .- . .. .. -- -- '- ‘ 4.10:0.87: 1.82:0.57.’ DETECTOR Figure 3.8: The B-delayed neutron decay branching ratios obtained from the different array detectors. The solid lines and values on the right are the weighted averages obtained for each of the five percentages from the detector measurements; note that the detector # 7 values are shown here but its values were not used in calculating the weighted averages. 96 3.4.2 Other Decay Channels for 15B fi-Delayed Neutron Emis- sion A fl-decay branch leading to single neutron emission via the first excited state of ”C at 6.08 MeV (compared to the five observable peaks resulting from decays via the 14C ground state) requires the excitation energy of 15C to be at least 7.31 MeV and should result in distinct neutron energy peaks”. No evidence for such peaks could be found in any of the individual sixteen detector neutron time-of-flight spectra. In order to look more closely for evidence of any additional neutron peaks, the results obtained from all the neutron detectors were summed. This summation first required that the neutron time-of—flight measurement be converted into an neutron energy measurement in software; this was necessary since the different detectors had unique time calibra- tions and a simple summing of time-of-flight spectra would not add the neutron peaks properly. By converting each detector measurement to an energy measurement, all detectors were put on equal footing and could then be added together. Figure 3.9 shows the spectrum obtained by adding all sixteen detector results together. Several points need to be made concerning this summed energy spectrum. First, all sixteen detectors contributed to this spectrum (including detector # 7). Second, since the purpose of this spectrum was to find evidence of additional neutron peaks (not to determine branching ratios), the threshold setting for each detector was set as low as possible, essentially the “intrinsic” threshold of the detector (estimated to be a neutron energy cut-off of about 0.7 MeV). Referring to Figure 3.9, there appears to be no new neutron peaks to indicate population of any state in 150 above 7.31 MeV; the five neutron peaks present correspond to the 15C states already identified from 1”It should be noted that the available phase space for the electron and neutrino during fl-decay behaves roughly as the fifth power of the decay energy, so population of high level states in 15C is diminished due to this effect. It should also be noted, however, that a “good” overlap of initial and final nuclear wave functions can result in a high-lying state being populated more favorably than “just accounting for phase space” would predict. 97 the individual detector spectra. It should be noted however that with the 0.7 MeV neutron cut-off, states populated in ”C below 8.0 MeV and decaying via the first excited state of “C ("’C states between 7.31 MeV and 8.0 MeV) would produce neutrons with energies too low in energy to be detected. It should also be noted that if a state in 150 between 7.31 and 8.0 MeV was populated, it would also be possible for this state to decay via the ground state of 14C, yielding neutrons with energies between 6.1 and 6.8 MeV. These neutrons would be detectable, yet none were observed. For the population of states in 15C above 9.40 MeV, two neutron emission via the ground state of 130 is possible. One might expect that the population of states in 15C this high in energy would be quite inhibited due to the severely decreased available phase space for the electron and neutrino; yet here too, good initial and final nuclear wave overlap can result in favorable feeding to these high lying states. The probability established for the ,B-delayed two neutron emission of ‘5 B was a limit of P2,, < 1.5% by Dufour et al. in 1984 [Du84] and a more recent measurement of P2,, = 0.4:t0.2% by PL. Reeder et al. in 1990 [Re90]. In the present work, an attempt was made to observe ”B fl-delayed two neutron emission using the neutron detector array by looking for neutron coincidences in detector pairs. This involved creating two dimensional spectra and plotting the neutron time-of-flight measurement for one detector vs. the neutron time-of-flight measurement of another detector. Figure 3.10 shows the fifteen spectra obtained by plotting detector # 6 vs. the other fifteen detectors; these are the result of approximately 5 million 158 decays. Using the upper limit of 1.5% for two neutron emission, one would expect less than one two-neutron event per detector pair given the total number of 1”B nuclei that actually decayed at the center of the array. Accounting for detector solid angle and neutron detection efficiency, a 1.5% two neutron decay branch would result in 98 about 0.6 events (less than this for neutrons below 1.8 MeV) per detector pair for the given 5.083 million ”B decays observed. Referring to Figure 3.10, random coincidence events are observed at a level of about 3—4 per detector pair. The heavy horizontal and vertical lines in each spectrum correspond to a coincidence event between the detection of a fl-particle in one detector and a neutron in the other (most of these neutrons are the five identified peaks). Notice that the neutron detectors (#’s 5 and 7) adjacent to detector # 6 show neutrons that scattered from one detector to its neighbor; this is observed by the diagonal pattern in these two spectra. Since the neutron detector array was thus not adequate for measuring the two neutron emission decay branch, the present work adopts the P.L. Reeder et al. [Re90] value of 0.4:l:0.2% for this branch in the determination of the 15B B—decay branching ratios. 99 0000 WWTfie T I l 5000 ~ - __, SUM or ALL ; ca . é mo _ 16 DETECTORS ; § 4 Q 3000 - 4 a 4 D 2000 " ‘1 8 1 1000 - - o . 1 0 L A 100‘ i A 2200 i A ‘300 4.00 500 CHANNEL N0. (ENERGY) 105- o s g 10" i N.“ 931.10 a i r“- a i 4,; g 1031- C o 10° -l -1 1‘1..4L-- l 0 A A 100‘ A200 300 -400 A A 9500 CHANNEL N0. (ENERGY) Figure 3.9: Neutron energy spectrum generated from the sixteen neutron detector time-of-flight measurements. Top figure is the energy spectrum with a linear y-axis, bottom figure is the same spectrum with a log y-axis. Note the evidence of only five fl-delayed neutron peaks. 100 :' g : ‘ ‘ ‘i‘w' Cub-3'00- H~ot ' l;_‘." "'5. ;"'""‘ "'l . "‘4’9- unabgu. ..b .r ' .‘1‘: ° ‘wfl ' -- - l 2 3 4 f 3 r i , i 5 '3 ..._ _, 9“ .....- .. ... “_- 4 s ' 7 " 8 l -' .' ‘ i I '. s ' ‘,- I I, l t ‘V-L' .1 hr a _..;‘}' ‘- Q a J," ...- , . ‘ "0 al.- o 4 9 10 ll 12 f’ F I . i.- t g 't _l 1."... . ...a-.. J ‘b' ...-'3» .’ . .-. , in" ,‘, ..‘4. ., A.” . *fi," #5.... ...,1 13 d 14 . ' 15 7" 16 Figure 3.10: Two dimensional spectra showing the neutron time-of-flight measure- ment for detector #6 (x-axis) vs. the neutron time-of-flight measurement for the fifteen other detectors (y-axis, and numbered for detector number). These spectra were used to look for two neutron coincidence events and evidence of 15B fl-delayed two neutron emission via the ground state of 13C. 101 3.5 The 15B ,B-Decay Branching Ratios Having measured the 0.46:l:0.08% 15B ,B-decay branch to 15C bound states, adopting the value of 0.4:l:0.2% for 15B two neutron emission [Re90], and having no evidence that any 15 C state other than those represented by the five observable neutron peaks in the array detector time-of-flight spectra were populated, it is therefore concluded that 99.14i0.28% of the 15B fl-decays populate the five lowest negative parity states in 15C (the five observable neutron peaks). Table 3.13 contains a summary of the deduced branching ratios. Before discussing the values in this table, it should be mentioned here that a re- cent measurement of delayed neutron emission probabilities of neutron-rich nuclides from Li to Al, including a value of P1,. > 77.3% for 15B, was made by Reeder et al. [Re91] using the Los Alamos National Laboratory time-of-flight isochronous spectrom- eter (TOFI) and a polyethylene-moderated neutron detection system which included forty 3He proportional tubes 16. The TOFI system measured the A, Z, and Q of each neutron-rich ion and the decay neutrons were observed by means of a delayed coinci- dence technique. Figure 3.11 shows the efficiency curve provided by Reeder et al. for their neutron detection system. The solid circles in this figure are the Monte-Carlo calculated efficiencies for the detector geometry, having values that range from 64% for 0.1 MeV neutrons to 42% for 3.0 MeV neutrons. Also shown in this figure are measured efficiencies for 9Li, 160, and a PuBe source (open circles). The efficiencies for the 9Li and 160 were calculated from the data obtained during the measurement and the previously known Pn values. Since the delayed neutron and PuBe sources are not monoenergetic, the experimental efficiencies are valid for the average energy of the known spectra. In their PM > 77.3% determination of 15B, they assumed a 16This type of neutron detection system had a high efficiency for the detection of a broad energy range of neutrons, although it provided no specific information on the neutron energy. 102 60% detection efficiency for the delayed neutrons (for an assumed average energy of z0.5 MeV). Using the branching ratios established in the present work, the average delayed neutron energy from 15B is much higher, 2.4 MeV; using the efficiency curve in Figure 3.11 this corresponds to a 47% neutron detection efficiency. In their pub- lished results, Reeder et al. [Re91] pointed out that a 47% assumed efficiency for the delayed neutrons from 15B would change their P1,. to 99%, in agreement with the previous measurement of Dufour et al. [Du84] of P1,, > 93.5% and the P1,, = 99.14% adopted by the present work. Recently the neutron detector array was used in another experiment at the N SCL to study the decay of 18N (Gorres, et al. — PAC91011). For calibration purposes, a "N beam was deposited into the implantation detector during a 16.48 s beam on period and its decay was observed during a 15.50 s beam off period. 17N is a ,B-delayed neutron emitter, having a half-life of 4.173 s and emitting neutrons with kinetic energies/ absolute branching ratios of 0.383 MeV/38.0:l:1.3%, 1.172 MeV/50.1:l:1.3%, and 1.702 MeV/6.9i0.5% [Aj86]. Using this information, the absolute efficiency of a neutron detector could be determined for the neutrons with these kinetic energies (particularly the 1.702 MeV neutrons), and from this an absolute branching ratio could be estimated for the 15B decay which feeds the lowest negative parity state in 15C (this produces neutrons with the kinetic energy of 1.759 MeV). Although, of course, (1) the experimental conditions under which ”B and ”N decays were not identical, and (2) the neutron energies (1.702 and 1.759 MeV) were not exactly the same. However, the threshold settings of the neutron array could be duplicated and the neutron energies differed by only 3.2%. Figure 3.12 shows the decay curve obtained for the 17N implantation (‘90 was an impurity) from which the number of 17N atoms that decayed during the beam off period could be determined. Figure 3.13 contains the 17N fl-delayed neutron 103 time-of-flight spectrum obtained from neutron array detector # 6; notice that the 1.702 MeV and 1.172 MeV neutrons are present, however the detector was not able to observe the 0.383 MeV neutrons. From the decay curve it was determined that 1.479E6 17N atoms decayed; as a result of these decays, 127 neutrons at 1.702 MeV were observed by detector # 6. Adjusting for the known branching ratio of 6.9:]:0.5% to this state, an absolute detector efficiency of (1.24:1:0.16)E—3 was obtained; this compared to the efficiency of (2.14:l:O.26)E-3 obtained using the PuBe source (the discrepancy among these two values will be discussed in the next paragraph). As a result of 4.905E6 15B atoms decaying (from the present work), 4080 neutrons at 1.759 MeV were observed by detector # 6. Normalizing this number of neutrons by the 1.24E-3 efficiency, gives an absolute branching ratio of 67.1:lz7.7%, compared to the 64.9:l:5.1% relative branching ratio determined for this detector. This agrees reasonably well, especially when it is considered most likely that the absolute detector efficiency for 1.759 MeV neutrons would be slightly higher than it is for 1.702 MeV neutrons, and this would give even closer agreement among the absolute and relative branching ratios. In addition, recall from earlier in this chapter that array detector # 7 showed abnormally low detection efficiency for the lowest energy (z1.76 MeV) fl-delayed neutrons from the decay of 15B. This detector did not exhibit a similar low efficiency for the "N decay; its detection efficiency for the 1.172 MeV and 1.702 MeV neutrons from the decay of "N appeared to be very similar to that of detector # 6. This would very likely indicate that the abnormally low efficiency observed for the 1.76 MeV 15B neutrons could not be soley attributed to the location of detector # 7 but rather some problem in the electronics. A rather large discrepancy is observed among the absolute efficiency values ob- tained for detector # 6 from the "N measurement ( (1.24:L-0.16)E-3 ) and the PuBe neutron source measurement ( (2.14:1:0.26)E-3 ). It is noted‘however, that there 104 is very good agreement among branching values obtained for the 15B fl-decay to the 3.103 MeV state in 15C derived from these two separate measurements; the 67.117.7% value could be properly termed an “absolute” branching ratio, whereas the 64.9:lz5.1% value a “relative” branching ratio. The disagreement among the absolute efficiencies lies in the 119.5 msr solid angle which was choosen for the array detector element in Eq. 2.2; this selected solid angle is the result of assuming the entire area of the detector (entire 157 cm tube-to-tube length) is active. Closer agreement among the efficiencies is obtained if a smaller solid angle is assumed for the array element; for example instead of assuming the active area of the detector is from tube—to-tube, one assumes the detector active area is from frame-to-frame", this would result in a solid angle of approximately 100 msr. The advantage of determining “relative” branching ratios, as was done in the present work, is that the solid angle cancels out in the cal- culated branching ratios and the same ratios are obtained regardless of the solid angle value. Changing the array element solid angle value in Eq. 2.2 to bring closer agree- ment among the efficiencies however would result in larger discrepancies among the PuBe source and the calculated Monte-Carlo values shown in Table 2.3. Discrepancy among these values would appear to indicate that the entire PuBe time-of-flight spec- tra shown in Figures 2.7 and 2.8 were “riding-on” a background which would inflate the PuBe determined efficiency values. This background could have been estimated if a “shadow bar” was used; the purpose of a bar is to mask neutrons that travel directly from the source to the detector, so any events observed in the spectra are attributed to neutrons that did not follow this direct path (scattered off surroundings) or any other source of background. Thus agreement among the 67.1:l:7.7% absolute and 64.9:1:5.1% relative branching ratio values would appear to indicate that the relative fi-decay branching ratios determined for 15B from the PuBe source efficiencies are 1“The frame corresponds to the mounting hardware which supports the 16 array elements around the implantation detector. 105 not significantly effected by this background component (it cancels out in the values determined for the relative branching ratios), however one must be very cautious in using the PuBe source to determine absolute branching ratios, and additional work must be conducted to determine the actual background attributed to this source. Referring to Table 3.13, the energies of the 15C states deduced from this work (recall that the 3.103 MeV state was fixed as a calibration), the known 15C states [Aj91], the fl-branching ratios, and the deduced log f t values are listed. The ft values were calculated using a half-life of 10.3:t0.2 ms, the measured branching ratios (BR), a Q5 of 19.1 MeV [Aj91], in the expression: f(QH - Ex)t1/2 BR ft = (3.15) The statistical rate function f (Q5 — E3) was calculated with the method of Wilkin- son and Macefield [Wi74]. Recalling from Chapter I the predictive ability of log ft values, it is reasonably clear that the five neutron peaks observed in the present work all represent allowed decays to negative parity states in 15C (J’r = - for 15B, NICO [Aj91]); decays to the ground state and first excited state of 15 C (both positive parity states states) represent first-forbidden decays. In addition, the 62.8%, 7.7%, 22.8%, and 4.1% observed branches correspond to the (Ex(MeV), J“) 3.103, g; 4.220, g-; 4.657, =3“; and 5.866, if known ”‘C states, respectively. The state observed at 6.31:1:0.07 MeV probably represents the 6.358:l:0.006 MeV 15C state, however it may be the 6.417:l:0.006 MeV state; it could also be a mixture of both. The literature lists only possible J’r assignments for these latter states; since the present work suggests this to be is an allowed transition, this would restrict the state’s J’r to be %-, g-, or film 106 Table 3.13: Neutron energies, measured ”C states (this work), known 15C states ‘1), fl branching and log ft values in 15B decay. All energies are in MeV. E, 15C (E3) 15C (Ex, J") [g (%) Iogft (this work) (Ajzenberg-Selove “)) 4.75i0.07 6.31i0.07 6.358i0.006 1.8i0.5 5.4lzlz0.15 é‘ 1+ 2+ 2 ’2 ’2 6.417:l:0.006 9.‘ i“ Z" 2 ’2 ’2 4.32:1:003 5.85:1:0.04 5.866:l:0.008 4.1:t0.9 5.10:1:0.10 % 3.21:1:0.01 4.66:1:0.01 4.657:l:0.009 22.8:t1.6 4.562t0.04 % 2.81:1:0.02 4.23:1:0.02 4.220i0.003 7.7:l:1.3 5.13:1:0.10 3 1.759 3.103 3.103:l:0.004 62.8i2.4 4.34i0.02 (calibration) (calibration) %_ (neutron bound —- 0.740 0.46i0.08 — states in 150) g”- g.s. 1+ 5 a) Ref. [Aj91] 107 1m r v T V ' V T V V r ' V V V I V V V V l' T V V r A A A A AAAA 7O 9L1 A‘AAAAl PuBe , E“; , § 5° ' o 2 T9 . If; 1 40 . 10 A A A A 1 A A O A N G ‘ 0| Neutron Energy (MeV) Figure 3.11: Efficiency curve for the polyethylene-moderated neutron detection sys- tem used by Reeder et al. [Re91] in their recent measurement of the 15B Pm. Calcu- lated Monte-Carlo efficiencies are represented by the solid circles and experimentally determined efficiencies by the open circles. See text for a detailed explanation. ACTIVITY (cts/s) 108 500000 ... .... -,- .- .—‘ , v v v I Decay of 400000 Y I V V V‘T I 300000 200000 Al\.AL1 P- l 17N a T nd 1 190 W 1 1 q 100000 ‘ ‘ ‘ ‘ 0.0 2.5 75 TIME (s) 5.0 10.0 12.5 15.0 Figure 3.12: Experimental decay curve for ”N inclusive fl-emission; 19O was an impurity. The solid line corresponds to a two-component fit, the reduced chi-square for this fit was 0.5. 109 150 r - f . - , - , 1 f , - - - f - L . ' Detector # 6 ‘ mf fi-peak 17N Decay . i . 100* .. ...: I j m ’ 1 g ’ 1 <3 70- > J 33 ’ c» . O ’ E . \ ’ . 2 . g z; . s ”r . 2 i m 4 O T m s . U ’ E o. ‘ as ..J l . 100 200 ”0 000 CHANNEL N0. Figure 3.13: Time-of-flight B-delayed spectrum obtained for the decay of "N from neutron array detector number # 6. Shown are the “fast” fi-peak and the 1.702 MeV and 1.172 MeV neutron peaks. Note that the detector was not able to detect the 0.383 MeV neutrons from the decay of 17N, however the spectrum location where they would be expected is shown. Chapter 4 Discussion — Comparison to Theoretical Predictions In this chapter, the experimentally determined 153 fl-decay properties from the present work are compared to theoretical shell-model calculations. Before the de- tails of the 15B specific shell-model calculations are examined and compared to the experimental results, a general discription of the nuclear shell-model will be presented. 4.1 The Nuclear Shell-Model Nuclear theorists have constructed a nuclear shell-model somewhat after the atomic theorists constructed their atomic shell picture. In the atomic theory the energy shells of increasing energy are filled with electrons consistent with the requirements of the Pauli principle. Filling these shells, an inert core is generally obtained and the valence electrons determine the chemical properties of the atom. The atomic shell-model has been able to predict an impressive list of atomic properties. When attempting to create a nuclear model based on “shells”, some major differences become apparent when compared to the atomic model. First, in the atomic model the interaction potential is the result of a central Coulomb field from the nucleus; for the nuclear case, the nucleons have to move in a potential that they themselves create (this major 110 111 tenet of the nuclear shell-model was already brought to light in the opening of Chapter I). Choosing the correct form of this “self generated” potential was very important if a good nuclear model was to be obtained. A realistic nuclear model would be able to successfully reproduce physically observed quantities, for example, first and foremost the nuclear magic numbers. It is observed that specific numbers of protons or neutrons create obviously more stable nuclei; these magic numbers are Z = 2, 8, 20, 28, 50, and 82 and N = 2, 8, 20, 28, 50, 82, and 126. The significance of these numbers in a shell- model is that they represent the exact filling of major nuclear shells, analogous to the stability of the noble gases caused by the exact filling of atomic shells by electrons. Several examples of the significance of the magic numbers are the enhanced binding energy of the alpha particle (Z = N = 2; being doubly magic), the element tin (Z = 50) having the largest number (10) of stable isotopes in nature, and the element lead (Z = 82) ending four long radioactive decay chains. Two nuclear potentials that were considered are the infinite potential and the harmonic oscillator. Neither of these potentials alone was successful in approximating the real nuclear potential, however an intermediate form which combined the two, known as a Woods-Saxon potential [W054] was better able to approximate the true potential. The Woods-Saxon potential can be written: _ —V0 _ 1 + exp[(r — R)/a] V(r) (4-1) where R is the nuclear radius (taken to be 1.25/3), V0 is the well depth of the nuclear potenial (usually on the order of z50 MeV), and a is the nuclear skin thickness or distance over which the nuclear charge density falls from 90% to 10% (typically 22.3 fm). The left side of Figure 4.1 (labeled Intermediate form) shows the energy levels 112 resulting from the model nucleus using the Woods-Saxon potential. Notice that this potential successfully predicts the magic numbers (numbers in the circles) for the lower energy levels (2, 8, and 20), however as the energy levels increase the calculation fails to predict the correct numbers. Again following the atomic shell-model, a nuclear spin-orbit potential can be added. The spin-orbit potential results in the two-fold splitting (except for I = 0 where there is no splitting) of energy levels with the same orbital angular momentum due to the intrinsic spin 3 = % of the nucleon. For example, the nuclear p energy level with orbital angular momentum l = 1, will be split into two orbitals, one with a total angular momentum of 1/2 (pl )2) and the other with a total angular momentum of 3/2 (p3/2). It should be noted that each orbital is specified by three labels: a single letter 3, p, d, f, etc. which stands for I = 0, 1, 2, 3, etc.; a subscript to denote the total angular momentum, j, of a single particle in that orbital; and a numerical prefix that counts the number of levels with that I value (for example, 1p means the lowest p state). This addition results in the successful prediction of all the known magic numbers; this is shown on the right side of Figure 4.1 (labeled Intermediate form with spin orbit). This nuclear shell-model not only successfully predicts all the magic numbers but is also able to predict other nuclear properties such as spin-parity assignments, nuclear magnetic dipole moments, and electric quadrupole moments. In its most extreme limit (known as the extreme independent particle model) the nuclear shell-model predicts that the last single unpaired nucleon determines the properties of the nucleus; the other nucleons form an inactive core which create the nuclear self potential. Despite its drastic simplicity, this extreme model is successful in predicting the pr0perties of numerous nuclei, particularly when the single unpaired nucleon is one less or one more and the other nucleons correspond to the filling of a major shell (for example $5N3, £1,709, and 330212,). For other nuclei, it is a next better 113 approximation to consider all the nucleons in an unfilled shell. For a nucleus such as §30a23 the extreme model would consider only the single unpaired 23rd neutron, where a more complete model would consider the interaction of all three valence neutrons. Present day shell-model calculations, such as the one used to predict the fl-decay properties of 153, are generally quite rigorous and their complexity should not be underestimated by the very basic explanation of the shell-model which was just pro- vided. Generally three steps, all of which are related to each other, must be carried out before a shell-model calculation can be performed which include (1) the choice of a single-particle basis, (2) selection of an active space, and (3) the derivation of an effective interaction. A brief discussion of these steps will now be presented, and a more complete, clear discussion of these steps can be found in “Introductory Nuclear Physics” by S.S.M. Wong [W090]. Referring to Figure 4.1, for a nucleus such as $5310, with 5 protons and 10 neutrons, 3 of the protons occupy the 1p shell (made up of the 1133/2 and 1191/2 orbitals), lying outside the closed ls shell (made up of the 131/2 orbital); 2 of the neutrons occupy the M23 shell (made up of the Ids/2, 231/2, and 1d3/2 orbitals), lying outside the closed 1p shell. The protons occupying the “proton” ls shell and the neutrons occupying the “neutron” ls shell are never excited and form an inert core (a 4He core) and the single-particle states they occupy do not have to be included in an active space. Likewise, single-particle states very high above the valence nucleons can be ignored in the active space if interest is primarily in the low-lying excited states of the nucleus (below approximately 15 MeV). All that remains then are the valence nucleons to form the active space from which nuclear wave functions can be approximated; these single-particle wave functions are then used to construct a complete many-body basis state. For 15B, the shell-model calculations discussed in the next section used the 114 complete psd model space, in which the 1193/2, 1p1/2, 1d5/2, 231/2, and Man orbitals are all included in the active space. Single-particle wave functions, (ix-(7",), are taken as eigenfunctions of a single- particle Hamiltonian, h(7"',-): h(fi)¢k(fi') = 0:961:03) (4.2) where 6;, is the single-particle energy. A many-body Hamiltonian is then generated from two parts: one, the single-particle Hamiltonian and two, a residual two-body interaction term, V(1"}, 17,-), which accounts for nucleon-nucleon interactions: A A H = Zhh‘i-H Z vow) (4.3) i=1 i¢j=1 The matrix elements of H in the many-body basis states can then be expressed as a sum of two terms: A ij = djk Z 6,, + ij (4.4) 11:] The first term of Eq. 4.3 is constructed out of eigenfunctions of h(7“',-) and the sec- ond term is the contribution to the Hamiltonian matrix element from the residual interaction. An effective many-body Hamiltonian can be generated semi-empirically from known experimental data. The single-particle energy term is obtained from binding energy differences between filled-shell and single-particle/single-hole nuclei, and the residual two-body term is obtained by fitting experimental data available in the mass region of the active model space. The semi-empirical methods used to determine the effective interactions for the 15B shell-model calculations are outlined in the next section. 115 'MOMQGII" farm with 30m orbit Intermediate form \ \ \ ”Us: a '35 {2; 3d—f l0 166—<>"’I-I"—2‘72 2 15% 23 18 156_<:‘)::343652——é l42 1. 26 :33 —< '942—'—,(— 10 136 A \\ 126 \ \1113,2 ll 1‘ 126 3D—f 5 112—--=::r3912 i “a 14 ‘06——=::-4L2l5'2 6 108 2’ ‘ ‘_2'12 1,, ,, a 100 j. ,” 9'2 10 92 in 22 92 —<: \ ‘H N O N ‘ 1n 1 2a 10 ss—-==:__"‘ 2052 s 64 tad/1‘72 4 8 58 I 13 18 ss—< . ‘ j.“1"'2 2 3% 20 6 40—-"“""—: 15,2 38 —‘-- 10 101052 0 ________,,,,, L t 2 3’2 ' 2 2———————un G ‘5‘: I A Ill IV II ll 66:}; - “H? N #00 Otth “ONE N m Figure 4.1: At the left are the energy levels calculated using the Woods-Saxon poten- tial (Eq. 4.1) alone (Intermediate form). At the right are the energy levels calculated when the spin-orbit potential is included (Intermediate form with spin orbit); notice the spin-orbit interaction splits the levels with l > 0 into two new levels. To the right of each energy level is, first the individual nucleon capacity of that level and, second the cumulative number of nucleons up to that level. The inclusion of the spin-orbit potential results in the magic numbers (shown in the circles) being exactly reproduced. From K. Krane, Introductory Nuclear Physics (New York: John Wiley and Sons, 1987). 116 4.2 Shell-Model Calculations for 15B Shell-model calculations to predict Gamow-Teller B-decay strengths for mass 15 were carried out in the complete psd model space, within the framework of a spherical shell-model formalism [Wi83] by B.A. Brown [Br90]. The Millener-Kurath-Wildenthal (MKW) interaction [Cu86] was used in which the 1p3/2, 1131/2, 1d5/2, 231/2, and M3” orbitals are all active (refer to Figure 4.1). The MKW interaction is constructed in the following manner. First of all, the single-particle energies were chosen to reproduce single-particle states in A = 17 nuclei and single-hole states in A = 15 nuclei with the assumption of a closed ls-l p shell configuration for 160. The residual interaction matrix elements connecting the 1p-shell orbits were taken from a fit to lp-shell energy levels in the A = 10-15 mass region obtained by Millener [Mi86]. The complete p—shell effective interaction comprises a total of seventeen parameters, two single-particle energies and fifteen two-body matrix elements. The interaction matrix elements connecting the 2sld-shell orbitals were taken from a fit to 2sld-shell energy levels in the A = 18-38 mass region obtained by Wildenthal [Wi83A]. The complete ds-shell effective interaction comprises a total of sixty-six parameters, three single-particle energies and sixty-three two-body matrix elements. Lastly, the cross- shell interaction matrix elements connecting both the lp-shell and 2sld-shell orbitals were calculated with the residual interaction of Millener and Kurath [Mi75]. This contributes approximately twelve additional parameters. The theoretically predicted shell-model Gamow-Teller fl-decay strengths are ex- pressed in terms of a “B(GT)” value which is directly related to the nuclear matrix element, leglzi B(GT) O( Ill/[15'2 (4.5) Recall from Chapter I that the nuclear matrix element accounts for the overlap of 117 initial and final nuclear states. Experimentally determined ft values (comparative half-lives) are related to B(GT) values through the following expression: 6177 3 ft B(GT) = (4.6) The 6177 s in the above equation is arrived at by combining constants used to cal- culate the decay constant and ft values. Table 4.2 presents the comparison of the experimentally determined 15 B Gamow-Teller fl-decay strengths to those predicted by the MKW shell-model calculations; Figure 4.2 graphically displays this comparison. The theoretical B(GT) values include the (go/g”)2 factor that properly accounts for the weak-interaction axial-vector and vector coupling constants (denoted by g,I and g”, respectively) for the decay of a neutron into a proton. The theoretical B(GT) values have also been multiplied by a factor of 0.6 to take into account the empirical quenching observed for Gamow-Teller decay strengths in sd-shell nuclei [Br88]. An in- vestigation of hundreds of experimentally determined ft values for sd-shell nuclei has been conducted by Brown et al. [Br85]. This investigation showed that experimen- tally determined ft values were consistently larger than the theoretically predicted ones. Multiplying the theoretical values by a 0.6 “quenching factor” generally brings about good agreement among the two sets of values. Referring to Table 4.2 and Figure 4.2, agreement among the experimentally de- termined and theoretically predicted Gamow-Teller fl-decay strengths is quite good for the largest decay branch (62.8% branch to the 3.103 Mev, %- state) while the shell-model underestimates the decay strengths to the higher lying states. In addi- tion, the shell-model predicts a total decay branch of less than 0.8% to all remaining negative parity states in 15C (states lying above the first five negative parity states), in agreement with the experimental results. Concerning the shell-model underestimation of allowed Gamow-Teller fl-decay 118 strengths to the higher lying states in 15C, it is noted that in this psd model space the active protons occupy the 1p shell and the active neutrons occupy the 231d shell. Previously half-life [Cu86] as well as other Gamow-Teller fl-decay strength [Sn83] discrepancies between the model predictions and experimental data have been found with this type of configuration. The allowed Gamow-Teller fl-decay of 16C to states in 16N is particularly noted (notice 336C“, has only one more proton occupying the 1p shell than §5B10, the neutrons occupying the 231d shell are identical for the two nuclei); here, essentially 100% of the 16C fl-decay strength feeds the 3.36 MeV level (284%) and the 4.32 MeV level (~16%) in 16N. Model predictions using the com- plete psd model space and Millener-Kurath interaction to connect the 1p protons and 231d neutrons predicts 16C B(GT) values noticeably lower than that experimentally observed [Sn83]. It is proposed that a better determination of the cross-shell resid- ual interaction between protons and neutrons for these nuclei might improve these discrepancies [Cu86]. Additional calculations were performed to estimate the first-forbidden fl-decay strengths to the ground state (y) and first excited state (%+) of 15C. These calcula- tions are different from the allowed-decay calculations described above and employ a first-forbidden decay operator. The calculations were performed with psd wave func- tions using the Behrens-Buhring formulation [Be72] as explicated by Warburton et al. [Wa88]. The results obtained with harmonic-oscillator radial wave functions are a branch of 0.53% to the ground state and 0.52% to the first excited state. The results obtained with Woods-Saxon wave functions are 0.23% to the ground state and 0.23% to the first excited state. The latter value for the total calculated branching ratio of 0.46% is in exceptionally good agreement with the experimental value of 0.46:1:0.08%. 119 Table 4.1: Measured and predicted Gamow-Teller fl-decay strengths to the lowest %-, 3:, %_, %- and é- “) states in mass 15; also included are the measured and pre- dicted energy levels of 15C populated. The 3.103 MeV 15C level was adjusted in the shell-model calculations to match the experimental value. (BR) denotes branching ratio. A11 energies are in MeV. I State “I 15B (this work) [A = 15 shell-model calculationsJ J” BR (%) 150 (E3) B(GT) b) 150 (Ex) B(GT) %- 62.8:t2.4 3.103 0.282i0.012 3.103 0.312 (calibration) (adjusted) %— 7.7:l:1.3 4.23:f:0.02 0.046i0.010 4.876 0.022 %- 22.8:t1.2 4.66:1:001 0.170:l:0.015 5.757 0.112 %— 4.1:1:0.9 5.85:1:0.04 0.049:l:0.010 6.333 0.010 g- a) 1.8:l:0.5 6.31:1:0.07 002410.007 5.881 0.001 a) Shell-model calculations predict a J’r = g: state following the {- state. Experi- mentally, there is uncertainty as to the J ” of this state (see last paragraph of Chapter 3, Section 5). b) B(GT) values calculated from Eq. 4.6. 120 Experimental Theory B(GT) Figure 4.2: Graphical comparison of the experimentally determined Gamow-Teller fl-decay strengths for 15B and those predicted by the theoretical shell-model for mass 15. The y-axis represents the energy levels (5,) in 15C. Refer to Table 4.1 for the actual B(GT) and E, values. Chapter 5 Conclusions In the present work, a number of goals have been successfully reached. It has been demonstrated that the N SCL A1200 radioactive beam device is capable of producing relatively pure radioactive secondary beams at exceptional rates, and in addition, these radioactive beams can be successfully transported to low background experi- mental vaults where decay studies can be conducted. Comparison of the number of 15B atoms created and studied in the present work using the A1200 to the number that where available in previous studies at the NSCL before the A1200 shows an approximately 1700-fold improvement. It is reasonable to conclude that the future looks optimistic for the decay studies of many other exotic nuclei at the NSCL. The newly constructed NSCL neutron detector array, a device designed for the study of fl-delayed neutron emitting nuclei, was used for the first time in the present study of 15B decay. This provided an opportunity to assess the array’s performance and learn about its capabilities and limitations, and identify areas where improve- ments could be made. A “working protocol” has been established for the use of the array. The electronic setup used in the 15B decay study, outlined in the present work, is the basis for other studies only needing those changes necessary to customize the implantation detector. A technique to determine the neutron detection efficiency of the array using a PuBe neutron source has been demonstrated. While this source 121 122 produces neutrons with a continuum of kinetic energies, it has been shown that a time-of-flight technique can be utilized to determine the neutron detection efficiency using 7-ray/neutron coincidences. Monte-Carlo neutron detection efficiency calcu- lations have also been performed for the array, and compared to the PuBe source results. It appears that the neutron detection efficiencies obtained for the array de- tectors using the PuBe source were adequate and reliable in determining the “detector solid angle independent” relative 15B fl-decay branching ratios, however if absolute branching ratios are to be determined from PuBe source determined detector effi- ciencies, work is needed in assessing the background attributed to this neutron source (this is discussed in the next to last paragraph of Chapter III, Section 5). In addition, different techniques have been explored to investigate the array’s ability to provide position information of detected neutrons. Here a technique employing timing signals of left vs. right detector sides showed position resolution of 13 cm (FWHM) could be achieved (this opens new possibilities for using the array in neutron correlation experiments) . In the present work, the half-life for 15B inclusive fl-emission was observed to be 10.3:l:0.2 ms, and an additional measurement requiring fl-neutron coincidences gave a value for this half-life of 10.5i0.5 ms. Both these values are in good agreement with the value of 10.5:l:0.3 ms in the literature, and confirm the 15B half-life value. The first fl-delayed neutron spectroscopy of 15B was performed using the neutron detector array. The population of the first five previously known negative parity states (J’r assignments for the first four states being known, the fifth having some uncertainty) that are neutron unbound in 15C was observed. In addition, the weak fl-decay branch to the 150 particle bound ground state and first excited state was observed and established to be 0.46:1:0.08%. Taking this as the zero-neutron emission probability, Po", and the measurement of P2,, = 0.4:l:0.2% by Reeder et al. [Re90], it 123 was concluded that 99.14:l:0.28% of the 15B fl-decays populate the five lowest negative parity states in 15C. As a result of these measurements the 15B fl-decay branching ratios have been established as 62.8:l:2.4%, 7.7:l:1.3%, 22.8:h1.6%, and 4.1:l:0.9% to the known (E,(MeV),J”) 3.103, %_; 4.220, g-; 4.657, g-; and 5.866, {- 15C states, respectively. In addition, it was deduced that the 1.8:l:0.5% branch to the 15C state at 6.31:l:0.07 MeV must be an allowed fl-decay. This helps to limit its J'r assignment mo: NW! to {3 , or The reported ,B-decay branching ratios are supported by (1) a measurement of 67.1i7.7% as the absolute fl-decay branch to the 3.103, if 15C state, and (2) the “adjusted” (refer to Chapter III, Section 5 of the present work) P1,, of 99% for 15B from the Reeder et al. [Re91] measurement. As a result of the present work, therefore, P0,, and P1,, for 158, as well as fl—decay branching ratios have been established. This establishes 15B as a potentially useful neutron detector calibration standard for other fl-delayed neutron experiments. Among limitations of the neutron detector array and areas where improvements could be made in addition to the work already addressed needed involving the PuBe source efficiency measurements, first and foremost is the neutron energy threshold of approximately 0.7 MeV. Since the amount of light produced in the plastic scintillation neutron detector is a function of neutron energy, it may be the case that this detector design is not adequate for the detection of low energy neutrons. The present detector design appears to be best for the detection of neutrons with kinetic energies in the range of 2 to 7 MeV. Presently, tests are being conducted to see if a third photo- multiplier tube placed at the center of a detector element can improve the detector’s ability to detect low energy neutrons. Another area of concern is multiple neutron detection using the array. In the present work, the low P2,, for 15B was impossible to differeniate from the background. For other situations where the P2,, is significantly higher (compared to the 0.4% P2,, for 15B), two—neutron decay studies may be very 124 feasible using the array. The advantages of using the array for such studies are the exceptionally large solid angle (1.9 steradians) and the ability to determine neutron positions; this opens the possibility of performing neutron angular correlation ex- periments. It should be noted that the efficiency to detect more than two neutrons at once (for example P3“, P4”, etc.) drops dramatically due to the fractional solid angle coverage (z1/9) and the intrinsic efficiency (R11 /5), and the feasibility of such measurements using the array is probably low. The agreement among the experimentally determined 15 B ,B-decay strengths from the present work and the shell-model predictions using the Millener-Kurath-Wildenthal interaction is, overall, quite good. It is thought that a better determination of the cross-shell interaction between protons and neutrons for the 15B case might improve its fl-decay description of exotic nuclei; the results of this work can aid in improving these shell-model interactions. Recently, two experiments were performed at the N SCL using the neutron detector array. These were decay studies of the fl-delayed neutron emitting nuclei 18N and 1‘Be. The array appeared to perform well in these experiments and analysis of the results are presently underway. An experiment to study multiple neutrons from the decay of “Li using the array is planned for the near future. Modifications are presently taking place which will allow for coincidence measurements between charged particles and neutrons from the decay of 11Li. With the impressive exotic nuclei production rates of the A1200 separator, it is thought that the array will be useful in studying many other fl-delayed neutron emitters in the coming years. Bibliography [A186] [A188] [Aj91] [Be72] [B074] [Br85] [Br88] [Br90] [Ce79] [Cu86] [Du84] [Fr81] [Ha81] [Hu90] [Kr88] F. Ajzenberg-Selove, Nucl. Phys. A460, 1 (1986). F. Ajzenberg-Selove, Nucl. Phys. A490, 1 (1988). F. Ajzenberg—Selove, Nucl. Phys. A523, 1 (1991). H. Behrens and W. Buhring, Nucl. Phys. A162, 111 (1972); “Electron Ra- dial Wave Functions and Nuclear fl-Decay” (Clarenson Press, Oxford) 1982. JD. Bowman, A.M. Poskanzer, R.G. Korteling, and G.W. Butler, Phys. Rev. C 9, 836 (1974). B.A. Brown and B.H. Wildenthal, AD and NDT 33, 347 (1985). B.A. Brown and B.H. Wildenthal, Ann. Rev. Part. Sci. 38, 29 (1988). B.A. Brown, private communication. R.A. Cecil, B.D. Anderson, and R. Madey, Nucl. Instr. and Meth. 161, 439 (1979). MS. Curtin, L.H. Harwood, J.A. Nolen, Jr., B. Sherrill, Z.Q. Xie, and B.A. Brown, Phys. Rev. Lett. 56, 34 (1986). J .P. Dufour, S. Beraud-Sudreau, R. Del Moral, H. Emmermann, A. Fleury, F. Hubert, C. Poinot, M. Pravikoff, J. Frehaut, M. Beau, A. Bertin, G. Gi- raudet, A. Huck, G. Klotz, C. Miehe, C. Richard-Serre, and H. Delagrange, Z. Phys. A319, 237 (1984). G. Friedlander, J .W. Kennedy, E.S. Macias, and J .M. Miller, “Nuclear and Radiochemistry” (John Wiley and Sons, New York) 1981. L.H. Harwood and J.A. Nolen, Jr., Nucl. Instr. and Meth. 186, 435 (1981). F. Hubert, R. Bimbot, and H. Gauvin, AD and NDT 46, l (1990). K. Krane, “Introductory Nuclear Physics” (John Wiley and Sons, New York) 1988. 125 [Le89] [Mi75] [Nfi86] [0039] [Mu84] [Mu88] [Pa72] [P066] [Re90] [3391] [Sa88] [Sc83] [Sh91] [Sn83] [vvass] [VVi74] [vvunn [vyissAq 126 M. Lewitowicz, Y.E. Penionzhkevich, A.G. Artukh, A.M. Kalinin, V.V. Ka- manin, S.M. Lukyanov, N .H. Chan, A.C. Mueller, D. Guillemaud-Mueller, R. Anne, D. Bazin, C. Detraz, D. Guerreau, M.G. Saint-Laurent, V. Bor- rel, J .C. Jacmart, F. Pougheon, A. Richard, and W.D. Schmidt-Ott, Nucl. Phys. A496, 477 (1989). D.J. Millener and D. Kurath, Nucl. Phys. A255, 315 (1975). D.J. Millener, private communication. David Mikolas, Doctoral Dissertation, Michigan State University, 1989. J.A. Musser and J .D. Stevenson, Phys. Rev. Lett. 53, 2544 (1984). AC. Mueller, D. Bazin, W.D. Schmidt-Ott, R. Anne, D. Guerreau, D. Guillemaud-Mueller, M.G. Saint-Laurent, V. Borrel, J.C. Jacmart, F. Pougheon, and A. Richard, Z. Phys. A330, 63 (1988). L. Pages, E. Bertel, H. Joffre, and L. Sklavenitis, AD and N UT 4, 1 (1972). A.M. Poskanzer, S.W. Cosper, E.K. Hyde, and J. Cerny, Phys. Rev. Lett. 17, 1271 (1966). P.L. Reeder, R.A. Warner, W.K. Hensley, D.J. Vieira, and J .M. Wouters, “Exotic Nuclear Spectroscopy” , Edited by Wm. C. McHarris (Plenum Press, New York) 1990. P.L. Reeder, R.A. Warner, W.K. Hensley, D.J. Vieira, and J .M. Wouters, Phys. Rev. C 44, 1435 (1991). M. Samuel, B.A. Brown, D. Mikolas, J. Nolen, B. Sherrill, J. Stevenson, J.S. Winfield, and Z.Q. Xie, Phys. Rev. C 37, 1314 (1988). H.W. Schuh, PHAEDRUS, Institut fur Kerphysik der Universitat zu Koeln (1983) [unpublished]. B.M. Sherrill, D.J. Morrissey, J.A. Nolen, Jr., and J.A. Winger, Nucl. In- strum. Methods Phys. Res. B56/57, 1106 (1991). K.A. Snover, E.G. Adelberger, P.G. Ikossi, and B.A. Brown, Phys. Rev. C 27, 1837 (1983). E.K. Warburton, J.A. Becker, B.A. Brown, and D.J. Millener, Ann. Phys. 187, 471 (1988). D.H. Wilkinson and BE. Macefield, Nucl. Phys. A232, 58 (1974). B.H. Wildenthal, M.S. Curtin, and B.A. Brown, Phys. Rev. C 28, 1343 (1983). B.H. Wildenthal, “Progress in Particle and Nuclear Physics” (Pergamon, New York) 1983. [Wi91] [W054] [W090] 127 J .A. Winger, B.M. Sherrill, and D.J. Morrissey, in Proceedings of the 12‘” International Conference on Electromagnetic Isotope Separators and Tech- niques Related to Their Applications, Sendai, Japan, Sept. 2-6, 1991 [Nucl. Instr. and Meth. (to be published)]. R.D. Woods and D.S. Saxon, Phys. Rev. 95, 577 (1954). S.S.M. Wong, “Introductory Nuclear Physics” (Prentice Hall, New Jersey) 1990.