g 11.13311? 12' ,YML’lhg .3663}; ‘0rfzrj ”Rem This is to certify that the thesis entitled RMIM/ Ba, Via/S A4 [82%)6 presented by Maw—k Frank/in 5370?]ka i has been accepted towards fulfillment of the requirements for AM S'_degreein / é? S/CJ' IJL/J‘A’A Major professor Date 4,9,4 tum _ 0.7539 OVERDUE FINES ARE 25¢ PER DAY PER ITEM Return to Book drop to remove this checkout from your record. ROTATIONAL BANDS IN 182RE BY Mark Franklin Slaughter A THESIS Submitted to Michigan State University in partial fulfillment of the requirements ' for the degree of MASTER OF SCIENCE Department of Physics 1979 ABSTRACT ROTATIONAL BANDS IN lngE BY Mark Franklin Slaughter Levels of the odd-odd deformed nucleus 182Re were studied using the techniques of in-beam y-ray spectroscopy. y-singles, Y-Y coincidence, y-ray angular distribution, and lifetime experiments were performed using Ge(Li) detectors. Additional levels of the two previously reported rotational bands were observed. The bandhead of the upper band, assigned to the 9-{9/2-[514+] a 9/2+[624+]} con- i 2 nsecs. The figuration, was found to be delayed by 6 l4- and 15- levels of this band are fed by transitions deexciting an isomeric level (T;5 = 88 i 8 nsecs) at 2256.4 keV. From branching ratios obtained for the 7+ band, together with the recently measured g-factor of the 64 hr isomer of 182Re, the value of gR for 182Re was inferred to be 0.15 i 0.07. Members of two other rotational bands were identi— fied. The first is thought to be built on the 2+ 12.7 hr isomer while the second, built on an isomeric level (T8 = 780 i 90 nsecs), decays via the 461.3 keV transition to the 2+ isomer. ACKNOWLEDGEMENTS I wish to thank Dr. H. G. Blosser, Dr. P. Miller, and the staff of the MSU Cyclotron Laboratory for making the experimental work possible, as well as Mr. R. Au and the computer staff for their aid in data accumulation and analysis. Dr. F. M. Bernthal and Dr. wm. C. McHarris were generous with their advice and criticism. I particularly wish to thank Dr. T. L. Khoo and Dr. R. A. Warner for their invaluable assistance, without which this project would never have been completed. I am grateful for the friendship and assistance of W. Bentley, Dr. C. B. Morgan, and B. D. Jeltema through- out the past several years. Finally, I especially wish to thank my advisor, Dr. W. H. Kelly, for suggesting this project, and for his interest, support, friendship, and, last but not least, patience over the past few years. I acknowledge the financial assistance of the National Science Foundation and Michigan State University. ii TABLE OF CONTENTS LIST or TABLES ...................................... LIST OF FIGURES ..................................... INTRODUCTION ........................................ EXPERIMENTS ......................................... LEVEL ASSIGNMENTS: 7+ AND 9' BANDS ................. LEVEL ASSIGNMENTS: 2+ and 4' BANDS ................. g-FACTORS ........................................... CONCLUSION .......................................... BIBLIOGMPHY OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOIOOOOOO iii iv 19 40 46 56 58 Table 1. LIST OF TABLES Page y-rays observed inbeam from the 181Ta(a,3ny)182Re reaction ..................... 7 Angular distribution results ................... 16 6 and lgK - gRl/QO from angular distribution results and branching ratios ................... 48 Theoretical and experimental gK ................ 53 Theoretical gKu.O...OOOOOOOOOOOOOOOOOOOOOOIOOOOO 55 iv LIST OF FIGURES Figure Page 1 Schematic figure showing the energy levels in a nucleus of mass W 160 versus angular momentum. Indicated on the figure are (i) the lowest non-g.s.b. energy levels for each spin (yrast levels), (ii) the regions of pOpulated states following (He,4n) and (Ar,4n) reactions, and (iii) the g.s.b. levels of a typical vibrator (dots) and rotor (daSheS)COO...0.00000000000000000000000 4 2 y-ray singles taken with the LEPs detector .. 6 3 XADC integral coincidence spectrum .......... 10 4 y-ray angular distributions, 7+ band ........ 12 5 y-ray angular distributions, 9- band ........ 13 6 y-ray angular distributions, 2+ and 4- bands. 14 7 Angular distributions of the 647.3 keV, 268.0 keV, 344.6 keV, and 461.3 keV y-rays... 15 8 y-ray singles from the 182W(p,ny)182Re reaction I.00.000.000.000...00.0.0000...DO... 18 9 Theoretical and experimental levels-- neutrons I...COO...0.0000000000000000....0... 20 10 Theoretical and experimental levels-- protons OOOOOOOOOCOIOIOIOOOOOOOOOOQOOOOOOOOOO 21 11 Level scheme ................................ 23 12 Coincidence gates associated with the 7+ band OOOOOOOOOOOOOOOOOOOOIIOOIOOOOOOOOOOOOOOO 24 13 Coincidence gares associated with the 9— band OOOOOOOOOOOOOOODID...OOOOIOOOOOOOOOIOOO. 25 14 Coincidence gates associated with the 4- band COO-.00...OI...OOOOOOOWOOOOOOOOIOOOOOO... 26 15 Coincidence gates associated with the 2+ band 0.0.0.0000...IOOOOOOOOOOOOOOOOCOIOO0.... 27 Figure 16 17 18 19 20 21 22 23 Page 344.6 keV, 398.3 keV, and 539.9 keV coincidence gates ........................... 28 Spectra created by summing gates set on members of the 7+ and 9‘ bands .............. 29 Angular distribution of the 289.0 keV y-ray . 30 Theoretical angular distributions for y-rays feeding an 8+ level ......OOOOOOOOOOOOOOOOOOO 32 Tl/Z curved for members of the 9- band ...... 35 (EI - EI_1)/ZI for the 9‘ band. The last point results from an attempt to place the 2256.4 keV level in the band ................ 36 Spectra created by summing delayed goinci- dence gates set on members of the 9 band ... 38 Delayed coincidence gates associated with the4 band O......OOOOOOOOOOOOOOIOOI.......O 42 INTRODUCTION A fundamental goal of nuclear physics is to quanti- tatively characterize the nuclear force. This requires an understanding of the interactions of nucleons derived from nucleon-nucleon scattering experiments and nuclear structure studies. Nuclear structure, in particular, has been partially understood in terms of the nuclear shell model, which in its simplest form, considers each nucleon to move independently in the average potential created by the others. This is only an approximation to the actual situation. To further the agreement with experiment "residual interactions" are in- cluded as perturbations. Among these is the p-n residual interaction. Odd-odd nuclei are particularly suitedtxaa study of the p-n residual interaction because of the large number of low-lying many—quasiparticle levels. Deformed odd-odd nuclei are of particular interest; however for experimental reasons these have been studied the least. Intrinsic states in de- formed nuclei have been successfully predicted by the Nilsson model which treats nucleons as moving in a non-spherical potential. Single-particle states in the Nilsson model are characterized by the asymptotic quantum numbers QH[anA2] where N and B2 are harmonic oscillator quantum numbers and A, Z, and n are the projections on the nuclear symmetry axis of the particle orbital, spin, and total angular momenta, respectively (Ma 70). H is the parity. In a deformed nucleus, levels due to the collective rotational motion of the nucleons also arise. For odd-odd nuclei these consti- tude rotational bands built on intrinsic several-quasi- particle states. The lowest level of each band, called the bandhead, is characterized by I=K=Q where I is the total nuclear angular momentum and K is the projection of I on the nuclear symmetry axis. For axially symmetric nuclei K is a constant, to first order, throughout a given rota- tional hand. If there is no significant mixing the rota- tional levels of a band can be fitted to the emperical expression. _ 2 2 Erot - AI(I+l) + BI (1+1) The constant A is hz/ZI where I is the nuclear moment of inertia (Sh 74). This thesis reports the results of a y-ray spectro— scopic study of levels in the odd-odd nucleus 182 Re populated in-beam by the (a,3ny) reaction. Prior to this work Hjorth et a1. (Hj 68) prOposed two rotational bands based on y-ray singles and y-ray angular distribution data taken with a Ge(Li) detector. Each band had six levels. K values of 7 and 4 or 5 were assigned. On the basis of y-ray singles and y-y coincidence data taken with Ge(Li) detectors, Medsker et a1. (Me 71) reported that the ordering of these bands was opposite to that prOposed by Hjorth et al. A 7+{5/2+[402+] a 9/2+[624+]} assignment for the ground band and a 9-{9/2-[514+] a 9/2+[624+]} assignment for the upper band were suggested. EXPERIMENTS 182 According to the Nilsson model Re has a ground state spin and~parity of 7+ resulting from the triplet coupling of the 5/2+[402+] proton and the 9/2+[624+] neutron. This ground state has not been observed in decay 182 studies. The 0+ ground state of Os B+-decays to low 182 spin states in Re which feed the 2+, 12.7 hr isomer. This isomer, which has been assigned to the singlet coupling {5/2+[402+] a 9/2+[624+]} (Bu 73) then decays directly to 132W (Sc 75). Therefore a y-ray spectrosc0pic 182 states in study of high spin states in Re must rely on in-beam techniques. The a-particle beam of theMichigan State Uni- versity cyclotron is suited for this work. For medium mass nuclei bombarded with G beams of approximately 30 meV the (a, xny) reaction dominates. The number of neutrons which are "boiled off" depends on the incident beam energy. The nature of this compound nuclear reaction favors the popula- tion of a variety of high-spin states which decay to ground along the so-called yrast line. A typical y-ray deexcita- tion scheme is shown in Figure 1 (Ne 70). Among any set of states at a particular excitation energy, the state with the highest K value will tend to be the most strongly pOpu- lated. A large number of isomeric levels are expected to occur because the decay of high K levels to lower levels of much smaller K is forbidden (Ma 70). Instead these states must often decay directly to ground and are (MeV) Excitation energy _ 5') Z‘l ' r I I I I '. A~Iso . - Population {allowing 20 _ “Ar. 4 n I6- ’ Population following I 2 '- “He, 4n 8 P No levels 0.43;“ l i l I l 1 IO 20 3O 4O 50 60 I (in units of h) Figure 1. Schematic figure showing the energy levels in a nucleus of mass m 160 versus angular momentum. Indicated on the figure are (i) the lowest non- g.s.b. energy levels for each spin (yrast levels), (ii) the regions of populated states following (He,4n) and (Ar,4n) reactions, and (iii) the g.s.b. levels of a typical vibrator (dots and rotor (dashes). hindered with respect to transition rates based on the Weisskopf estimates (Le 67). For this study the a particle beam of the MSU cyclotron was used to perform the (a,3 ny) reaction on a 0.1 mil self-supporting 181 Ta foil. A rough excitation function established that the optimum beam energy for this reaction is 38 MeV. Singles data were taken with a Low Energy Photon (LEPs) Ge(Li) detector with a resolution of 650 eV at 122 keV. The detector was oriented at 1250 relative to the beam direction. This orientation reduces effects due to the angular distribution of the y-rays (by rendering the term in A = 0 - see page 5) and permits 2 accurate evaluation of y-ray peak intensities. Data were taken for y-rays of energy up to 1 MeV. The resulting singles spectrum is shown in Figure 2. Table 1 lists 181 2Re reaction y-rays associated with the Ta(a,3ny)18 with intensities evaluated from these data. Unless otherwise noted only y-rays seen in coincidence with assigned transitions are included. Three parameter (7 energy-y energy-y timing) coincidence data were taken with two true coax Ge(Li) detectors. Detector efficiencies were 4.5% and 7% relative to a 3” x 3" Na(T1) detector for gammas at 1333 keV with a source to detector distance of 25 cm. Absorbers of about 12 mils each of Cu and Cd foil were placed in front of the detectors to minimize the contribution of X-rays to the count rate. Nine magnetic tapes of coincidence data, each ‘EJNNVHS 83d SlNflOCJ _ . w . . 8 C.) :1” £299 - $2“th - 2'98; \ sees O _ O S'SHS \ O 6'689 , (Y) £‘86h x CI (p 8'86h , LlJ UJ swan -- m __J I'OSh ... 2 LD Z'l-uhl-I f :1 Z Z 8268 (I?) 3168‘ «- 8 - C) ..J 911% .x (\J LIJ LlJ gees , Z a: Z N 0'682 — < (I) ease I F... 6'898 f U xx _ 8:98! —~ 8 818! C) l'hSl - F" mat , l'éOI - 2'96 ~— 8'64 - l l 1‘ b» co In :1- m c) C) O C) y-ray singles taken with the LEPS detector. Figure 2. TABLE 1 y-RAYS OBSERVED IN-BEAM FROM THE l81TA(a,3ny)182RE REACTION Energy (keV)a Intensityb Energy (keV)a Intensityb 55.6c 27 217.0 4.3 (0.5) 76.3 2.4 (0.2) 220.8 2.5 (0.3) 79.8 3.4 (0.2) 230.1 (0.3)e --- 95.7 4.2 (0.3) 231.8 5.5 (0.3) 107.1d 7.9 (0.5) 234.9 23 (1) 119.5 5.3 (0.3) 237.6 16 (1) 131.4 8.8 (0.2) 258.9 15 (1) 136.4d 17 (1) 260.9 8.9 (0.5) 152.3 (0.2) 1.6 (0.4) 263.3 6.3 (0.4) 154.1 80 (5) 268.0 3.2 (0.2) 160.4 (0.2) ' 276.0e 6.1 (0.4) 11.7 (0.7) 161.3 (0.2) 281.2 (0.2) 11 (1) 175.1e 8 (1) 282.3 (0.2) 6 (1) 179.3 8 (1) 289.0 100 180.2f 31 (2) 292.2 4.4 (0.3) 181.8 43 (3) 303.0 6 (1) 185.3 36 (2) 303.6 4 (1) 191.6e 6.3 (0.4) 321.3 4.2 (0.3) 197.2e 18 (1) 332.3 2.5 (0.2) 209.3 37 (2) 339.5d'e 14 .(1) 210.6 5.5 (0.3) 341.7 1.8 (0.2) 212.6 23 (2) 344.6 3.4 (0.3) Table 1--Continued Energy (keV)a Intensityb Energy (keV)a Intensityb 358.2 (0.2) 1.5 (0.2)- 498.3d 21 (1) 391.2- 5.1 (0.3) 539.9 8.4 (0.5) 395.9 6.4 (0.4) 543.3 13 (1) 397.8 17 (1) 583.8 6.9 (0.5) 437.6 6.5 (0.4) 585.7 13 (0.8) 442.2 9.2 (0.6) 624.5 9 (1) 450.1 18 (1) 647.3 4.9 (0.4) 461.3 33 (2) 662.7 3.6 (0.3) 493.8 11 (1) aUnless otherwise indicated, the uncertainty is i 0.1 keV. _ bIntensities are normalized to that of the 289.0 keV y-ray. ' cFor experimental reasons this transition is not seen in this study. It is placed by Burson, et a1 (Bu 73). dThis peak is an unresolved multiplet of 182Re y-rays. eThis peak is an unresolved multiplet. Other com- coments (not belonging to 182Re) are due to transitions in nuclei produced by the competing reactions. fThe'2-+3+ transition is placed by Burson, et al. (Bu 73). (Not shown in the level scheme of Figure 9.) containing about three million events, were filled during the two day experiment. One of the integral coincidence spectra is shown in Figure 3. Following the coincidence run, the LEPs detector was used to count the remaining target activity. Because the decay of the two 182Re isomers to states in 182W is well known (Sc 75, Je 74) the resulting apectrum allowed us to estimate that about 90% of the 182 Re activity was from the 64 hr isomer. Timing experiments were performed with the cyclotron beam sweeper and the LEPs detector. The beam sweeper de- flects a variable fraction of the cyclotron beam bursts away from the target. Data were taken, controlled by the program TOOTSIE (Ba 71), on the cyclotron Sigma-7 computer during the time the beam is off the target by separating this interval into nine approximately equal time bands. Two time ranges were investigated. In the first the beam was deflected from the target for 8 beam bursts or approximately 400 nsecs. In the second timing experiment alternate beam bursts were deflected with the total time between bursts about 54 nsecs. A y-ray angular distribution was performed using a goniometer and the LEPs detector. Data were collected at six angles (taken in random order) relative to the beam 0 0 direction: 90 , 105°, 115°, 130 , 140°, and 145°. Un-> fortunately, by the time data were taken at the last angle, 105°, y-ray peaks from the decay of 182Re to 182W over- whelmed the peaks of interest. This resulted in substantially 10 9000 l L . Q'EHQ \ 6'689 Z'BSI‘I — 1'09). — ' ' 8268 '— 36“; race — O'SQZ '1'! 98 4282 N. O'SEZ ’ L. 9'3)? '\. 9603 " 8'98! 818‘ 2" 425' VHS!" \ 1 3' CD C) CH WBNNVHQ 836 81NH03 3000 2000 CHANNEL NUMBER XADC integral coincidence spectrum. 1000 Figure 3. 11 poorer statistics for peak areas of 182Re y-rays as compared with those obtained for the other angles. y-raye angular distributions are customarily analyzed in terms of the Legendre polynomials. Figures 4, 5, 6, and 7 show the results for some y-rays of a least squares fit of the normalized data to W(8) = A0 + A2P2(cose) + A4P4(cose) AZ/AO and A4/A4 coefficients derived from the fit are listed in Table 2. Target and product x-rays were used for the normalization. It was found that better fits were obtained with the 1050 data omitted. This information was therefore ignored in the calculation of the results reported here. A Preliminary singles data shown in Figure 8 from the 182W(p,ny)182Re reaction indicated that two rotational bands, new to this work and identified in the (0,3ny) coincidence data, were of low K. In the hOpe of obtaining more informa- tion about these bands another coincidence experiment was undertaken. A 29 MeV proton beam was used to perform the (p,3ny) reaction on a 184W foil mounted in Formvar. No new information regarding the previously identified bands was obtained so the data were not further analyzed. 12 CASCADE CROSS-OVER 282.3 . 593.3 260.9 998.3 A INTENSITY 397.8 V 159.1 1.0 1 0' 10' 20‘ 30‘ 90‘ 50‘ 80‘ 70' 80‘ 9010' 10‘ 20' 30' 90' so" so" 70" 80“ so" ANGLE ANGLE Figure 4. y-ray angular distribution, 7+ band. 13 CASCADE CROSS-OVER V INTENSITY fl 1.0 . 281.2 258.9 999.2 239.9 209.3 391.2 181.8 o. )0’ 20’ 30’ 90‘ 50’ 60‘ 70’ 80’ 90’0' 10" 20" 30° 90° 50“ 60'" 70° 80" at; ANGLE ANGLE Figure 5. y-ray angular distribution, 9- band. 14 INTENSITY T 95.7 1.2 )- 1.0 79.8 L 1 l l l l l l L d 0’ 10' 20‘ 30’ 90’ 50' 60' 70‘ 80' 90'0’ 10' 20' 30' 90' 50' 60' 70' 80' 80' ANGLE ANGLE Figure 6. y-ray angular distribution, 2+ and 4- bands. 15 2d. 2». 1.9 .. 1.8 . 1.7 . 1.6 .1 1.5 3 L9. 1.3 .. L2. 268.0 INTENSITY 461.3 INTENSITY F 1.0.. l l L L l J J__ l l l l l j 0' 10° 20' 30' 90' 50' Go' 70' 80‘ so'o' 10‘ 20‘ 30‘ 90' 50' 60‘ 70' 80' 90‘ ANGLE ANGLE l l J__l Figure 7. Angular distributions of the 647.3 keV, 268.0 keV, 344.6 keV, and 461.3 keV y-rays. 16 TABLE 2 ANGULAR DISTRIBUTION RESULTS Transition Assignment K 142/A0 114/1).0 (keV) 154.1 8”+7+ 7 0.227 i 0.011 0.037 i 0.013 185.3 9++8+ 0.304 1 0.016 0.044 t 0.017 212.6 10++9+ 0.314 i 0.027 0.045 f 0.035 237.6 11++10+ 0.396 t 0.018 0.072 1 0.023 260.9 12++11+ 0.427 f 0.026 0.081 f 0.038 282.3 13++12+ 0.405 f 0.030 0.081 f 0.044 339.5 9"+7+ 0.304 t 0.102 0.058 t 0.137 397.8 10++8+ 0.310 i 0.076 -0.063 f 0.105 450.1 11++9+ 0.224 1 0.029 -o.072 1 0.035 498.3 12++10+ 0.335'1 0.017 -0.135 f 0.018 543.3 13++11+ 0.341 i 0.091 -0.074 1 0.150 181.8 10'+9' 9 0.159 f 0.018 -0.012 f 0.025 209.3 11'+10‘ 0.219 1 0.012 0.032 t 0.015 234.9 12'+11' 0.261 t 0.036 0.029 i 0.049 258.9 13‘+12‘ 0.209 i 0.058 -0.013 i 0.075 281.2 14'+13' 0.325 1 0.151 0.067 1 0.203 391.2 11'+9’ 0.368 f 0.065 0.002 f 0.106 444.2 12‘410’ 0.451 f 0.008 0.158 1 0.012 289.2 9‘+8+ - -0.147 1 0.006 0.028 1 0.009 344.6 17++15’ 0.608 t 0.119 -o.112 i 0.159 647.3 17++14‘ 0.591 t 0.197 0.310 f 0.317 l7 TABLE 2--Continued Transition Assignment K AZ/A0 A4/A0 (keV) 107.1 6'+s‘ 4 -0.382 1 0.051 0.054 1 0.091 131.4 7'+6‘ -0.384 f 0.024 0.026 i 0.036 160.4 8'+7‘ -0.469 t 0.036 -0.021 t 0.063 217.0 10’+9' -0.527 i 0.059 0.142 1 0.086 95.7 5++4+ -0.223 f 0.031 0.032 t 0.048 119.5 6++5+ -0.266 1 0.018 0.032 f 0.028 161.3 8++7+ -0.271 f 0.027 0.065 f 0.043 18 Door . SCH UGQH mm .6 .2: mmm232 )_m_ZZc.mv3mm Gnu Eoum noaocwn hon)» .m muamfih 03w n N ll. 0:6 .6 3 H 33 H V N ..NJ or) LEVEL ASSIGNMENTS: 7+ AND 9‘ BANDS The single particle levels of a deformed nucleus can be calculated in the Nilsson model from the quadruple and hexadecapole deformation parameters 62 and E4, the spin-orbit coupling parameter K, and the parameter n which functions to depress states of high angular momentum (Ni 70). Because these parameters vary slowly over the region their values can be estimated by taking the average of those experimentally deduced for the neighboring even-even tungsten and osmium nuclei. In this manner we obtain E =0.24 and 6 =0.05. The 2 4 other parameters can be determined from equations given by Nilsson and Tsang (Ni 69). Single particle levels calcu- lated from these parameters are shown in Figures 9 and 10 compared to experimentally determined levels for neighboring 182Re is odd A nuclei (Ba 73, Ar 75). The ground state of therefore expected to result from the coupling of the 5/2+[402+] proton and the 9/2+[624+] neutron. Recent atomic beam experiments (Ru 75) have established that the 12.7 hr isomer has spin 2, probably from the singlet coupling of the above particles. No measurements for the longer lived 64 hr isomer were reported. However, log ft values deduced by Sapyta et al. (Sa 70) indicate that the 64 hr isomer has spin and parity 7+, 6+, or 6-. This result is consistent with the triplet coupling 7+{5/2+[402+] a 9/2+[624+]}. The coupling rules of Gallagher and Moszkowski (Ga 58) predict that for odd-odd nuclei the triplet coupling will 19 ‘ ENERGY (MeV) -2; Figure 9. 20 NILSSON LEVELS (Neutrons) EXPERIMENTAL LEVELS ISZRe IV2+[6|5] 7/2-[503] 3/2-[512] l/2 - [510] 9/2 + [624] 7/2- [5:4] 5/2 - [5 )2] v2 - [52 I] 7/2 9 [633] 5/2 + [642] __ I/2 - [SZI] |8|w 3/2 - [5 l2] 7/2 - [503] 1/2 - [5 IO] 9/2 + [624] 5/2- [SIZJ 7/2' 5|4 7/2 + [633] Theoretical and experimental levels-~neutron. 21 NILSSON LEVELS (Protons) EXPERIMENTAL LEVELS I82Re ISIRe '83Re 2 " lll2- [505] _ I/2 + [660] 3/2-[532] _ v2 - [54)] I _ __ 3/2+[402] ’>‘ g 112 - [54)] 5 v2 - [54 I] a: 1.1.1 5 0.. __ 5/2 +[402]_____ 5/2+[402] _____. 512+ [402] __ 912- 5:4 __ 9/2 - [5I4] [ J ‘ 9/2 -[5l4] __ 7/2 + [404] __ l/2 *4 [411] 7/2 4 [404] " [’ ___. I/2 + [4n] I/2 + [4n] __ 7/2 - [523] -2; Figure 10. Theoretical and experimental levels—~protons. 22 produce the lower energy state. Therefore, the expected ground state spin and parity are 7+. Unfortunately, because of the large spin difference, no communication between the two isomers is anticipated, so the above prediction cannot be verified. Nevertheless, for the purposes of this work, we will consider the 64 hr isomer to be the ground state. According to this assignment the level scheme con- structed from the coincidence data is shown in Figure 11. Members of the two rotational bands reported by Hjorth et al., here assigned to be the 7+ and 9- bands respectively, were prominent in the integral coincidence spectra. How- ever, as reported independently by Medsker et al., gates set on these transitions shown in Figures 12-13 indicate that the arrangement of the two bands is opposite to that proposed by Hjorth et a1. with the 154.1 keV transition of the lower band being fed by members of the upper band via the 289.0 keV transition. Gates set on the 154.1 keV peak reveal only the y-rays known to be feeding that level. There are no other unplaced y-rays in the singles spectrum of sufficient intensity to deexcite the level fed by the 154.1 keV transition. Therefore this transition must directly feed either the 2+ or the 7+ isomer. Because the (a,3ny) reaction populates states which decay mostly to the 7+ isomer, the latter situation is more likely. Level systematics and y-ray angular distributions support the assignment of the 154.1 keV level to the 8... member of the 23 L. 0.03 m6... «1 ...o ndnn. (I. -0. ..hoo _ ...:0. .0. o: .ofimson Ho>mq .HH ousmwb 5‘ '0 oh .o .m 825: 33. iv 4 ‘7 .. 0 Non 60.0%.. .0. 0.38.0 .10.. .0. . o $.005fivnwu 4: anO JQOLw/ne .... 8;". ...... e 63...... G A. 0.23.. were. .2 flag. ......mev .n. c o w 0 . . . (anodes. . .1 . . . are: . . u ._ . . _ _ . . _ . . . . as . .%%.+J...n= ./ he . . (PIA. _ - . . . . . . . . 82.38 4.8% 4H. lllll L . ... «8% ‘0 A. = .I. rely. .v ... 0.28 f 0% % 24 154 1 . 2000 ~ g N M \O L 141:;ch 1:: 01—1 HHO‘N O 1000 - “‘6. <3 ‘2- —J 1 L.|.J Z 2: 18543 :I: 800 ‘ \o L) '1 6. v H :2 N 0: .. ... . LLJ . c: :5 .. ‘0. .00 L :8 3 5 a 1 NNM (n g} 1— ‘ ~ 1 Z w 1 ~ 3 '54 .1M“1.mulu..1. ..- .... D 260.9 U 200 1 m r. H [1:100 0 Q o o <‘ HN!‘ O H 1‘ L'T F1” 0 o "‘ N" S E?» 2 100 N '3 m . r 1 1 1, 1 0 ‘ ' ' 11"”...(1nal111 1 . 1. 1000 ' ' 2000 CHANNEL NUMBER Figure 12. Coincidence gates associated with the 7+ band. 25 2000 - _J 1000 9 L1.) E J“ I 2000» 2 t.) Fl 1"”) LI: 47 6' LlJ ‘3 86.6 0. 1000 6365 1 ML") NO! (I) }_ . Z :J ‘7 7‘ ‘. 0 208.3 (.1 2000 - o, ‘ 0‘ Q CO 0 N 1-1 1-1 CD 61 o 1—1 0 <11 '3’ 1000 2 $35 ‘ 1000 2000 CHANNEL NUMBER Figure 13. Coincidence gates associated with the 9- band. 26 107.1 100 b V '2 GQ‘ o I". '31 MQI‘O F'HDr-i 0 F1 1‘ H N 50 - _J IJJ 2: 2: t (I) 22 LL] F. a L1J I- 2 F ,_ . 3 : * IJJ 0: L. O" 0] 0:2 d3 T01. sec) Figure 20. Tl/Z curves for members of the 9- hand. 36 umfimuum cm Eouw muasmmu unflom puma $29 000 .8:82 0:» :e 30>0H >0x e.em- mewsmotee cu .wemn am may you H~\A 00¢ NHN CON Hm I H m. .HN muswfim 00m J1 IZ/"Ia-Ia 37 characterized by a sharp peak, typically 15 nsec FWHM (full width at half maximum), corresponding to prompt events. By setting coincidence gates off the prompt peak transitions feeding an isomeric level can be emphasized. In the delayed coincidence gate thus produced, peaks from delayed transitions will appear more intense than those from prompt transitions. Delayed coincidence gates on easily resolved members of the 9- band were summed and an appropriate fraction of the integral coincidence spectrum subtracted to partially eliminate prompt and chance contamination. From the result- ing spectrum, Figure 22, we conclude that transitions of 268.0 keV and 358.2 keV feed the isomeric level at 2256.4 keV. These two y-rays are not in coincidence with each other. As a check, delayed coincidence gates were set on these peaks to emphasize transitions deexciting the isomeric level. Only the 344.6 keV and 647.3 keV peaks and members of the 9- band appear in both gates. Therefore, we conclude that the isomeric level decays exclusively through the 9- rotational band. The angular distributions of y-rays from the 344.6 keV and the 647.3 keV transitions are characterized by positive A2 coefficients. This establishes that neither are stretched dipole transitions. The angular distribution of the 344.6 keV y-ray is consistent with the assignment of spin 15 to the 2256.4 keV isomeric level. In that case the 647.3 keV y-ray would have to be a quadrupole 15+l4 transi- tion. The 647.3 keV transition is quite intense relative to 38 . .och to was no endgame so you mmumm cocoowocwoo oohmamo oneseom ma oounouo muuommm mmm232 JwZZH0mmucs cm cw mmHH “no mo coHumasono on» How @0000: coHuHmcmuu odomouomov wast Hoo.o H mmo.o ooo.o H Hoo.o monuo>n moo.o H mmo.o uuuuuuuuuuuuu so.o H om.o uuuuuuuuuuu -ma o.mom ooo.o H omo.o oHo.o H Heo.o mo.o H em.o HH.o H me.o -aH ~.Hm~ u uuuuuuuuuu u- sso.o H ~oo.o uuuuuuuuuuu so.o H om.o -mH o.om~ moo.o H emo.o soo.o H ~mo.o mo.o H om.o mo.o H mm.o umH o.em~ eoo.o H mmo.o moo.o H omo.o ~o.o H mm.o mo.o H ~m.o uHH m.oo~ ---- ......... moo.o H oeo.o uuuuuuuuuuu ~o.o H m~.o nos o.HoH ~oo.o H rso.o soo.o H oso.o 0onno>n ooo.o H ooo.o .......... us- oo.o H as.o uuuuuuuuuuu +aH o.mom moo.o H omo.o ooo.o H Hao.o ~o.o H.Hs.o HH.o H om.o +MH m.~o~ uuuuuuuuuuuuu ooo.o H emo.o anuuuuuuuuu- HH.o H mm.o +~H o.oo~ ~oo.o H oao.o ooo.o H Hao.o ~o.o H ~e.o so.o H oa.o +HH o.em~ ~oo.o H oao.o soo.o H omo.o mo.o H ma.o oo.o H oe.o +oH o.os~ uuuuuuuuuuuuu ooo.o H omo.o .uunuu-nuuuu mo.o H om.o +o m.mmH ..... uuuunnuu moo.o H omo.o nuuuuuuuuuu mo.o H ~m.o +o H.emH o onqmmnunqu use one Ho aomwwmwnue monommu so mOHaflm UZHEUZémm 62¢ mEADmmm ZOHEDmHmEmHD m¢ADUZ< 20mm 5mm I xm_ Q24 0 m mflmda 49 Also within the rotational model, the mixing ratio can be calculated from the branching ratio, A, of crosSover- to cascade transition intensities according to (Al 64). '1 1(3)5 +1 -1+ - - _=_ Y (I )(I ma 1 K)_1(4) 62 A (Ey')5 2K2 (21 - l) Table 3 gives values of 6 and lgK - gRl/QO calculated from experimental branching ratios for the 7+ and 9- bands. Transition intensities were obtained from y-ray singles data taken at 1250 with respect to the beam direction. Also for transitions in the delayed 9' band, intensities were found from the singles spectrum created by summing the time band spectra from the "slow" timing experiment. Values of 6.and ng - gRl/Qo, derived from these two sets of data were averaged to obtain the results listed for the 9' band. It can be seen that the mixing ratios calculated by the two methods agree within the experimental uncertainty. Also, the branching ratio calculations indicate thatlgK - gRI/Qo, as predicted by the rotational model, is constant for each band. Furthermore, the average lgK - gRl/Qo determined from the angular distribution data agrees with that calcu- lated from the branching ratios. We therefore have a more or less model independent check of the more precise branching ratio results. The intrinsic quadrupole moment of 182Re has not been measured. However, because Q0 varies slowly over the region it is possible to use the measured 00 of 182W, 6.4 50 barns with an assigned uncertainty of approximately 15% (Lo 70). The sign of (gK - gR) is the same as that of 6 derived from the angular distribution data. For the 7+ and 9' bands the 6's were found to be positive. Using this value of Q0 and the average of ng - gRI/Qo from the branching ratio calculation we obtain for the 7+ band _ + . 182 The g-factor of the 64 hr isomer of measured to be 0.399 1 0.008 (Si 74). This can be substi- Re has recently been tuted into Equation (1) for the magnetic moment. With the assumption of K = 7 for the ground band, Equations (1) and (S) can be solved simultaneously for gK and gR. This gives 9K = 0.44 t 0.02 and gR = 0.15 i 0.07. gR is significantly lower than the expected “0.3, although values this low have 161Dy and 177Hf (Hu 69). An incorrect K been found in assignment for the band built on the 64 hr isomer would not alter this result. It is clear that the 64 hr isomer has at least spin 6, and for high K, u (see Equation (1)) and hence gK is insensitive to gR. gK is, in effect, determined by Equation (1) for high K and gR is subsequently fixed by Equation (5). gK can be determined independently from Equation (2) and empirical gn of neighboring odd mass nuclei (Kh 74) for the 5/2+[402+] proton and the 9/2+[624+] neutron.. This calculation gives gK = 0.43 in agreement with the experimental result. One possible explanation for the 51 unusually small value obtained for gR is that the 00 of 182Re is much smaller than that obtained for neighboring deformed nuclei. It is clear, however, that either gR or 00 deviates substantially from the anticipated value. The small value of gR for 182 Re obtained here might be expected on the basis of partially confirmed calculations of gR for several nearby odd-mass nuclei performed by Prior 179 et al. (Pr 68). These researchers predict that Hf and 181W have gR values of 0.14 (or 0.12) and 0.05 respectively. The reduction in gR as compared to that of other odd-mass nuclei is attributed by Prior et al. to the influence of the outer shell nucleons, in this case the 9/2+[624+] neutron. These results can provide a possible explanation of the relatively small value of-gR obtained for 182Re. This is because the moment of inertia, I, can be written as the sum of the moment of inertia of the protons in the nucleus, Ip' and that of the neutrons, In: I = I p + In (6) Furthermore, one can write ' I. I R I Ip+In Generally, both 1P and In of an odd-odd nucleus will be greater than the corresponding values for the nucleus comprised of one less proton and one less neutron. However by comparing the values of h2/21 of 181W, 181Re, and 182Re (estimated from the energy difference of the first two 52 excited levels of the ground bands) one finds that the odd proton of 182Re does little to increase the 1p of 182Re 181W while the odd neutron apparently drasti- cally increases the In of 182Re over that of 181Re. Thus, over that of according to the above equations, one would expect that the 182 181 Re would be smaller than that of Re and close 181 gR of to the 181 W value. The predictions of Prior et al. for W have not been tested experimentally. However, 167Er and 161Dy have been confirmed similar predictions for (Pr 68). Table 4 lists theoretical values of gK calculated in the asymptotic limit of the deformation parameters com- pared to experimental gK obtained from branching ratios of the 7+ and 9- bands. Q was assumed to be 6.4 barns and 0 9R was taken to be 0.15. Although the theoretical calcula- tion was carried out in the asymptotic limit of deformation, no significant changes are introduced when the Nilsson wave functions for a deformation apprOpriate to 182Re are used (Ni 55). It can be seen that the experimental gK is consistent with the 9-{9/2-[514+] a 9/2+[624+]} assignment. If the validity of the rotational model is assumed and gR and Q0 are known, then gK can be calculated from the experimental mixing ratio 6. This experimental gK can be compared to theoretical predictions thereby serving as an aid in identifying the band structure. Unfortunately, branching ratios were not obtained for the proposed 2... and 4- bands, and the angular distribution results were .omnm.mm m.o u www.mm .mH.o H mm .mcumn e.m n o0 mcwaammm Aev can any mcoHumovm ou mchuooom moHumu mcHsocmun haul» Bonn cmumasoamom S3 Am