HIGH- SP'N ROTATEONAL BAND STRUCTURE OF ' W AND 178W 31533 Nation? 3r ”rug! m» S L“ the agree eofPh. D. TAT UN N‘rz'RSITY CAROL WINE DOES 1975 D E This is to certify that the thesis entitled HIGH-SPIN ROTATIONAL BAND STRUCTURE OF 177w AND 178w presented by Carol Lynne Dors has been accepted towards fulfillment of the requirements for Ph.D. Chemical-Physics degree in Lidia... M +31 [<6 Major professor October 6, 1976 Date 0-7539 Ki: unmnv muons 1 ABSTRACT HIGH-SPIN ROTATIONAL BAND STRUCTURE OF 177w AND 178w By Carol Lynne Dors The rotational band structure of 177w and 178w has been investi- gated using the techniques of in-beam gamma ray spectrosc0py. Of par- ticular interest in this region of deformed rare-earth nuclei is the anomalous behavior which occurs in yrast sequences at very large values of angular momentum, and the possible involvement of i13/2 neutrons in this phenomenon. In the experiments discussed here, the 7/2+[633] band in 177w was populated to spin 33/2 and the ground band of neighboring 178W to spin 16. The {13/2 band in 177W was compared with similar bands in other odd-A tungsten nuclei, and the results were applied to the systematics of the doubly even tungsten ground band structures. Levels in 177W were populated in the 177Hf(a,4ny) reaction. The ground state is assigned as 1/2-[521]; other low-lying bands which were seen include the 7/2+[633], 5/2‘[512], and 7/2’[514]. The 7/2+[633] band displays a highly perturbed structure which can be theoretically reproduced through Coriolis-induced mixing of higher energy positive parity bands. The 177Hf(a,3ny) reaction was used to populate states in 178W. The Kfl=0+ ground band was observed up to spin 16. On a plot of (112/223)-1 vs. (hw)2 the band shows some deviation from normal Carol Lynne Dors rotational behavior at high spin. The Kn=2— octupole band was located at 1045 keV and has an alternating energy sequence, with the odd spin members "favored". A pair of two-quasiparticle bands has been identi- fied and is tentatively assigned as Kfl=6+ and K"=(6,7)-. The B- vibrational band was identified from spin 6 to spin 16. A discussion of backbending and the i13/2 neutron orbitals is made in the light of a systematic study of odd-even isotopic pairs. The result suggests a possible correlation in the tungsten nuclei between the amount of decoupling in the positive parity bands in the odd-A iso- topes and the degree of backbending—type behavior observed in the neighboring even-even nucleus. MSUNC-l92 HIGH-SPIN ROTATIONAL BAND STRUCTURE OF 177w AND 178w BY Carol Lynne Dors A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry Program in Chemical Physics 1976 ACKNOWLEDGMENTS I wish to thank Fred Bernthal for suggesting this project. His guidance on experiment details, interpretation of the results, and his assistance in preparation of this thesis are sincerely appreciated. I would also like to thank T. L. Khoo for his valuable advice and helpful time-consuming discussions. Bill Kelly deserves my sincere gratitude for his never-ending words of encouragement and his special advice. I would like to thank Ray Warner for the many hours he spent giving experimental assistance. His friendship and advice have been invaluable. Thanks to Chuck King, Brian Jeltema, Clare MOrgan, Larry Samuelson, and Mark Slaughter for giving of their time during the long hours of a cyclotron experiment. I wish to thank the cyclotron engineering staff, especially Peter Miller and Harold Hilbert, for assistance in cyclotron set-up and trouble-shooting. I would like to extend my thanks to the Nuclear Beer Group with- out whom Friday afternoons would not have been the same. A special thanks to Alice Ridky for typing the final copy of this thesis under the usual pressure of a deadline. Finally, I particularly wish to thank my parents for their encouragement, and my husband, Tim, for his perspiration, inspiration, and motivation. ii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . v LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . . vi Chapter Page I INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . 1 II THEORETICAL CONSIDERATIONS. . . . . . . . . . . . . . . . 4 2.1 Description of the Total Hamiltonian . . . . . . . . 4 2.2 Statement of the Wavefunction. . . . . . . . . . . . 7 2.3 Rotational and Particle-Rotation Eigenvalues . . . . 7 2.4 Intrinsic Wavefunctions and Nilsson Single- 9 Particle Energies. . . . . . . . . . . . . . . . . . 2.5 Treatment of Pairing Correlations. . . . . . . . . . 14 2.6 Summary of Eigenvalues and Discussion of Correction Terms. 0 O O O O O O O O O I O O O I O 0 O O O O O O 15 III 177w EXPERIMENTAL DETERMINATIONS. . . . . . . . . . . . . 18 3.1 Gamma—Ray Singles Spectra. . . . . . . . . . . . . . 18 3.2 Angular Distributions. . . . . . . . . . . . . . . . 29 3.3 Gamma-Ray Lifetimes. . . . . . . . . . . . . . . . . 31 3.4 Excitation Functions . . . . . . . . . . . . . . . . 34 3.5 Gamma-Gamma-Time Coincidences. . . . . . . . . . . . 37 IV 177w EXPERIMENTAL RESULTS . . . . . . . . . . . . . . . . 41 4.1 The 1/2‘[521] Band . . . . . . . . . . . . . . . . . 41 4.2 The 7/2+[633] Band . . . . . . . . . . . . . . . . . 42 4.3 The 7/2“[514] Band . . . . . . . . . . . . . . . . . 49 iii Chapter VI VII Page 4.4 The 5/2'[512] Band . . . . . . . . . . . . . . . . . 52 4.5 Possible 3-Quasiparticle Band. . . . . . . . . . . . 52 4.6 The Single Particle Level Structure of 177w. . . . . 55 178w EXPERIMENTAL DETERMINATIONS. . . . . . . . . . . . . 59 5.1 Gamma-Ray Singles Spectra. . . . . . . . . . . . . . 59 5.2 Angular Distributions. . . . . . . . . . . . . . . . 61 5.3 Gamma-Ray Lifetimes. . . . . . . . . . . . . . . . . 69 5.4 Excitation Functions . . . . . . . . . . . . . . . . 72 5.5 Gamma-Gamma-Time Coincidences. . . . . . . . . . . . 80 DISCUSSION OF 173w EXPERIMENTAL RESULTS . . . . . . . . . 83 6.1 The KW=O+ Ground Band and B-Vibrational Band . . . . 83 6.2 The Kfl=2— Octupole Band. . . . . . . . . . . . . . . 85 6.3 The R"=(6+) Band . . . . . . . . . . . . . . . . . . 89 6.4 The R"=(6,7)’ Band . . . . . . . . . . . . . . . . . 94 CONCLUDING REMARKS: BACKBENDING AND THE i13/2 mmKML. ... ... ... ... ... ... ... ... 99 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Appendices A Gated Coincidence Spectra of Transitions in 178w. . . . . 111 B Angular Distribution Plots of 178W Transitions. . . . . . 123 C Gated Coincidence Spectra of Transitions in 177W. . . . 129 D Angular Distribution Plots of 177w Transitions. . . . . . 142 E Level Scheme of 18303 . . . . . . . . . . . . . . . . . . 143 iv Table 4-1 5-1 LIST OF TABLES Energies (EY)’ relative intensities (IY), angular dis- tribution coefficients, multipolarities, and spin assignments for transitions in 177W. In the cases where no Ah/Ao is listed, the angular distribution data for those transitions were fit with Ah/Ao constrained to zero. The transitions labeled with an asterisk are components of closely spaced (<0.5 keV) doublets. . . . Hindrance Factors for [633]+[512] Transitions . . . . . Input parameters for the Coriolis bandmixing procedure, calculated energies and amplitudes of the resulting mixed wave functiorls O O O O I O O O O O O O O O O O O 0 Hindrance Factors for Transitions from K=(23/2) Isomers . Energies (EY)’ relative intensities (IY)’ angular dis- tribution coefficients, multipolarities, and spin assignments for transitions in 178W. In the cases where no Ah/Ao is listed, the angular distribution data for those transitions were fit with Aq/Ao constrained to zero. The transitions labeled with an asterisk are components of closely spaced (A] as a function of spin for several rare earth nuclei. Data are taken from Hg70 (161Er), Be75 (179W), Li73 (181W), and H670 (179hf). Inset shows even—even tungsten yrast bands taken from W372 (180W) and Je74 (182W) . . . . . . . . . . . . . . . A plot of the yrast levels in tungsten nuclei, mass 177- 182 . . . . . . . . . . . . . . . . . . . . . . . . . . . Gated spectra of the first four ground band transi- tions 0 O O C O O O C O O O O O O O O O C O O C I O O O 0 Gates on the high energy ground band transitions. . . . . Gated spectra of crossover transitions from even-spin members of the K"=2- octupole band. . . . . . . . . . . . Gated spectra of crossover transitions from odd-spin members of the K"=2' octupole band. . . . . . . . . . . . Gates on some interband transitions between the K"=2_ octupole band and the K"=0+ ground band . . . . . . . . . Gates on the interband transitions from the higher energy levels of the octupole band to ground band levels . . . . Gates on the interband transitions from the K"=6+ to ground band, and on the transition between the K"=(6,7)’ and R"=6+ bands . . . . . . . . . . . . . . . . . . . . . Gated spectra of cascade transitions in the K"=6+ band. Gated spectra of crossover transitions in the K"=6+ band. C O O O O O O O O O O O O O O O I O O O O O O O O 0 Gates on the cascade transitions in the K“=(6,7)- band. . Gates on the crossover transitions in the K"=(6,7)' band. 0 O O O O O O O O O C O O O O O O I O O O O O Angular distributions of some crossover transitions in the K=2 octupole band . . . . . . . . . . . . . . . . . . Angular distributions of some crossover transitions in the K=2 octupole band . . . . . . . . . . . . . . . viii Page 97 100 104 112 113 114 115 116 117 118 119 120 121 122 124 125 C-lO C-ll C-12 D-l D-2 Page Angular distributions of some interband transitions between the K=2 octupole band and the ground band . . . . 126 Angular distributions of cascade transitions in the K"=(6,7)" band. . . . . . . . . . . . . . . . . . . . . . 127 Angular distributions of various interband transitions and of the unassigned 29l-keV transition. . . . . . . . . 128 Gated spectra of transitions in the 1/2-[521] band. . . . 130 Gated spectra of transitions in the 1/2-[521] band. . . . 131 Gate set on the 84-keV E1 interband transition from the 7/2+[633] to the 5/2'[512]. . . . . . . . . . . . . . . . 132 Gates on the cascade transitions in the 7/2+[633] band. . 133 Gates on the cascade transitions in the 7/2+[633] band. . 134 Gates on the crossover transitions in the 7/2+[633] band. . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Gates on some crossover transitions in the 7/2+[633] band. C I O O O C C C C C C O I O C C O O O C C C O O O O 136 Gated spectra of crossover transitions in the 7/2+[633] band displaying high energy coincidences. . . . . . . . . 137 Gates on transitions associated with the possible three quasiparticle band. . . . . . . . . . . . . . . . . . . . 138 Gates on cascade transitions in the 7/2-[514] band. . . . 139 Gates on some crossover transitions in the 7/2_[514] band. 0 O O O O O O O O O O O C O O O O O O O O O I O C O 140 Gates on some crossover transitions in the 7/2'[514] band, and a gate on the lOl—keV cascade transition in the 5/2‘[512] band. . . . . . . . . . . . . . . . . . . . 141 Some angular distributions of the transitions in the 1/2'[521] band. The 79-keV transition is.Ml/E2, the others are E2 . . . . . . . . . . . . . . . . . . . . . . 143 Angular distributions of some cascade transitions in the 7/2+[633] band. . . . . . . . . . . . . . . . . . . . . . 144 ix Figure Page D-3 Angular distributions of the 7/2+[633] crossover transitions . . . . . . . . . . . . . . . . . . . . . . . 145 D—4 Mixed multipolarity angular distributions of cascade transitions in the 7/2_[514] band . . . . . . . . . . . . 146 D-5 Angular distributions of the interband 84-keV and l44—keV transitions, and of the l44—keV cascade member of the possible three quasiparticle band . . . . . . . . . . . . 147 E-l 18305 level scheme. . . . . . . . . . . . . . . . . . . . 149 CHAPTER I INTRODUCTION The purpose of this study was to elucidate the even-parity band structure of 177W and to investigate any implications for the level structure of the yrast cascade in neighboring 178W. The measurements on 178W, an isotone of 176Hf, were also intended to identify and characterize any high-K, multiparticle structures. The odd-even 177W, 178W was chosen on the basis of the available nuclear pair Nilsson deformed single-particle levels which would most likely be populated. The 7/2+[633] level which originates from the spherical i13/2 orbital would be low-lying, as should several high-Q neutron and proton negative parity levels. The investigative technique, in-beam gamma-ray spectroscopy was chosen both because the product nuclei are not easily accessible to charged particle spectroscopy, and because the rotational bands that would be systematically populated should have characteristic "fingerprints" which would make their identification, and association with particular Nilsson levels quite unambiguous. The experiments were performed using the Michigan State University sector-focused isochronous cyclotron running in the N=2 harmonic mode for the high energy (25-50 MeV) alpha-particle beams. When the experi- ments were begun, N=2 was a poorly developed mode of operation for the machine, and alpha beams were extracted largely by trial and error since the settings were not well calculated. Toward the conclusion of the experiments, state-of-the-art turn patterns could be easily attained in about two hours, with up to 1-1/2 microamperes of beam impinging on the target. During this time also, a high voltage rf beam sweeper was built which uses deflecting plates to select only every second to eleventh beam burst, allowing timing in the range 100-500 nsec [Kh72]. In addition, a high voltage beam pulser was available to study states delayed by more than 1 usec. Computer developments were also made in this time period to bring the Xerox 2—7 computer perhaps to its limit of computing capability. The most useful computer development to y-ray spectroscopists was the three parameter event recording and sorting programs. Up to three 4096-channel spectra in coincidence mode can be accumulated with data storage on magnetic tapes; "replaying" of the data with results stored on temporary disk files then allows fast, relatively efficient sorting with background subtraction included. A newer development involves installation of a CAMAC system interfaced to a PDP 11-40 computer, but for this work, only the Sigma-7 with a PDP ll-20 handling peripherals was available. At the time the tungsten experiments were begun, Ge(Li) detectors were technically much the same as they are today. The decay studies which had been performed originally with NaI(Tl) detectors had already been redone to make use of the improved resolution of Ge(Li) detectors. The in-beam gamma-ray spectra which had originally been taken with NaI(Tl) detectors were seen to contain a profundity of supplementary data, and in fact, today the decay studies are viewed to be the supple- mentary ones. The tungsten experiments that will be discussed partly involved the retaking of old data that had been obtained with NaI(T1) detectors, but with illuminating new results, a wealth of new states could now easily and quickly be sifted out of the pile of data, sorted into rotational bands, and included in the rapidly growing list of system- atics. Ultimately the goal of nuclear experimentalists is to make the list of systematics form a simple and clear description of nuclear structure. With that goal in mind, this thesis is designed mainly to display the addition of a few more pieces of information to test the theories of deformed nuclei at moderately high spins. The structure of the thesis will be: 1) a discussion of some of the relevant theory involving well deformed, rotating nuclei; 2) experimental data and level schemes for each nucleus; 3) a dis- cussion of how the data fit into the applicable systematics, and any perturbation in the systematics due to this new data set. CHAPTER II THEORETICAL CONSIDERATIONS In order to understand the features of spectra belonging to nuclei in the deformed rare earth region, one seeks an appropriate phenome- nological model. The most successful model applicable in this region has been the Collective MOdel of Bohr and Mottelson.which was intro- duced in 1952 [3052] to describe the rotational spectra and collective properties of deformed nuclei. The intrinsic states on which the col- lective properties are built, were described by Nilsson [N155], and the combined properties were summed up by MOttelson and Nilsson in a unified model [M059] which with some refinements and additions is widely used today in interpreting the level data in the mass region 150 < A < 190. 2.1 Description of the Total Hamiltonian The Hamiltonian for a system of nucleons moving in a non-spherical potential consists of two basic types of interactions, one which is associated with the collective motion of all nucleons and which gives rise to the rotational spectrum, the other an intrinsic motion of each nucleon in a deformed orbital giving rise to the single-particle spec- trum. The Hamiltonian for a particle strongly coupled to a rotating core can be written (see e.g. Pr62 for further discussion): H = H + H (1) The rotational Hamiltonian may be written: 2 + =23<12- ~13) + 2%(32—j§>--2-—:(ffi_+1_3’+)<2) rot The last term in this expression contains the interaction between the particle and rotational motion, while the first and second terms refer to collective and particle motion,respectively. The total Hamiltonian may thus be reconstructed in the following way: H = H (collective variables) + H. (intrinsic variables) + H (3) c int coup with Hcoup representing the particle-rotational coupling, and with the second term in H , the so-called recoil term, incorporated in H rot int' Figure 2-1 shows a vector diagram of an odd-A deformed nucleus consisting of a single particle which is coupled to an axially- symmetric rotating core. Since the core rotates freely in space, the coordinate system using body-fixed axes (1,2,3) is chosen to simplify the description. For the axially-symmetric case, the 3-axis is the nuclear symmetry axis and the particle angular momentum, I, precesses about the 3—axis with projection Q. In the axially-symmetric case, the core angular momentum R is perpendicular to the 3-axis, and the total momentum I has a projection K equal to 0. In a rotating system like this, it is easily verified that one influence of the rotation on the particle motion will be the familiar Coriolis effects [St72]. Figure 2-1. Vector diagram of a particle coupled to an axially symmetric rotating core. 2.2 Statement of the Wavefunction In order to solve for the energy levels of the system, the wave- function introduced is (see e.g. Pr75 for details): I m, w = x95 (4) a separable wavefunction consisting of the intrinsic and rotation coordinates. The wavefunction is normalized and symmetrized so that JS'gives unitary transformations from space-fixed to body-fixed coor— dinates, invariance with respect to 180° rotation of the 3-axis, and the total parity is the parity of the particle state: r = /(21+1)/161r2 {x93 Emmi) + <—1>I'jx_fla§,_K} (5) 2.3 Rotational and Particle-Rotation Eigenvalues The first term in the total Hamiltonian, Hc’ will yield the familiar rotational band energies: 2 E = g-j-[Iu-i-l) — K2] (6) Operating on the wavefunction with the rotation-particle coupling term in the Hamiltonian, Hcoup’ yields the following matrix elements: , h2 h2 «92,19 |—-fi(1+j_+1_j+) [$21 ,K1> = -—fi/(I:~X1) (IiK1+l) (7) I , > X‘QZIJJQI 6K1,K2il 601,92i1 The eigenvalues of <92|j+|01>'must be evaluated using a specific particle wavefunction x9. If a Nilsson-type wavefunction is assumed, then one obtains: (8) Q Q - < . > = 1 2 . . QzlJilfli jig Cjz cjz minnomlfl) aghazfl where Cj's are coefficients used to expand spherical harmonic- oscillator wavefunctions to account for the fact that in a non- spherical basis 3 is not a conserved quantity. For the special case where j can be considered to be a good quantum number, the simple result may be added to the Coriolis energies giving: h2 Zn/YITK1)(I:K1+1) 2 <312.1(2I-11—(I 3 +1, 3 )|91,K1> = " 23 + - — + (9) x /(j:91)(j:91+1) 6K1,K2:l 691,02i1 The first term in this Hamiltonian steps down both K and Q, the second will step them up, mixing states differing by one K-unit via non- diagonal matrix elements. The Coriolis effect can easily be seen to be largest for states of small 0 projections in high-j orbitals. Due to pairing correlations between nucleons, these matrix elements are found to be too large and a pairing reduction factor which will be discussed later in this chapter must be included. For K = Q =-l there will be diagonal matrix elements which have 2 the form: 1 _ 1 _ 1 h2 , , 1 l _ h2 1+— 1 <’— 23(—1) 2(I+2)a (10) where a, the decoupling parameter is given by [Og7l]: a = -<flfij l 2 I _ l - -1 .. §> _ -<2|J+| 2> (11) and is evaluated using a specific particle wavefunction x0. If again a Nilsson-type wavefunction is assumed, then<1 takes the form: 1 = _ _ j+—- . 1 2 a g < 1) 2 (3+3) ch(%)| (12) Thus, K =-% bands have a perturbed structure with alternating levels lowered in energy from the normal I(I+l) energy dependence. The sign of a determines whether (I+%) = even or odd spin levels will be decreased in energy. In [Bu7l] there is a tabulation of values of the decoupling parameters for neutron and proton K = %-orbitals in the N=5 and 6 shells. Experimentally, these bands are easy to locate due to the strong alternating energy sequence of levels, and they can usually be assigned to a particular orbital by studying the sense of the perturbation. 2.4 Intrinsic Wavefunctions and Nilsson Single-Particle Energies To solve the eigenvalue problem for the single particle or intrinsic energies, a wavefunction xQ with convenient particle coordinates is chosen. In the Hamiltonian, the potential used by Nilsson [N155] for the single particle problem consists of the fol- lowing terms: Ho + 2Khw(2°; - UZZ) (13) 10 where H0 is the deformed harmonic oscillator potential and may be separated into an isotrOpic part and a part which depends on the deformation: Ho = H: + H6' The parameters (K,u) are adjusted so that at zero deformation the solution will yield the empirically determined energies of the spherical shell model. The wavefunctions formulated by Nilsson [Ni55] are linear combin- ations of cylindrical harmonic-oscillator functions. The lack of spheri- cal symmetry causes j to no longer be a good quantum number; however, j z commutes with the total Hamiltonian so that Q is still a strictly good quantum number in this representation. Since £2 and s2 commute only with HD and not the total Hamiltonian, the eigenvectors for each 0 are, then, composed of a sum of terms each characterized by N,£,A,2. N is the total number of oscillator quanta, and the other quantities are shown on the vector diagram, Figure 2-1. Operating on the Nilsson wavefunctions with the above Hamiltonian yields eigenstates having energies which are a function of deforma- tion. Each Nilsson level which can hold two paired nucleons is then labeled with the asymptotic quantum numbers Q“[anA]. For large deformations, the 2-3 and 22 terms in the Hamiltonian are treated as perturbations in which case A, Z and n (the number of nodal planes 2 along the symmetry axis) become good quantum numbers. Levels can be calculated incorporating both quadrupole (62) and hexadecapole (eh) deformations [N169] where the deformation parameter £2 = 6 + %62. For the nuclei 177W and 178W, the deformation is estimated to be about £2 = 0.23, ch = 0.05. Using a code from the University of Roches- ter [NILs],the Nilsson levels for this deformation were calculated for both neutrons and protons and are displayed in Figures 2-2 and 2-3. ENERGYlH-V) ll (59') V21510) . \\ \ \lk’n SA: 'A ‘ E \ G I 2.199 3/zttszwl . 7/21514) 4. ‘ \ ‘ . x 1.080 \ \ .889 r -——— e—d-EN 35953) 5;/ 7/2tt833) 4’ I 1.275 I / ,’ 1.555 / {El-HEIIIIIIIIIIIII1457!, , 7 c .23 s/z‘tsw2) 1' / £3.05 // «3.0638 was 2‘37“; NEUTRON ORBITALS FOR 177-8N Figure 2-2. Single particle deformed neutron orbitals and quasi- particle energies for N=103, calculated with the values of the parameters which are listed above. 2.9 2.00 1.60 1.20 0.80 0.90 ENERGYIMOV) 0.00 -0."lO -0.80 " 1.20 12 tsp“) 1/2‘1660] j ama’x;=.~ Ifijlsso Nix V 21591) fi\\\ \ d (‘_)]2+A§' ”A \\‘\ ‘ \ \\\‘\\ \ EU” \\ \\ ‘1 _ \‘ \\ 53$ \}Q================{2L2 :2 ¥ 1 20180 L 2.121 5/ TIME] fl \ ‘ ~ 4 g 1.928 ) _ ’ L .305 9/ 2151'” - - ’ I z «.962 / 7/2’14041 , ’ , 1.259 / / / , ’ , 1.679 l/zttlm) I I , [($23 / «3.082 7/2'1523) I “399 PROTON ORBITALS FOR 1773M Figure 2-3. Single particle deformed proton orbitals and quasi— particle energies for Z=74 calculated with the values of the parameters which are listed above. 13 The most noticeable feature of the neutron orbitals is the absence of positive parity states other than those which originate in the i13/2 spherical state. These states will have a relatively pure j-value, 13/2, since the nearest positive parity states which can easily mix with them are the 99/2 which are about 2 MeV higher in excitation. Thus, for mixing calculations involving bands associated with the i13/2 states, only the set of orbitals in the i13/2 family need be included. In Section 2.1, it was mentioned that the recoil term, %;(jz-j§), was commonly assumed to be included in the intrinsic Hamiltonian. It has recently been shown [0375] that the Nilsson Hamiltonian in its usual form does not incorporate this term unless the model parameters K and u are made to be deformation dependent. A calculation of the single particle energies taking the recoil term into account explicitly has been attempted [Re76], and the authors found that the values of the potential parameters, K and u, obtained in their procedure gave better experimental agreement to the levels in N=89 nuclei. In general, inclusion of this term may cause a several hundred keV shift in the bandhead energies - with the largest effect occurring for bands having large values of the inertial parameter,-§§, and for high-j low-Q orbitals. A preliminary calculation of the positions of the i13/2 orbitals using a Woods-Saxon potential and taking the recoil term into account [L172] showed shifts of only about 100 keV from the positions of these states calculated with the standard Nilsson model. Until recently there was little agreement on how to handle the term cor- rectly although a few attempts have been made (e.g. Og7l), so all the calculations of intrinsic states in this thesis were done without taking the recoil term into consideration. 14 2.5 Treatment of Pairing Correlations The theory of superfluidity introduced by Bardeen, Cooper, and Schreiffer in 1957 [Ba57] describes long range pairing correlations in an electron gas. A similar pairing phenomenon occurs in nuclei and the BCS model has been successfully used [B058] to correct Nilsson single-particle energies for this effect. A pair of nucleons which occupy identical time-reversed orbitals interact with each other through a pairing force; a consideration of all such pairs, then, gives an energy level which is lower than the normal ground state of the nucleus. Excited states of this system are quasiparticle excitations, where a quasiparticle is a fractional (V2) 3 hole state mixed with a fractional (U3) particle state. The occupa- tion parameters Uj and Vj can be obtained from the expression [Og7l]: U32 A 6 _ }=l~.1i_SL_ (14) QP And, finally, the energies of excited states, Eqp’ can be found from: = _ 2 2 Eqp Wasp A) + A (15) where Esp are the average field single-particle energies, A is the energy of the Fermi surface which is normally close to the last filled level in the ground state of the nucleus, and 2A is the energy differ- ence between the normal and paired ground state. A value for A, the gap parameter, can be obtained from the experimental odd-even mass 15 differences, and is found to be larger, in general, for protons than for neutrons [N169]. The gap parameter can be suitably approximated [N169] by: A = $23: MeV. (16) The ground state of an odd-A nucleus can be shown to be a one- quasiparticle state, while the lowest intrinsic states of an even- even nucleus are two quasiparticle excitations, the ground state being a quasiparticle vacuum. Quasiparticle energies which have been calcu- lated from the Nilsson levels shown in Figures 2—2 and 2-3 are also displayed in those figures. It should be noted that in the BCS model, the number of nucleons is not a conserved quantity, so applicability is limited to systems with large numbers of nucleons. Also, a more sophisticated treatment should include the effects of blocking [0g7l] in odd-A nuclei, i.e. pairs are hindered from occupying orbitals that are blocked by the single particle. 2.6 Summary of Eigenvalues and Discussion of Correction Terms Thus, the total Hamiltonian for the strong coupling problem has been discussed term by term, and the matrix elements may be written, in summary: 2 Eqp +{11-+ B[I(I+1)-K2]}[I(I+l)-K2+10 na for most experiments and was readily obtainable for the runs. The energy resolution of the beam was at least 0.1%, with alpha particle energies of 24 to 50 MeV available in the N=2 mode of operation. The reaction cross sections for (o,xn) reactions as a function of alpha particle energy were calculated using the code CSBN [CSSN]. The maximum cross sections for (a,2n) through (a,5n) reactions are spaced about 10 MeV apart, and the curves are broadly peaked with some overlap between them. On the peaks of the cross-section curves, the amount of contaminant production is about 3% of the total cross section. The reactions are thus moderately selective, and the optimum 18 19 alpha particle energy for a desired product nucleus could be found experimentally by minimizing production of the contaminant gamma rays. The optimum excitation energy required to induce the (a,4n) reaction 13 close to 50 MeV, so the highest energy alpha beam which could be obtained by the cyclotron was used for the 177W experiments. The (a,5n) product gamma rays can be seen in some of the spectra as intensely as the (a,3n) product, but in most of the runs the (0,3n) products were the main contaminants. The contaminant gamma rays were readily identifiable from the 178W experiments, especially from the excitation function data. Mbst of the gamma rays which are of interest in 177W are below 650 keV. There is a heavy population of gamma rays below 200 keV. Therefore, the detector which was chosen for the singles experiments was a LEPS (Low Energy Photon Spectrometer). This detector is a small volume(2.5cm3) planar Ge(Li) crystal having 0.7keV resolution at 122 keV. In Figure 3—1 a spectrum of the gamma rays produced by bombarding 17711f with 50.2-MeV alpha particles is shown. The LEPS was placed at 125° with respect to the beam and the counting period for this and all the singles spectra was typically about 100 minutes at counting rates of 4-8XI03 counts/sec. A copper-cadmium absorber was always used to shield the detector from X-rays which would otherwise dominate the spectrum. The EC/8+-decay half-life of 177W is 2.2 hrs, so that in a long experiment the radioactivity from this decay is seen quite strongly. The two most prominent decay peaks in 177Ta are the 115-keV and 186- keV gamma rays - the former is a triplet and the latter a doublet 20 Figure 3-1. I llllllll r P'-‘ ‘ lIrlTl T l C) C) r 8 :0 ozz "‘ H? o a! h- ONE—"32" H8 “o, 1.61 (‘0 IIS (2 3.. oer 994 (I. O 8 [.01 w ...; an O m f 091 l... LO 2 l\ 0 95+: 0 D L- I\ IS! -wO Shh— .- 0) Z .... O 1*”! *WI "‘1 _J 681 LL] ”€521- II. Z (.21 80 Z < 258 O __ d D $ us [0 N 101- 292 56 Uh€~ — he 662 6L (3 L- ‘8 SM»: 8 ' toe - _ - C) e _ 662,162 N 293 _H 99 I Inn] 1 1 , ‘ ; J i J 1 U) :f' :r 00 CD CD CD CD 0-0 0-0 H .—o SanOO SiNf‘lOO Spectrum of 177Hf(rx,4n) taken with the LEPS placed at 125°. 21 [A172]. A consistent analysis of these two peaks in particular using the analysis routine SAMPO [R069] indicated the "goodness" of the shape parameters used in the analysis from experiment to experiment. The second most prominent contaminant lines belong to the neighboring even- even tungsten isotopes 178W and 176W. Since the yrast sequences in the even-even nuclei get most of the feeding, these transitions are quite intense. An efficiency curve for the detector was measured and the relative intensities of the gamma rays could be determined with 6-8% accuracy. In many cases the limitations on the accuracy was the stripping of the parts of peaks that were multiplets. An internal energy calibration was performed allowing the peak energies to be determined with 0.05 keV accuracy for the best cases, and within(11 keV accuracy for the close multiplet components. Table 3-1 contains a list of all the gamma rays seen in this experiment with the energies and relative intensities of the transitions in 177W indicated along with angular distribution coefficients and transition assignments which will be discussed in later sections. A low energy gamma-ray singles spectrum was taken with only a thin copper absorber on the LEPS in order to detect any low energy gamma rays not previously observed. The gamma ray of particular interest was the 34.1-keV transition which had been seen in the con- version electron decay spectrum [Ha74] but in none of the in-beam y- ray spectra. The main purposes of this experiment were to determine whether the same gamma ray was strongly pOpulated in-beam and to see if it had the appropriate relative intensity to be the intraband Table 3-1. Energies (EY)’ relative intensities (I , angular distribution coefficients,multi- polarities, and spin assignments for tran- sitions in 177W. In the cases where no Ah/Ao is listed, the angular distribution data for those transitions were fit with Ah/Ao con- strained to zero. The transitions labeled with an asterisk are components of closely spaced (eev » » ucoacwfimm< .mmoou H m coauanfiuuman umadwn< Nun eNeeN 23 N NeNm_-mNH mN NN_.N2 No.0N NN.o- No.oh Nm.o- vaN.N vawN.NNN N . NeNmL-NH -NN NNve vamN oeN NNNRL m+.mw NNvN.e NmeN.NmN -m -NN N . - . . - . . . Nmme_+aHN +NN so o+ mo 0 No 0+ aN o vaN m vaoa omN Nmmeii %+mw NN N.ON N.o NevN.m vamN.meN Nmme_+NNNm iN NNV NN..N2 No.0N NN.o No.0“ NN.o- Neon.w NnVNm.eeN NeNmLLm+me NN .Na No.0“ NN.ou mo.0N Ne.ou NNvm.NN Anvae.amN N . . - . . - . n . NmmeL+NHN +mN Na N: No o+ No 0 No o+ mm o NNVNN vamo eNN N N . . NNNRLLM+Lm Nave m NevaN ONN o .N o N <\ a <\ a N.ueN .Neev N>eNV m N N mama: Hmm< .mwmoo H m aowusnwuumwo Hoaawm< N.e.ucoov Nun eNeea 24 N NmmeL+NHN +mN Nm N.oe N.o- No.ON eN.o NNvNN vamm oNN NH :+N Nevm.m vamm.NNN N . . - . . . NeNm_-NHN -NN NN N2 N 0+ m o- Neva m vamm NNN Neve.N vaNe.mNN Nmme_I N NN..N: No.0N mo.ou No.ON me.os ANvN.eN NmVaN.NNN +NNN I+NN NNNmmrm+hm. Nm so.ON No.ou no.6“ eN.o NNVmN vamm.NON NNNm_ m+hm_ Nm N.ON NN.o Naoae NRVeN.NaN m N cl. 0 .NNNALIRHN -NN N o+ N o vaNN NaveNm emN NH :+N Nm .Nz. N.0N o.o No.oe mm.ou vaN.e vaNe.NNN o: om «N a <\ a N.N:N .Nehv N>exv ucoaamwmm< r r .NNeoo N m coausnfiuuoan Hwasws< A.e.uaouv Num manna 25 N .NNmH-NHN -mN Nm N.oN N.o- No.0“ NN.o NNva Nnva.oqm Nmmoa+mHN +mw Nm No.ON No.o- No.0N NN.o NNVmN NnVNm.mNN NNNmHLm+me Nm No.0“ ON.o- No.0“ ON.o NNvNN vaNN.mNN NNNm_ Im+.&m. Nm oo.oN oo.o No.oN mN.o vao.NN NnvNN.Nom NNNnH_m+me Nm no.ON oo.ou No.0“ NN.o NNVnN vaNm.mmN NmmoH+NHN wa Nm .Nz. N.ON N.N- vaN.m vamm.NoN NmmoH+NHN +Mw N.0N No.o NNVNN vamN.NoN NNNngnm me N.ON N.ou No.0N NN.o NNvNN vamN.omN AN :V+N NNV vaN.N NNVo.NNN ooxv acmaamamm< .mmooo >H >m coauanauumwo unaswa< N.N.ucoov N-N mNpmN 26 Nmmoa+mm++mm NN no ON No on No a“ oN o NNVN NN Novmm «we N N . - . . Nmmo_+mm++mN Nm no 0+ 0N o NNVNN vaNN mNN NNNNHLMN+me Nm N.ON N.o NNva Neva.NNN NN NN NNNm..mw+me Nm mo.ON No.0- No.ON NN.o NNvN.NN vaNN.NNN NNNNHme+me Nm No.0N oo.o mo.OH NN.o NNVoN vaNo.moq NNw¢+NNw Navo.m Nevom.qoq NN NN NNNmaLflw+me NN No.0N No.o No.0“ ON.o Navm.NN NNVNN.NNN my “NNNNH .mi..m. NNVaN Amy NN.NNN NNN -NN -NN « N N . - . - . - . . Nmmoa+mm++NN Nm «0 o+ «o o no o+ 0N o vaNm vawo Nom 0 ... o N «N ¢ <\ < N.uaN .Nouv N>oxv N N uaoacwamm< .mmmoo H w coauanfiuumwn unasma< N.N.uaoov N-N oNnmN 27 NNNmHme+LNm N.ON N.o NNVoN NNvm.o¢m NNNmHnflw+me NNvNN NNvN.NNm Nmmo_+mw++mw Nm No.ON NN.o NNVoN NovoN.ONm Nmmog+mw++mw Nm N.ON m.o NNVmN vaNN.Nmm NNNm_-mw me NNvNN NNvam.mNm NNNm_-mw me N.0N N.o NNvN.NN NNvNN.ooN NNNm.-mm+me NNVNN NNvNN.NNN .NNmaymm+me Nm No.ON oo.o- No.oN NN.o NNvNN Novqo.NNN NNNmHme+me Nm N.ON N.o NNVoN NovnN.ooN 305533 32.4 of .3 A.uaN>.Nuuv CNS: .NNaoo N m coausflfiuman umgwg N.c.uaouv Nun «Nana 28 N N . NNNE+INH+NN NNVNN AN: NS N N .- . . NNN£+NH+NN Nm m 0+ N o NNSN NNVN NS o z o N «N < «N < 33 Na: 93: N N uaoaamwmm< .mmmoo H m coauanfiuumwn umaawa< .N.u.uaoov Num mNan 29 9/2++7/2+ cascade transition. Indeed, it was seen and the energy was well measured. The intensity, however, could not be accurately determined since there were no calibration sources available having more than one peak in the range that was being studied. The efficiency curve for the detector is well-known above about 50 keV, but below this value the curve is changing so rapidly that accurate extrapolation is not possible. A portion of the low—energy spectrum is shown in Figure 3-2. From this spectrum, it is evident that there is no prominent low energy gamma ray besides the 34-keV gamma, and that,although it is relatively weak, further in-beam experiments could be carried out on the 34-keV transition in order to determine its placement. 3.2 Angular Distributions When the incoming alpha particles impinge upon the target nuclei with velocity 3, they align the nuclei such that the angular momentum vectors ($x3) are all predominantly in a plane perpendicular to the beam. As these nuclei decay by emitting electromagnetic radiation, they lose some of the original alignment with each transition. In [1073] it is noted that the lowest members of a band will have only 20-50% of the original alignment. Although the mixing ratios of dipole and quadrupole radiation cannot be very accurately determined using these distributions, the qualitative information contained in the shapes of the curves can be helpful in confirming placements of gamma rays in the level scheme. 3O CD C) [III r’l l l' [IIIII l T l llrll [’l I l c: (\l SII > 0) Z “2 o [0 tr) «4 "c" h8"-==:— 3". 8 61. E P\ P\ '4 a: c: 8 a "' —=EE==—— _ a. —s 61.1 [D a lLlI LL! llLlLJl I l TIILIII L: o (D U) 1? 00 CD CD CD C3 '4 r4 r4 '4 SlNHOO Figure 3-2. The low energy portion of the high gain spectrum taken with the LEPS. CHANNEL NUMBER 31 In order to measure the anisotropies of the gamma rays, the LEPS was placed about 3" from the target on a moveable arm and singles spec- tra were taken at 90°, 105°, 125°, and 145° with respect to the beam direction. Since the erays are emitted isotropically, the Xeray intensity can be used to normalize the runs. The normalized inten- sities are fitted to the equation I = l +(A2/A0)P2(cose) + (Ag/A0)Pq(COSB) The data along with the fitted curves for some of the gamma rays in 177W are shown in Appendix D. Angular distributions of a few gamma rays from each band are displayed, with the data transposed to the 0-90° quadrant which is plotted. Since the distributions are sym- metrical about 90°, only one quadrant is shown. The angular distribu- tions that are not shown in these figures were either very weak, or parts of multiplets and so had very large error bars on the values of the transition intensities. The values of Az/Ao and Aq/Ao from this experiment are also listed in Table 3-1 along with the multipolarities deduced from these values. Where a good value for Ag/Ao could not be obtained, the data were refit with values for Au/Ao set equal to zero. These are shown in the table with no Ag/AO indicated. 3.3 Gamma-Ray Lifetimes The measurement of the half-lives of gamma-rays can provide a valuable tool in the placement of some intraband transitions and the confirmation of K-values for the bands. In 177W, the gamma-ray 32 lifetimes in the range of 5 nsec to 500 nsec were measured by per- forming two timing experiments. The first utilized the time bunching of particles in a cyclotron, each bunch being associated with an rf cycle. In the second experiment, 8 of every 9 of the bunches was swept away by a pair of deflecting plates. In both cases, the decay of the gamma rays between the beam bursts was studied. Two parameter (EY_t) data are acquired by the data acquisition program TOOTSIE written by D. Bayer [TOOTS]. The program allows for 10 time bands to be set and the apprOpriate gamma spectra are chan- neled into these bands. One band is set on the prompt portion of the TAC for energy identification, while the other 9 are evenly spaced between beam bursts. Using the LEPS as a start and the cyclotron RF for the stop sig- nal, a TAC peak with 9 nsec FWHM can be easily obtained. Thus it is possible to measure the half-lives of some y-rays decaying between beam bursts. For 50 MeV alpha particles, since the time between bursts is about 49 nsec, lifetimes as short as 5 nsec can be readily measured. In Figure 3-3, nine spectra taken between beam bursts during the l77Hf(a,4n) reaction are shown. The spectrum at the top of the page is the least delayed, the spectrum at the bottom is the most delayed. The most prominent delayed transitions which were seen in this experi- ment were the 84-keV line, the 79-, 9S-, lOl-keV lines, and the 106-, 237-, and 352-keV lines. The latter three transitions belong to the ground band of 178W and have a measured half-life of 10 nsec. The l97-keV transition of 19F having a half-life of 87 nsec is seen in these spectra to show little measurable decay. The 79-, 95-, and lOl-keV 33 177Hdushu 50 MeV T between beam bursts 1‘3 - O—l C3 .c u: F”Td 2.8 nsec/BAND 560 1060 CHANNEL NUMBER Figure 3-3. Spectra taken between beam bursts during the 177Hf(u,lm) reaction. Delay time increases with each spectrum from top to bottom. 34 peaks decay to some extent in the course of 27 nsec but a further sweeping experiment was performed to accurately measure their life- times. The half—life of the 84-keV transition was measured in this experiment to be 9.7:O.7 nsec. The relevant data for the 84-keV half- life are plotted in Figure 3-4. In the l of 9 sweeper experiment, the lOl-keV gamma ray was seen with a lifetime at 40:3 nsec. The 79- and 95—keV states also had com- ponents with the same half-life. The data from this experiment are plotted in Figure 3-5. 3.4 Excitation Functions For a description of the process by which levels in a (particle,xn) reaction are populated see for example New70. Here, it will be sufficient to note that as the energy of the incoming particle is increased, the population shifts to higher spin levels. Thus, at least within a band, another confirmation of the correct placement of a gamma ray can be made by comparing the change in relative intensity with an increase in beam energy, normalizing to an intense gamma ray either at the bottom or top of the band. The excitation function data set for 177W was taken as part of a study for 178w. Singles spectra were taken with an 8% efficient detector (detector efficiencies are relative to the efficiency at 1.33 MeV of a 3"x3" NaI(Tl) detector 25cm from target) at beam energies of 34, 38, 43 and 46 MeV. The (a,4n) reaction cross section peaks at an alpha particle energy of 50 MeV. The 43 and 46 MeV beams were well below 3S Peak Area .... CD 4: lLl 11/2=9.7[7] nsec l l l l 0 5 10 15 20 25 nsec Figure 3-4. The half-life data for the 84—keV transition in 177w. 36 1'1/2[0V9.]= H O (.0 o .. .. 2 E 3 L+0[5] nsec < - 1 , .. é . .. a) F ‘ a. _ .. 100: E A! I [ 1 l D dr 79 keV 101 keV H C) 0) I l'tj111' Peak Area I 100 l 4 1 1411:] 3 § 0 ' 160 ‘ 260 ‘ ' 160 ’ 260 nsec nsec Figure 3-5. The half-life data for the lOl-, 79-, and 9S—keV transitions in 177w. 37 this maximum, but the (a,4n) gamma rays are strong enough in these spectra to obtain some information about the relative spins of the more intense transitions. The spin assignments for 177W'were con- firmed by the excitation function data, but no placements were made entirely on the basis of these data. 3.5 Gamma-Gamma-Time Coincidences The most important and most extensive type of experimental data which were taken for this study consisted of three parameter-y-y-t- coincidences. In this experiment two detectors were placed about 2" away from the target at 180° with respect to each other. The energies of gamma rays from each detector, as well as the time between them are recorded as a word on magnetic tape. A typical experiment consists of recording about 3X107 events. The prompt gamma rays which form a cascade will occur within 100 psec of each other. Using a 10% detector with a closed end coaxial shape, and a 72 efficient detector of the same shape, a time resolution of 15 nsec FWHM was obtained. Due to walk in the timing information of the low energy signals, the TAC peak generally had an asymmetric shape with the low energy gammas producing a tail which had to be included when setting a prompt time gate. By sorting the gamma rays into sequential time intervals, the prompt gammas as well as the delayed gamma rays could be studied with chance or random background sub- tracted. 38 As well as sorting gamma ray spectra according to the time when they occurred, the spectra were sorted according to energy gates set on either detector while displaying everything that was in coincidence in the other detector. The displayed spectra were also background sub- tracted. Using the program KKRECOVERY by C. B. Morgan [KKREC], up to 120 2048-channel spectra may be generated in the sorting process. The sorting process takes about 30 minutes per tape (3 million events) on the Xerox 27 and thus it is feasible to set gates on every peak, in both detectors. After performing the experiment with the two detectors mentioned above, it became clear that the large density of low energy gamma rays required a coincidence experiment with the high resolution LEPS detector. The LEPS is such a small volume detector that only 9 million events were acquired in 24 hours, but the data were highly resolved and many of the level assignments were made on the basis of these data. In Appendix C important coincidence gates that were used to make the level assignments are shown. In order to display the high energy coincidences, spectra taken from the first coincidence experiment are shown. To display low energy coincidences, spectra, or parts of spectra taken from the LEPS high resolution experiment are shown. The spectra are arranged according to increasing energy within a band with the cascades first, then the crossovers. The coincidence information was used to construct a tentative level scheme. The data from the angular distributions, excitation functions, and singles spectra were then used to lend support to the 39 scheme. The rotational structure of 177W which was generated from these experiments is shown in Figure 3-6. Three bands, the 7/2+[633], 1/2-[521], 7/2-[514] are strongly populated. The identification and characteristics of the three prominent bands, and the tentatively assigned 5/2-[512] band will be discussed in the next chapter. Figure 3-6. Level scheme of 177W. Except for the members of the 1/2-[521] ground band, every level should have added to it an energy A. Transitions labeled with an asterisk are members of close-spaced (<0.S keV) doublets. 4O HNSH .N)... 7:3 .9» v.5. _ -Nh v.09 HQHIJ1IJN3 mNo. amaILIIJS= oi... . .93. some some .99.... $.08 ..35 .83 n 090 :LIJSN ..mnwgomxh ..~.w Tlllouxfiw N\.n O c~3-~> adllflldJNx. a «.2. «3 .NB 394.com... EFT—alhk j -Na c.0353 i.e.. “dun _ ha. «Nam 98.. ads .3. -Nh. some new». Sh! -Na. . _ .~\_N fine... a .88 Figure 3—6. CHAPTER IV 177w EXPERIMENTAL RESULTS 4.1 The 1/2’L521] Band The first 4 members of this band were previously seen in the decay of 177Re which was studied using conversion electron [Ha75] and gamma ray [G070] techniques. The conversion electron study indicated that the 1/2-[521] is the ground state in 177W. The transition between the 7/2- and 5/2_ band members was seen in decay, but not in the present study. In the (a,4n) reaction, the band was populated up to spin 25/2. Only crossover transitions were seen, as is usually the case for a strongly decoupled K=l/2 band. The rotational constant, g;, calculated by fitting the first 3 energy levels to the equation 1+1/2 (Hi-)1 h2 E — Eo +-§§{I(I+l) + a(-l) 2 has the value 14.91 keV for this band, while the decoupling parameter, a, is +0.70. As expected,the value of %% decreases higher in the band, while second order effects e.g. breakdown of pairing correlations due to Coriolis-induced decoupling, increase with spin - a fact reflected in an increase in the calculated value for the decoupling constant if higher levels in the band are used in the computation. To account for these effects, a third parameter, B, which is second order in I(I+l) could be included to incorporate the variable moment of inertia, thus 41 42 giving a better fit to the data. This parameter was used in identifying the other negative parity bands, but a two parameter fit was sufficient for identification of the 1/2-[521] band. Bu7l contains a tabulation of these parameters for various bands in odd proton and odd neutron nuclei in the deformed region. The values for the 1/2-[521] band in 177W are consistent with the same band in other nuclei with 62 = O.2-0.3. 4.2 The 7/2+[6331Band The 7/2+[633] bandhead appears to feed either directly into the 1/2-[512] ground band, or, in accordance with the coincidence data taken by Griffin in the decay of 177Re [Gr76], into the 5/2-[512] bandhead whose location above the 95-keV level is not known and is designated as A. The 7/2+[633] band deexcites through a very strong El transition, the 84.3-keV gamma ray. The bandhead has a half-life of :10 nsec. Both in 17311f and l7511f a corresponding situation exists [Hu73]. A comparison of the gamma-ray transition rates compared to the Weisskopf estimates, Fw’ given in Table 4-1 shows that the [633]+[512] transition in 177W is .314 times faster than the corresponding one in 177Hf, and proceeds ”6 times faster than the same transition in 175Hf. Table 4-1. Hindrance Factors for [633]>[512] Transitions .. Fw=(T1/2)Y(€XP)/ 9 BY (keV) (Tl/2)Y(exp)(X1O sec) (Tl/2)Y(Weiss) 173H£ 90.5 54-2 3-1x105 175Hf 207.4 2-5 1‘5x105 177w 84.4 5.7 2.3x10“ _—_..—-——.....-- 43 The rotational band which is built on this Q=7/2 member of the i13/2 group of orbitals is a highly perturbed structure. Figure 4-1 shows the band plotted in the usual way, EI—EI_l/ZI versus 212. On a graph like this, a well-behaved rotational band which follows the prescription hz 2 2 EI — Eo-+-§5 I(I+l) + BI (1+1) h2 will fall on a straight line with the rotational parameter is as the intercept and the slape equal to the second order rotational parameter, B. For a deformed nucleus with a single particle strongly coupled to a rotating core, this simple two parameter rotational equation should approximately hold. In the case of high-j (i13/2,h11/2 or hglz) orbit- als, the Coriolis force will be large and the off-diagonal elements of the Hamiltonian will produce a highly distorted set of energy levels as shown in Figure 4-1. In order to analyze this band, a bandfitting procedure as outlined in Be74 was used, proceeding in the following manner: First, the posi- tions of the unperturbed average-field single—particle levels that originate in the i13/2 spherical state were estimated for the appro- priate deformation using the computer code of Nilsson [N169]. The parameters necessary for this calculation are 62, an, Kn, and u . The deformation parameters, 22 and en, were extrapolated from a plot of theoretical predictions for rare earth nuclear deformations found in Nilsson's paper [op. cit.], and Kn and “n were obtained from equations 44 U I U I U ' r I r 1 I I o . c .- a C k‘ D- \\\ \ b \x" 3 ’I .. ’1 I b C <\\ \ fl 3 t D / 5 / m c r ,_ X (‘3 r- 52 I“ 9 b '* ls: ’5F (K N \ N a" -o M : >- \ \ I\ y. . O 4 ‘~\ L w o «a % !§ I g A 5 L {If I 3% IZ/[I‘IEI-IEI] Figure 4-1. A plot of the 7/2+[633] bands in 177W and in 175Hf. 45 given in the same reference - = 0.624 - 1.234 4‘— . A Kn -- 0.064]. - 0.0026 1000’ un 1000 The single particle energies were then corrected for pairing correla— tions using the BCS formalism described in Chapter II. The necessary parameters for this calculation were A, the pairing gap parameter, which was estimated from the systematics of odd-even mass differences in the W nuclei [op. cit.], and the position of the Fermi surface, A, which was extrapolated from calculations in 0g7l of A for similar N=103 nuclei. The quasiparticle energies, plus the decoupling parameter, a = -<;%{j+J-%>z and the appropriate Coriolis interaction strengths, 3 which were calculated by the Nilsson code, were used to set up, for each spin state, the appropriate Coriolis interaction matrix. The rotational Hamiltonian, then, consists of the following elements: — h2 I-l/Z HKK — Eqp + {fi-O-B(I(I+l)-K2)}{I(1+1)‘K2+("l) 86K,1/2} h2 - HI<.I<+1 = ’{fil’ BI(I+1)}/(T’K)(I+K+l) (UKUK+1+VKVK+1) x gK,1<+1 This interaction matrix is then diagonalized in the space of the i13/2 orbitals. The factors gK,K+l are attenuation coefficients which are necessary to reproduce the experimental energies. In general, the attenuation is found to be greater for states close to the Fermi surface, so some calculations [e.g. Li73, Hu73] have successfully 46 assumed a parameterization of a gaussian form for this factor. It has been claimed [R174] that if the calculation is done in the framework of the self-consistent cranking model, then no attenuation of the Coriolis matrix elements is necessary. The experimental energies were fit by adjusting up to 10 vari- ables - the gK,K+l’ g;, B, and one quasiparticle energy - in a least- squares fitting routine BETABLE [BETA] which minimizes the differences between the calculated and experimental energies. The rotational parameters, 2% and B, were initialized at the average values taken from the yrast sequences in the neighboring even-even nuclei. The results of the bandfitting procedure for the 7/2+[633] band are summarized in Table 4-2. The only i13/2 state which has been experimentally located in 177W is the 7/2+[633]; positions of the other members of the family are not yet known. The fitting routine, then, has too many degrees of freedom, and a reasonably good fit to the known energy levels may be obtained with a wide variety of parameter sets. Most of these sets are not physically realistic, however. If a member of another low-lying i13/2 band could be experimentally located, the position of the Fermi surface would then be constrained such that the quasiparticle energies could only vary within much smaller limits, yielding more believable results. In view of the attenuation coefficients calculated for positive-parity bands in other nuclei [cf. Be75], the most reasonable parameter set obtained here is the one given in Table 4-2. One important conclusion of the fitting is that the energy of the 9/2+-+7/2+ transition must be very small, about 30-35 keV. The transi- tion will be a highly converted Ml+E2 similar to that of the 86-keV Table 4—2. Input parameters for the Coriolis bandmixing procedure, calculated energies and amplitudes of the resulting mixed wavefunctions. 47 Noo.o moo.o 0Nm.o mNo.o mom.o Nam.o cam.o o.mwo N.oma N\NN woo.o «No.0 NNm.o NNN.o mms.o smN.o NNo.o m.nmm m.mmw N\mN moo.o Noo.o amm.o NON.o nNs.o NNm.o NNN.o N.NNo o.NNo N\NN soo.o ooo.o som.o NNN.o mmq.o NNN.o smo.o N.mmq a.omq N\mN Noo.o 040.0 Nsm.o maN.o oN¢.o NNN.o mNN.o N.mom N.Nom N\MN Nmo.o enm.o Nmm.o Nom.o NoN.o mmo.o 4.NNN n.0NN N\HN NNN.o Nam.o mNm.o NNN.o Nmo.o N.HNN m.mNN N\m aoa.o NNN.o «No.o NNo.o N.omN q.aNN N\N ono axm Hoooa+N\ma Hmaoi+N\NN HqNoi+N\m _mmo_+N\s HNsoH+N\m HNmoi+N\m .ooo_+N\H m :Nam mm A>mxvmowwuoam Ho>oq omwm HoooH+N\mN vmwum> Nam.o soc coo.m NNoN _mNo.+N\NH on.o mN.o omw.q oNON _4Noa+N\a amm.o Nm.o Noo.m o HNNQH+N\N oNa.o «N.o NNN.o awn HNsOH+N\m mam.o mm.o sow.o «no "Nmoi+N\m coo.N NN.o «No.0 mNN .oooH+N\H H+e>e>+a+VH v N+a.ew .Ae_+fi_a+xv A>mvawwmsmwm NmUNnuo AHNNmi-N\mVaem+>mx omN u ‘ >mx can u a qu.o «Aum-++h+wv. >m N.a- u m >03 4N.NN n.wm .qu mant 48 woo.o omo.o aNN.o oNa.o NNm.o om4.o mmq.o N.NamN m.mamN N\Nm «Ho.o owo.o Ham.o Nso.o 4mm.o Nam.o NON.¢ a.mmsN N.mmsN N\Hm moo.o ooo.o NmN.o sam.o NNm.o oNq.o NNs.o m.mmAN w.amaa N\mN NNo.o mmo.o Nmm.o moo.o Nmm.o Nam.o «mo.o a.meN m.mNmN N\NN moo.o meo.o mNN.o som.o NNm.o ans.o «Nm.o N.N44N N.NsaN N\mN oao.o Nwo.o mam.o mae.o on.o mNm.o qwo.o H.0NNN o.NwNN N\NN Hoooi+N\mN HmNai+N\NN HQNEH+N\m ”mace N\N .Nqo_+N\m Hamel N\m Hoosi+N\H onom Axum sham + + A6. ucoov NLV magma 49 transition with mixing ratio 6 = -0.45, where 6 is the ratio of the L=2 amplitude to the LPl amplitude. There is a 34.1-keV conversion elec- tron peak.with E2/Ml - 0.0066 [Ha75] seen also in the gamma decay [Gr75] and in in-beam spectra which is a possible candidate for the lowest 7/2+[633] band cascade transition. In order to resolve the placement of the 34-keV gamma ray, an accurate intensity measurement of the gamma ray which is seen in the (a,4n) spectrum, and perhaps even a coincidence experiment would be necessary. The difficulties involved in the determination of the intensity of this gamma ray were discussed in Chapter 3.1. The coinci- dence experiment would entail the problem of getting good timing sig- nals from very low-energy detector pulses. The peak is also weak, as seen in Figure 3-2, but if the transition cascades into the very intense 84-keV line, then the coincidence relationship would be easily verified. In the level scheme shown in Figure 3-6, the 34.1-keV gamma ray is given two tentative placements - as the interband transition deexciting the 7/2-[514] band, and as the lowest cascade member of the 7/2+I633] band. The theoretical bandfitting prediction suggests the second placement, while preliminary gamma-decay coincidence results [Gr75] suggest the first. 4.3 The 7/2‘[514] Band A third rotational band which was strongly populated in this experiment is believed to be built on the 7/2—[514] single particle state. Twelve members of the band are seen and are plotted in the 50 usual way in Figure 4-2. Using the standard rotational equation given in section 2 of this chapter, and the energies of the first three levels, the calculated parameters of the band are h2/23 = 13.62 keV and B I -0.0155 keV. The corresponding 7/2-[514] bands in 179W and 181W are also plotted in Figure 4-2 for comparison. The small perturbations at high spins in these bands arise from a propagation of <1,KIV II,K+L> interactions which mix highly decoupled Ksl/Z Coriolis bands with K=3/2 bands, K=5/2, etc. until the K=7/2 bands are reached. In this deformation region, the presence of many negative parity states which can interact with each other accounts for the impurity of the quuantum number, and also for the complexity of the mixture involved. The 7/2-[514] bands shown here all have (I+l/2 - odd) spin levels as the favored ones, that is, these levels are lowered in energy as a result of mixing with a K=l/2- band which has the same sequence of levels depressed. Since the effect of decoupling in a K=1/2 band is to I+1l2(I+l/2) to the level energies, then add the term 6K,l/2 a(-l) clearly a band having a negative decoupling factor, a, is causing the perturbations which are seen in the 7/2-[514] bands. A tabulation of decoupling factors and Coriolis interaction matrix elements is given in Bu7l for N-S neutron orbitals and from these values, the 1/2-[530] can be seen to be the most likely cause of the perturbations observed in the 7/2-[514] sequences. 51 q — 7/2'[51‘+) BANDS l l l l 2250 300 350 L100 L1'50 21 L 200 l 150 L 100 I: l\ L‘. O o 181” D 173” .J L- 15 l 3' r4 Figure 4-2. 1 l :2 <3. 07 l 9’. Iz/(“Ia-Ial A plot of two known 7/2-[514] bands in neighboring odd tungsten nuclei compared with the 7/2‘[Sl4] band in l w. 13- 52 4.4 The 5/2’[512] Band Two members of the 5/2—[512] band have been tentatively identi— fied, the 101-keV and 130-keV transitions. The 101-keV line is very strong in the decay of 177Re [Gr75] and its multipolarity, obtained from conversion electron data [Ha75] is.Ml+E2 which suggests that it is an intraband transition from a low spin level. The levels in the 7/2-[514] band are preferentially populated in the (a,4n) reaction and some small amount of feeding into the 5/2-[512] band is seen. The implication of this pattern is that levels with a particular spin value in the 7/2 band are likely to be lower in energy than the same spin members in the 5/2 band. Therefore, it is expected that no levels above the 9/2 member of the 5/2-[512] band will be strongly popu- lated. The 11/2-+9/2- transition is predicted to have an energy of 160 keV, and a weak 158-keV line seen in the coincidence data is tentatively assigned as this transition. 4.5 Possible 3—Quasiparticle Band The l44-keV gamma ray is seen strongly in coincidence with many members of the 7/2+[633] band. It appears to feed into the 21/2+ level and is possibly an interband transition from a three quasi— particle state. Three band members are proposed to be built on this state with both cascades and crossovers seen. The band follows a smooth rotational behavior with a: of 8.13 keV (for K = 23/2) or 9.86 23 (for K = 19/2). 53 The angular distribution of the l44—keV line shown in Figure 4-3 is characteristic of mixed multipolarity with A2 = -0.72i0.05 and A“ - 0.18:0.05. Initial spins of 23/2 and 19/2 are both consistent with the angular distribution coefficients, but the Ag value has the wrong sign to be compatible with a J = 21/2 assignment. 1 The lifetime of the l44-keV gamma ray is very short - within the limits measurable in the timing experiments. As shown in Table 4-3, the hindrance per degree of freedom is £15 which is much smaller than ex- pected for a transition from a three-quasiparticle to a one-quasipar- ticle band as illustrated by a comparison with data for a K=23/2 + 21/2(K=7/2) transition in 17711f. This low hindrance for the transition:h1 177W remains unexplained if, in fact, the transition is correctly placed. Recently, a similar puzzling situation was found in 18108 [Ne76] where a gamma-ray cascade was seen feeding promptly into either the 19/2 or 21/2 level of the 9/2+[624] band. No other interpretation of the sequence of levels in 177W is apparent at this time, since the high- spin members (1919/2) of other positive parity bands which are close to the Fermi surface are not expected until about 1.8 MeV excitation. Table 4—3. Hindrance Factors for Transitions from K = (23/2) Isomers Fw=(T1/2)Y(6XP)/ EY (keV) (Tl/2)Y(9XP)(SBC) (Tl/2)Y(weiss) 177W 144.3 S5X10-9(est) €Jxlou 39-9 177Hf 55.1 33 5x101“ 90 INTENSITY 54 1.1.. 1.0 .. .9 - .8 - .7 - .8 ._ .5 .. .‘+ .. .3 _ .2 _ 1 AH/AO = 0.18:0.05 . d 144 keV A2/A0 = -0.7210.05 .0 0°10 °20°3o°t+0° 50° so°7o°80°90° ANGLE Figure 4—3. Angular distribution data and fitted curve for the 144-keV transition in 177W. 55 4.6 The Single Particle Level Structure of 177W Most of the evidence for placement of the single particle orbitals in 177W comes experimentally through either indirect or negative proofs. The rotational bands built on the single particle states all have structures which are characteristic of similar bands in isotonic and isotopic nuclei. The 1/2-[521] band is highly decoupled with intraband transitions proceeding by E2 gamma-rays. The 7/2+[633] is also a perturbed structure and can be explained by a mixing of appropriate i13/2 bands. The 7/2-[514] band has some small perturba- tions at high spin values which is typical of the same band in 179W and 18111 Although only weakly populated, the proposed 5/2-[512] band has a rotational constant gé-similar to that in the 179W 5/2-[512] band. The relative energies of the bandheads are much more difficult to determine. The 1/2-[521] state was interpreted through the decay pat- tern [Gr75, Ha75] to be the ground state. From the systematics of the deformations for tungsten nuclei [N169], a deformation of £2 = 0.245 and 8n = 0.03 is predicted for 177W. A calculation of the position of the l/Z-[521] Nilsson orbital places the state about 200 keV above the 5/2-[512] which is the normal ground state in the N=103 isotonic series [Bu71]. This change in the normal ordering of levels in 177W has been interpreted as an implication of a smaller value of £2 for 177W [Ha75]. However, in view of the uncertainty in the theoretical calculations, the discrepancy is not unreasonable. The level which should be seen closest to the ground state is the 5/2-[512]. Since each of the two other bands expected to be populated 56 has KF7/2, both would be likely to feed into the 5/2-[512] state rather than directly into the ground band by K-forbidden transitions. The only strong interband transition which can be seen with the data available is the 84-keV El gamma-ray which depopulates the 7/2+[633] band, but which is only weakly in coincidence with gamma-rays from the 3/2 and 5/2 members of the ground band. There are no intense gamma-rays seen in the depopulation of the 7/2-[514] or 5/2-[512] bands nor are there any unexplained strong coincidences in the ground band gates. The implica— tion is that the interband transitions must be too low in energy and too highly-converted to be easily seen in the in-beam Ge(Li) spectra. Even assuming that the gamma-rays cannot be detected, certain rela- tionships between the bands can be discerned. The 7/2-[514] band re- ceives a larger percentage of the population than does the 5/2-[512]. There are only a few weak transitions connecting the two bands. There- fore, it seems plausible that the levels of the [514] band must be lower in energy than the corresponding members of the [512] band. This would place all the levels with the same spin value lower in energy for the [514] band and would explain why it is populated more strongly. A consideration of the gamma-ray lifetimes can also be useful in determining the relative bandhead positions. The 7/2+[633] bandhead has a half-life of 10 nsec. A scheme can be constructed with the 84-keV gamma ray feeding into the 5/2_[512] level which may then depopulate into the 1/2-[521] ground band via a relatively long-lived low energy gamma ray. The intensities of the 79-keV and 95-keV ground band transitions were each found to have a delayed component having a 37 nsec half-life. An unidentified 101-keV gamma ray appeared to have the 57 same lifetime, and it also had enough intensity to account for the ground band components. However, the 101-keV line is assumed not to be the transition from the 5/2- bandhead, because the coincidence data from the decay study of Griffin do not support this assignment. It is possible, though, to place an upper limit of z37 nsec on the lifetime of the 5/2-[512] since no appreciable longer-lived delayed components in the ground band intensities can be seen. The study of 177Re decay by Griffin [Gr76] was prompted initially to supplement the in—beam data which were unable to easily identify the relative locations of single-particle orbitals in 177W. Since the ground state spin of 177Re is 5/2, only low-spin states would be populated in 177W. Griffin performed both singles and gamma-gamma coincidence experiments using a small volume planar detector for characterization of low energy gamma rays. Unfortunately, results of the study were not statistically conclusive. Lack of coincidences between the 95- and 101-keV gamma rays suggested the relative position of the 5/2-[512] at A-keV above the 5/2 1/2-[512]. This assignment has been adopted here, although the in-beam data do not require it. The energies of calculated Nilsson levels can now be compared with the experimental levels to see if the deformation can be inferred from the relative positions of lowelying states which are populated. At the deformation mentioned at the beginning of this section, not only is the 1/2-[521] state 200 keV too high, but in order to lower the 7/2-[514] single particle energy to reasonable agreement with experi- ment, the Fermi surface must be placed 200 keV above the 5/2-[512] state, not an altogether unreasonable assumption. If a smaller 58 deformation for 177W is assumed, however, the orbitals under considera- tion begin to slowly approach each other in energy and, in fact, at £2 - 0.210, there is a crossing of the 1/2-[521] and the 5/2-[512] orbitals. The fact that the 1/2-[5211 appears as the ground state in 177W whereas the 5/2-[512] is the ground state in other N=103 isotones was suggested by Harmatz, et, a2. [Ha75] to be an indication that perhaps the deformation of this nucleus was smaller than that of the other isotones. Indeed, at a deformation of £2 = 0.210 with the Fermi sur- face placed 150 keV above the 1/2-[521] and with the quasiparticle energies corrected for zero-point rotational energy, the 7/2-[514] and 5/2-[512] states are predicted to be only 48 keV apart, and 86 keV above ground. Since this set of results is roughly consistent with the experimental data, it can be indirectly inferred that 177W may possess a deformation somewhat smaller than other nuclei in the 103 isotonic series, and also somewhat less than expected from the systematics pre— dicted by Nilsson [N169]. CHAPTER.V 178w EXPERIMENTAL DETERMINATIONS 5.1 Gamma-Ray Singles Spectra The levels in 178W were populated in an (a,3n) reaction on 17711f. The Hf foil targets were the same ones that were used in the 177W experiments described in Chapter III. The beam energy used for most of the experiments was chosen to be about 38 MeV. Data were taken between 0 and 1500 keV using the 8% efficient detector. Most of the spectra were accumulated with 8192 conversion gain in the ABC's to improve peak definition while accommodating the large energy range. A singles spec- trum taken with the detector at 125° with respect to the beam is shown in Figure 5-1. The most obvious feature of the spectrum is the prominence of the ground band or yrast cascade. The members of this band can be identi- fied by sight up to the 12++10+ transition at 579 keV. The (a,2n) and (a,4n) product nuclei are both populated weakly at this alpha energy and since the reaction strength of these odd-nuclei is spread more evenly over many bands, no set of contaminant transitions dominates. 178W decays with a 21.5-day half-life to the ground state of 9.4 m 178Ta which decays to l7811f. The transitions in 17811f which constitute the ground band are seen also as weak contaminants. An efficiency curve for the detector was obtained and relative intensities for the transitions were determined, normalized to the 237- keV (4++2+) transition. Energies and intensities of peaks that are 59 'VVVV—v—V V V I'VfTr' 325150 0 0 89% L5” Shh 13” El” 368 985 083 fl9€ SSE 395 315 908 153 083 £83 933 S33 96 691 381 Ill 691 £81 901 — 69 ”L ‘I Imjmnln j A an414 A In 2' 3 S SlNHOU 177Hf[o<.3n] 38MeV £381 ”£31 680! L801 flIOI 346 396 136 £88 LLL ”L9 059 089 h19 6L5 ‘ hZS 119 505 4 JJJJJ I _L IV C) C3 o-O SlNflOD at 125° with respect to the beam. 9000 9500 $000 500 6000 8500 7000 7500 8000 CHANNEL NUMBER 00 3000 Figure 5-1. Spectrum of 177Hf(a,3n) taken with an 8% efficient detector 61 believed to belong to 178W are listed in Table 5-1. In general, gamma- rays that have a relative intensity of 0.8 or less which have not been assigned, are not listed in the table unless coincidence information demands that they should be. Since most of the contaminants are known to be 179W, 177W, l7811f, and 177Ta, the energies of these gamma-rays are not included. The spin assignments for transitions depend on the K—value of the band in which they appear. The bandheads assigned K"-=(6)+ and K"=(6-) have tentative Kevalues which are used in the table to assist in identification of the transitions which are associated with each of these bands. 5.2 Angular Distributions The set of angular distribution data for 178W consists of spectra taken at 90°, 115°, 125°, and 135°. The peak areas were obtained and the curve was fit to W(0) = Z AKFK(cosO). Az/Ao and Ag/Ao were Ks0,2,4 extracted for each transition. In most cases, the errors are large compared to the errors for the 177W transitions of comparable inten- sity. The chamber used for the (a,4n) experiment has a wider window than the one used for the (a,3n) distribution and the smaller angular range which is obtainable in this case had a significant effect on the precision of the curve-fit. Of course, the detector resolution, which is slightly worse for the 8% detector than for the LEPS also affects the results by making the doublet peaks more difficult to analyze reliably. Table 5-1. Energies (EY)’ relative intensities (IY)’ angular distribution coefficients, multi- polarities, and spin assignments for tran- sitions in 178W. In the cases where no Au/Ao is listed, the angular distribution data for those transitions were fit with Aq/Ao con- strained to zero. The transitions labeled with an asterisk are components of closely spaced (<0.5 keV) doublets. 62 AuN+-ev-Nux aflvm.N Amvoe.oNN Aeves.o Amvmm.mNH Ae+Nv+euM Nm .N:_ mo.emo.o No.4ee.ou Amve.m AmvNN.oNN Am+evuelx Na .Ha NN.AeN.H- ANVe.N AmVHN.NeN anm+uequus Na .Nm eo.Noa.o Aava.o Anvme.mea Aave.N Amvom.NnN Aevoo.N AmvNH.omH xN+wv-eux Na .Na mo.eeo.o no.44e.ou Amve.m Amvem.NmH Aevoo.N Amva.NmN sees Amvm.e Amvem.eHN A+o++Nv+oux Nm no.4eo.o eo.Neo.o anNN Amvoa.eoN Names .Ae+Nv-eua a.“ H.o- anN.e Amvemm.wm +eua+ueus Hm no.4NN.ou aNVeH Anva.mN 5.... 2: Ne 35 .3: see uooaowfimm< .umooo >H rm soausnwuumaa umaama< Hum wanes 63 Aevm.e AeveeN.eNN “Nee.a AONvNN.NNN AOH+NNV+eIM N.A H.H- anm.H AmNVem.NNN Ae+mvuenm Nm eo.eeo.o No.4Nm.o xNVm.m Amvmw.mNN Am+nlex eo.ANo.o aNVN.N Amvmn.eNN AoN+NHvueux N2..Nm H.oe N.ou Amvmm.N Amvem.wHN Ae+eav+els Aevem.o Aevmm.NHN Amvoe.N Anemo.NON Am+ev+eux H2..Nm a.“ e.o- anN.H Amva.m0N No.4NH.ou anm.N AnvNN.HoN Ae+ofivueux Nm .Hz. NN.New.ou Aavm.N Amvoe.emN aN+Nv+elx AHVN.N Amveo.mwfi N.mmom+e.NNNm Aflve.N Amvom.NwN o<\:< o<\~< A.uoq .Huwv A>oxv usuaawamm< .wmooo >H >m ooausnawuman uoaawa< A.e.u:o0v Nun «News 64 Aavm.a Amvmu.mem ANVm.N Amvme.mem Ann+quuNus Aeve.n Amva.NNN aN+mvneuu Ne no.4HN.o Amves.m Amvmo.eom e.NNNN+N.NNmN No.4mN.o- Amve.e AmvNe.oeN A+e.+m.+Nuev+e+A+eueve xNvN.N Amveo.mwN A-e+-equuz NN No.NoN.o hevN.e Amva.NmN AHvN.o AmveN.eeN zmxi ANVm.N AnveNm.eeN xNN+NNvueuz AmvNN.o Avaee.oeN AavN.H Amvae.HeN aNH+NHvueux AmvN.e AeveHN.eNN A+N++ev+ous Nm mo.emo.o no.4NN.o Aevooa AmvNo.NmN e<\e< e<\N< A.ueN .Heuv A>mxv usuacwamm< .mmuoo >H >m oowusnauumwn umaswa< A.e.uaouv Hum mNems 65 Aue+uNavnNIM ma+e++mv+ous Nm No.4No.ou No.4NN.o anNm Amveae.eee Ae+HNv+mus Amvoa.N Aeva.mee ANVm.H “meme.eme Amvmo.N Amvea.NNe Am+oNv+eue anH.N AmvaN.HNe Am+NNvleus N.“ m.o- fiNvm.m Amva.mHe xN+av+eIs N.“ N.o Amve.e Amveo.Nem AeN.ev ANvN.N Amvem.omm AIN+uequue Ne mo.eno.o mo.NNN.o ANvo.e Amva.mwm Aue+umquue Nm eo.ANo.o eo.ANN.o Amvm.e Amvee.eNm Am+oNvueux Ne eo.Aeo.o eo.AON.o AevN.e Aevem.mem Ae+wv+mux H.oe N.o Amve.m AmveN.wmm A+e++ev+eus Nm No.4No.o No.4eN.o Aevee Ancem.amm e<\:< e<\N< A.uee .Heuv A>mxv usuaowfimm< .wwmou >H >m ooauonauuman umaowa< A.e.ucoov Nun «News 66 AmN+vaaeux AavN.N Amvms.mcm A+ouav+NN+A+ousv+NH Aavme.o Aevme.emm AION+INanNux flavo.N AeveN.mem ANN+eNvueue NN No.4mo.o- wo.eme.o ANve.H Anemo.mmm A+N++oNv+oux Nm no.4eo.ou eo.AeN.o AavNN nevNN.mNm A+ouev+m+auNuequ anN.o Amva.eNm AuaN+uNanNnx “Hem.N Amvea.mom AaN+vanenx Advm.N Amvam.wee Amvmm.o Amveo.eee “A-N+-ONV-NuM ANVN.N AmvemN.Nee No.4eo.o eo.NmN.o anN.N Aevem.mee A+ouev+ea+x+ouev+ee ANVoN.o aNNvee.oee fiNVN.m Amvmm.eme o : o N e e i e 35 .3: 3.5 w > > ocean Hmm< .mwooo H m aoauanfiuumfin weasma< A.e.ueoev Nun eases 67 A+ouev+N+AuNusqu “eve.e aflvm.mme Aueuxve+N.mm0m Amvme.N anm.ONe A+ouxv+m+auNuevue Na .Hm eo.eeo.o eo.ANe.ou ANvN.N ANve.ooe A+ouxv+e+anuxvue eo.eeo.o eo.4ea.o Amvm.e Aavw.Nmm A+eusv+e+A+ouev+e Aavm.N Aavm.NeN A+ouxv+oN+AuNuxv-NN xNvm.o anmm.eNm A+ouev+e+xuNuevnm Hm mo.AmN.o- AevN.e Amvmm.NNN A+Ouev+m+x+ouev+m N.“ N.o- Amvee.o vaNN.eNN A+euxv+ea+a+euxv+oa anmm.o “Nvmm.eee A+ouev+e+A-Nuxvum Hm eo.Noo.o No.4NN.ou AmvN.e fleece.Ome A+ea++eNv+oum AavN.N AmvNN.eNe A+NN++eHv+oue Na No.AmN.o Amvm.m AmvNN.eNe A+0N++Nav+eue Ne Ho.eoo.o Ho.NNN.o Aevm.HN Amvmo.mNm o l. o N <\ < <\ a A.eeN .Heuv A>mav ucmaawflmm¢ > > .Noeoo H u coausnawumwn Headwa< A.e.eeoeo Nun eHeee 68 aNVe.m AHVe.NNNN A+ouxv+e+a+euxve No.Neo.o- AaVON Aavm.NNmN A+oueV+N+A+e.+m.+Nwsv+e .mzNN Amvo.m Aavsm.qnma Aavm.o xNve.eoNN Aueuevm+a.mmom AeHvN.N anN.ew0N I a a n o o A+ouxv+e+x+e +m +N xv+e ANvfl m Aavo NNOH AevN.N AHvN.eHON A+ouxv+e+AuNuxvum Nm mo.NNN.o- anN.N aNVH.NOON A+ousv+e+A+ensve AmvN.eH Ade.oNe A+oaev+o+auNuevue anN.m AHVe.Nem o z o N 3 e i e 35 .05 $9: usuaawamm< r > .uomoo H m aofiuanauumfin wo~=wa< A.e.eeouV Hum wNemH 69 The values of A2/A0 and AA/AO for the more intense transitions are listed in Table 5—1. For transitions where the data were too poor to determine AA/Ao, the value of AA/Ao was constrained to be zero, and A2/A0 was then calculated. For these cases, no Au/Ao is listed in the table. Plots of some of the ground band distributions are shown in Figures 5-2 and 5-3 arranged according to increasing energy within the band. The data have been transposed to the 0-90° quadrant. Selected distributions of intense transitions in other rotational bands in 178W are shown in Appendix B. Multipolarities deduced from the distribu- tions are also shown in Table 5-1. The values of A2/A0 were, in general, more reliable than the values of Ag/AO and could be used to estimate the mixing ratios for the more intense transitions. Assuming alignment of the original target nucleus, the mixing ratios were cal- culated using the tables found in Ma74. These ratios were used as an independent check of the gK values found from the branching ratios, and also were used in the determination of the sign of gK. 5.3 Gamma-Ray Lifetimes Isomers in 178W were sought in the range 5—500 nsec using the various techniques described in Chapter 2.3. The shortest time range studied was that between consecutive beam bursts which at 38 MeV occur every 54.2 nsec. In this experiment, transitions from the RTE-6+ bandhead at 1665.7 keV were found to have a half-life of 10.110.2 nsec. The isomer decays into the 6+ and 4+ members of the ground band and was found to ac- count quite well for the delayed intensity of the first three ground band INTENSITY INTENSITY 7O I.“ d 1.3 d 237 keV 448 keV 1.11 . 1.3 . 1.2.. 1.1 I 106 keV 352 keV A I A ANGLE 0’10'20'30°90'50°60°70’80°80°0°10°2F30°90°50°80°70780°80‘ ANGLE Figure 5-2. Stretched E2 K=0 ground band distributions. INTENSITY INTENSITY 71 1.8 .. 1.7 1 1.6 q r, on :n 3‘ u- h- ‘0 a: -‘1 in 1.0 .. 579 keV 1.8 . 1.7 . 1.6 . 1.5 . 1" a: -1 .3. 1.2. 1.1. H 1.0 . 524 keV 614 keV Figure 5-3. 3.....1-...11.....1 0' 10 ° 20°30° '10' 50°GO° 70° 80° 90.0. 10 ° 20°30° '10' 50° 80° 70° 80°30° ANGLE Stretched E2 K=0 ground band distributions. 72 transitions. The half-life data for the two delayed gamma rays which deexcite the isomer are plotted in Figure 5-4. The half-life of the 73-keV transition which deexcites the Kfl=(6-) band at 1740 keV was not measured in this experiment due to the limitations placed on accurate timing of low energy signals by the detector which was used. There is sufficient information in the (a,4n) timing data, in the delayed gates which were set on the coincidence data, and in the first three time bands of the (a,3n) timing data, however, to corroborate the fact that no prominent isomeric states with half-lives greater than 15 nsec can be identified in 178W. The lifetime of the Kfl=(6_) state can be esti- mated from the (a,4n) data as being less than 10 nsec, but the question of whether or not it is greater than the lifetime of the Kn=6+ state could only be determined by performing a separate experiment at the (a,3n) energy using a planar, small volume detector for good timing accuracy at low energies. Conversion electron measurements indicate that the 73-keV transition is delayed by 8.3 nsec [Ca76]. 5.4 Excitation Functions With the 8% efficient detector at 125° with respect to the beam, the spectra shown in Figures 5-5 to 5-7 were taken at beam energies of 34, 38, 43, and 46 MeV. The counting period was similar for each of the four spectra making it possible to relate the intensities of individual peaks directly to the production of the isotope to which the peaks belong. The transitions in the ground state band of 178W are a good measure of the (a,3n) yield which peaks near 38 MeV. The 84.4-keV 73 r r r r | I r 3 ._ 1° 5' 1322 keV 3 ° " -1 ° " a ‘— - -1 < C-l F" J o _ _ 0) CL 100: I '2 1 J 1 1 l 1 1 I I r I | 1 I L- .— a 103 d o _ m d L — < 4 3‘ o _ a) O. 100:. _ I tl/2(ave.]=10.1[2] nsec i b L 1 1 1 l 1 1 .- 0 25 nsec Figure 5-4. Half-life data for the transitions deexciting the l666-keV isomer in 178W. Figure 5-5. Excitation function spectra taken at 1250 using the alpha particle energies shown. These portions of the 8000—channel spectra display the 50-325 keV gamma-ray energy range. 74 oooN coma mmmznz JwZZ02 rm 2 E L 9 3 3 7a 9.09 6 39 9 33 .160 I. 90 9 33 .1 z 9 ...: 99 Y. .1 .19 9 9 L9 6 7.. .l > 2 mm 2 no I. 99 9 3 It 0 6 .6 2 97.9 .1 9 39 .6 37v .... .l I; I. h. 99 3 1° 6 9 9 I. 3 0 06 I. 6 z I 3 >2. m: . I. E E 9.1 o 139 Z 9 39 37.. .l .... 99 z to .I 9 I. 3 z 09 9 o .I 7.. 0 I. 9 I. >0: mm 3.3..th LEI (.81 I... 99 In." E... LE £31 £31 901 901 901 901 o.m El. ‘18 St El. '19 El. '18 75 one: comm mwmzzz szz0: rm . 3 9 9 Co 9 S 0 .1 huh. h. h. 0 h. S 99 3 3 .fl 9 E E I. 99 9 T. I 9 9 9 99 6 9 cc 3 9 o 9 C. 3 S .06 h .l .l h >0: mm . 8 E C. 3 9 o 9 F. 99 0 0 9 he; h. .... S 09 S ”9 *1 h h huh.” h I. 3 9S 9 _ h. 3 110 Eco E E E 5 95 S 9 9 SI 9 91.6 56 L 999 EC. 3 .l 3.... I. ”96 he #1 T. h. 3 06 h 9 9 >.z my . 3 9 9 9 0 .... S SS 9 h. . h I. he 39 5.19 h. .9. £9 6 09 93 [.9 h. ”h. 3 ”a... 65 E E h. 3 C. ”NT. 9 10 3.... E 9 S 9 S ”9 .16 I. ”96 99 T. 9 I. 9 9 he... .1 3 9 05 >32 my Exit: .. L p 1- - Portions of the excitation function spectra displaying the energy range 325-700 keV. Figure 5-6. CHANNEL NUMBER C3 CD I T 13" I U V I ff" TI r I TUT V—TI r U I D 00 16$! [:01 1251 IEEI NZEI hZEI anI ,1 4291 O D :> :> :> :> ”3 d> d) (D (D be I Z Z Z (O 00 CD :1' 3' :1- 0’) 0’) CD -CD C) 'P\ ZLII ZLII ZLII ZLII CD CD 10 (0 CD H do 5 5 4101 «101 4101 )3.” 2001 2001 2001 H 8 \—-I f: us us 19 us I 96 196 6 96 D» ‘ E3 szss sea see 6E6 "uj v4£€6 LE6 226 Les [“7 zee zee zee zee 1 0 1CD Lh8 LhB CD «as - 96 «he seehha , segue u) see ' 118 118 LL LLL LLL LLL E3 ‘10 :1“ C3 C3 _ C3 111111 1 1 1 1111111 A L JJAJUILIA l 1 j- 00 (0 C0 (0 C) CD CD CD .4 r4 r4 r4 SlNHOO SlNflOO SanOO SlNflOO Figure 5-7. Portions of the excitation function spectra displaying the high energy peaks in the range 700-1375 keV. 77 transition in 177W provides a convenient gauge for the (a,4n) reaction cross section. Qualitatively, it is seen that for the medium and large peaks, an assignment to an isotope can be made from these results. The most difficult assignments to make involve weak transitions, closely spaced multiplets, and multiplets which include decay products. In Table 5-1, most of the gamma rays which are not placed in the level scheme but which are assigned to 178W were identified in the excitation function as (a,3n) products. Within a particular rotational band in a nucleus, spin assignments can be verified by considering the relative population of a state as a function of alpha particle energy. Figure 5-8 shows the ground band of 178W with the intensities of the gamma-rays normalized to the 34 MeV intensities and also to the 12++10+ intensity. The spin change between successive cascade members is 2 units making this band the best example of what to expect in this type of qualitative experiment. The other bands have transitions with smaller spin differences and slowly increase in slope as the spins go higher, but the rate of change in slopes is not as rapid as for the yrast cascade. Figure 5-9 shows the excitation functions of some of the transi— tions in other bands plotted along with the ground band transitions. A direct comparison in spins may not be made between bands, but very high spin values are indicated for both the 182- and 291-keV transitions, and the spin values of 6,7 and6for the states depopulated by the 73- and 972-keV transitions are certainly not improbable. 78 Z'OOF I ' T T b let-.151“ 1.80.— r 1.60- lei-.12+ P- >- E 1.90- 9 Lu P- 2 1- F1 8 N 1.201- *J E g 1' 1.0 s : e 1233-0101 0.801- \ was“ - _. ems" I: I 0.60]- T *...o l I .1 1 38 "10 ‘H ‘18 BEAM ENERGYIMcV) Figure 5—8. Excitation functions of the K=0 ground band of 178W. The peak intensities are normalized to the 12++10+ transition intensity, and to the 34-MeV peak intensities. 79 2'00? T r r I 1' ZSIIIOV ‘ FIT-412’ 1.801— .. >' 1.60 .. r. T ‘A’ .‘i’ . - fi 1821-ev c1 SZOInaV w :1 73II0V < E g - 10*—.e* - 1.201- , _ . / 3724432311“! J ; 6+ ”1*!- 1,0. e : _ 9502" _ 1 1 1 1 38 ‘10 ‘H ‘18 BEAN ENERGYIMcV) Figure 5-9. Excitation functions of selected transitions compared to the ground band functions. The intensities are normalized to the 4++2+ transition intensity, and to the 34-MeV peak intensities. 80 5.5 Gamma-Gamma-Time Coincidences Using the same geometry described in Chapter 3.5 for 177W, three-parameter coincidence events were recorded on ten magnetic tapes, each containing 3XI06 events. The detectors used were both large volume - 8% and 10% efficient - and the TAC resolution was about 24 nsec FWHM. Gating on the tails of the time peak showed no new informa- tion, but using the main portion of the TAC with a 300 nsec time acceptance gave gated spectra with the best overall energy effi- ciencies. The low energy efficiency for the 10% detector was still quite poor, so both sides were gated and the R-side (displaying the 10% spectrum) was used to identify high energy coincidences, while the Y- side showed the low energy coincidences quite well. The coincidence gates for most of the transitions which have been placed are shown in Appendix A. The gates have been arranged according to rotational bands, with cascade transitions shown first, then cross- over transitions in increasing energy. Samples of both X and Y gates are shown, and are mixed for the sake of displaying important coinci- dences. Figures A-1 and A92 are gates for transitions in the K30 ground band. Only a few of the more important coincidences from meme bers of other bands have been labeled, since the scales are very com- pressed. The transitions from even members of the K=2- octupole band are shown as the gates in Figure Ar3 and it should be noticed that very few transitions from odd spin levels can be seen, and then only very weakly. Next the gates on transitions from odd members of this band 81 are displayed and the most intense feeding to an even level can be measured by the intensity of the 937-keV peak which is the 2-(K=2) + 2+(K90) transition. In Figures Ar5 and Ar6 the interband K=2 +~K=0 gates are shown with the most obvious transitions being to the ground band levels that are fed. Figures Ar7 to A-ll display the gates for the transitions in the Kfl=6- and Kfl=6+ band. Based on the coincidence information and the gamma ray singles experimental data, the level scheme shown in Figure 5-10 was con- structed. All of the transitions except the 1275-keV transition from the 1381-keV level have some coincidence support. The four bands which are shown will each be discussed separately in the next chapter. Several transitions can be placed from the coincidence data as definitely feeding into the ground band. These are the 465-keV and 674-keV gammas which feed into the 10+ member, the 559-keV which feeds the 12+ level, and the 460-keV gamma feeding the yrast band at 14+. Several of these lines have been identified as transitions from the B-band and are placed on the level scheme; the origin of the 465-keV line is unknown. Figure 5-10. Level Scheme of 178W. The transitions labeled with an asterisk are members of close-spaced (<0.5 keV) multiplets. 82 15' 34091 52 7.. ___[__ 568.0 629.8 6’9 13' 1 31417 I 4613' 14' /12’_1m 6M. 2 'I 73.9 ‘5 5, 228.5 «5.5 \f; 351.6 / , 1274.5 Figure 5-10- CHAPTER VI DISCUSSION 0F 17811 EXPERIMENTAL RESULTS 6.1 The K=O Ground Band and B—Vibrational Band The rotational band built on the K=O ground state is identified here up to spin 16+. In the decay of 178Re studied in 1970 by Goudsmit, et. al. [0070] the yrast cascade could be seen up to spin 6+. The same transitions, as well as those associated with levels up to spin 10+ were previously measured in-beam with NaI(T1) detectors using the 181Ta(p,lm) reaction [M165] and up to spin 14+ via 17BHf(a,4n) reaction [La65]. With the available energy resolution, the latter two experiments showed that the ground band level energies followed the simple I(I+l) energy relation within experimental errors. A plot of the ground band level energies from the current experiment is shown in Figure 6-1. For purposes of comparison, the ground bands of 180W, 182W, and l70Yb are also shown. This type of plot, which is used to emphasize deviations from linearity, displays (112/2(0-l on the abscissa versus (hm)2. For a constant moment of inertia, a horizontal straight line would be obtained. A "backbending" type nucleus would display an "S-shaped" curve with the backbending phenomena showing up as a sharp increase of the moment of inertia. None of the nuclei on the graph here would be considered strong backbenders. There may be some sort of trend showing up in the ground bands of deformed W-nuclei, so this plot, and the implications of the degree of non—linearity of the plots of ground band energy levels that is involved will be discussed in detail in the next chapter. 83 84 Figure 6-1. IZOF 0.04 0.06 0.08 0.|0 0.|2 0.02 ”I w )2(MeV2) Plots of-gg versus (hm)2 for the yrast sequences in 2 178,180,182w and 170Yb. 85 In the decay of 178Re [0070], levels at 1083 and 1276 keV were characterized as 2+ and 4+ members of a K=0 band. Levels up to spin (10) in this band were identified in the 181Ta(p,4n) in—beam experi- ments [Ca75] with the bandhead tentatively placed at 1001 keV. A Kfl=0+ band arising from a collective B-vibration is expected to lie below the pairing gap at about 1 MeV. This band has been located at 1150 keV in 17611f [Be71] and at 1196 keV in 178Hf [Ga62]. These bands decay primarily by interband transitions to levels in the ground band with the AI=0 transitions having large E0 components. In the present 177Hf(a,3n) experiments, several gamma rays which feed promptly into the high spin ground band levels have been identi- fied, and it is found that five of them appear to originate from the spin 6 to (14) members of the B-vibrational band. No intraband feeding is seen, and in fact, only the AI-O interband transitions proceed with hz measurable intensity. The rotational parameter,-§3, for the B-band is 14.12 keV, and plots of the level energies versus I(I+1) for the ground- and B-bands are shown in Figure 6-2. 6.2 The K=2- Octupole Band The bandhead of the K=2_ octupole band is located at 1045 keV and was seen, along with the next two members of the band, in the decay of 178Re [6070]. In that work, 2-+2+ (ground band), 3-+4+ (ground band), and the intraband 4-+2- transitions were seen. In-beam, the band is populated up to spin 13, and decays mainly via E2 crossovers. 86 “000 r r I I 1 35001— _J 3000- .1 E 2500~ ‘ >- o 95 2000 a E F— ..1 m > g 1500- .1 GROUND BAND 1000*— .. 5001- l 01 1 l 1 1 l 0 50 100 150 200 250 300 I[I+1] Figure 6-2. Plots of level energy versus I(I+l) for the Kn=0+ ground band and Q-vibrational bands in 178W. Data for the 2 and 4 levels of the B-band taken from 0070 and Ca76. 87 .1 a —1 .1 .1 .J l L L J L 100 150 200 250 300 350 .21? K=2' OCTUPOLE BAND 178w 50 1 1 l l J 18 we 8 6 L1 1 a 91 IZ/[I"I3-13] Figure 6-3. Plot of EI'EI—l/ZI versus 21? for the Kn=2_ octupole vibrational band in 178w. J (0 r4 4h a "i. . 88 This band displays some remarkable characteristics, the most obvious of which is the perturbed structure. By looking at the band on the level diagram (Figure 5-10), it is easily noticed that the energy spacings do not follow a smooth rotational I(I+l) dependence. The feature is more evident on a plot of EI—EI_1/21 vs. 212 (Figure 6-3). The odd spin members are all depressed with respect to the even spin members; the odd spin levels are "favored". The second remarkable feature is the feeding from the members of this K92 band into the ground band. In general, the even spin members decay through intraband transitions to the bandhead. The 4- level has a weak branch to the 4+ ground band member, and the cascade transitions 6-+5-, and 4-+3- can be weakly seen. The odd spin levels, on the other hand, have stronger branches to the K=0 ground band, and feed into Iil members in two cases. The calculations of Neergaard and Vogel [Nee70] can be at least qualitatively applied to describe the features of this band. Quantita- tively, they were successfully used to predict the level energies and B(E3) values for the octupole bands in several rare earth even-even nuclei, one of which was 17611f [Kh73a], which should be similar to 178W. The model predicts the relative locations of K=0-, l-, 2-, 3- octupole states and then mixes these bands through the Coriolis inter- action. Mixing of the KeO- band members only propagates through odd spin members of other bands, since only odd spin members occur for K?0-. This admixture causes the depression of the odd spin levels with respect to the even levels which have mixtures only of K=l. 2, 3 com— ponents. In general, it is the K=0 component which enhances the 89 transitions to the ground band. For 17611f, Khoo [Kh73a] calculated the transition rates for the interband transitions and showed that the transitions with K=0 components were faster than those without, implying that although (AKeO, 1) transitions are both allowed, the El matrix element is larger for the transitions with AK=0 components. Qualitatively, this can be inferred from the deexcitation pattern of the octupole band in 178W, but the mixing calculation was not done since the positions of the lowest Kn=0-, 1-, 3- states are not known, and theoretical calculations are not available for this nucleus. 6.3 The K"=(6+) Band The level at 1665.7 keV which has a half-life of $10 nsec is tentatively assigned as a K=6 bandhead. Deexcitation of this band occurs mainly through the 971- and 1323-keV transitions into the 6+ and 4+ members of the ground band. No transition to the 2+ ground band level was found, nor was a transition to the 8+ member which is diffi- cult to confirm since its energy would be within 1 keV of the 8+ +6+ transition. There is a weak decay branch of 285.5 keV to a level which ‘was seen in the decay study [6069] and which was assigned tentatively in the (p,4n) study [Ca76] as a 4+ level. The l666-keV level was given a K=5 assignment by Canty et.aZ. [Ca76] based on EllMZ multipolarities from conversion coefficients for both the 971- and 1323-keV transitions. .Angular distribution data of Canty [Ca76] indicate negative signs for the A4 coefficients for both transitions which are incompatible with 1AI=1; the conversion electron data for the 97l-keV peak is consistent ‘Jith an Ml/EZ mixture, and, in fact, the fit to an El requires an 90 unprecedented amount of M2 (22%) to be included. The assignment of K96 is supported by all data except the conversion results of the 1323- keV line. Considerations discussed in section 6.4 of the K—assignment for the l740-keV state and the 73-keV El transition which feeds into the K=6 bandhead provide some cross-evidence for the plausibility of a K=6 assignment for the lower band and K=6,7 for the upper band. The rotational structure of the band built on the 6+ level is very regular and can be seen up to spin 13. A plot of the levels in this band is shown in Figure 6-4. The rotational parameter gg-is 12.2 keV which is consistent with the K=6 two-quasiparticle bands in neighboring 17611f [Kh73b]. The decay of levels in this band proceeds via both cascade and crossover transitions. The branching ratios can be used, then, to calculate a value of IgK-gRI, with the sign determined by the sign of 6 for the cascades in the band. The method used here has been successfully applied to several bands in 17611f [Kh73b], where sup- portive charged particle reaction data were available. A thorough consideration of the calculation of gK from branching ratios is con- tained in the reference cited above. In general, for a singlet two- quasiparticle state, in the asympototic limit gK = 0 for neutrons gK = l for protons. ng-gRIZ Q 0 IBK‘SRI 2 Q 0 The quantity is calculated from the expressions [A164]: =[o.87{E(I+I-1>}2/-<§3ec>] as a function of spin for several rare earth nuclei. Data are taken from Hj70 (‘GlEr), Be75 (179W), Li73 (181W), and H670 (179Hf). Inset shows even-even tungsten yrast bands taken from Wa72 (180W) and Je74 (182W). 101 whether the tungsten behavior is attributable to the i13/2 neutrons or if the hg/Z protons are contributing to the perturbation in a signifi- cant manner becomes relevant here, since it has recently been argued [Ne76] that it is the hg/Z protons which are inducing the strong back- bending seen in the osmium isotopes. In the osmium region of interest, the Fermi surface is located near higher—0 i13/2 orbitals than in the tungstens, so the decoupling effect of the Coriolis interaction is expected to be more effective for the tungsten i13/2 neutrons (c.f. equation 2-9). To calculate the amount of decoupling of the i13/2 neutrons in the odd-A nuclei, first, the energy levels associated with i13/2 bands are fit using the procedure described in Chapter 4.2. Since states having Kil are mixed by the Coriolis interaction, the wavefunctions which are determined for each level are constructed of a linear combination in Q of the i13/2 orbitals. These eigenstates, which are written as ZfIIIQ>3 are then transformed according to the weak coupling scheme of Vogel [V070] to the IIRj>’basis. Then, using a procedure described by Bernthal in Be74, the expectation value of the rotational angular momentum is calculated for each spin state using the overlap of the two wavefunctions [V070], j I Q ’= /§' (IQj-sleoM-nqu fQ CjK’ Z 0:1/2 where the C2£ are the Nilsson coefficients, to give [Be74]: <$F>>= E <11Rj|1§2>~2 R(R+l). R.j 102 The values for ’thus calculated are compared with the minimum (decoupled) value possible for i = I—}. A plot of [<§Z>’- <§§ed>1 vs. spin is shown in Figure 7-1 for some rare earth nuclei including 18303 and 177W. In a completely decoupled i13/2 band (the particle angular momentum aligned with the core angular momentum), the quantity on the abscissa should tend to zero. For higher spin values, the aligning (Coriolis) force becomes very strong and the values approach the decoupled value. If the amount of decoupling in the band built on a single i13/2 particle is to be a harbinger of "backbending" then a trend between odd and even-even systems should be evident on this plot. On examination of some of the nuclei represented on this plot, it can be noted that the band in 179Hf, which is not in a region of back— benders, displays the behavior expected of a strongly-coupled system i.e. the total spin reflects only an average increase in the angular momentum of the core. At the other extreme, 161Er shows the most de- coupled positive parity band plotted in Figure 7-1 and is indeed in a region of well-known backbenders. The case of 18303 is not quite as simple. Neighboring 18203 and l8“Os both have anomalous yrast se— quences, and one would expect that the odd neutron in 183Os would be highly decoupled. At very high spins, this seems to be the case, but at lower spins it shows behavior intermediate between strong and weak coupling. At very high spins - 25/2 and greater - the wavefunctions may not be as reliable as they are for lower spin states due to effects which the normal model does not take into explicit account i.e. there may be shape variations, moment of inertia changes, and changes 103 in the single particle spectrum. For this reason, the 18303 case may not be easily explained by the i13/2-neutron decoupling picture shown here. The ordering of the odd tungsten nuclei proceeding toward a greater degree of decoupling is 181W, 177W, 179W; the amount of back— bending in the neighboring even-evens increases in the order 182W, 178W, 180W consistent with the A—l trend. In Figure 7-2, the yrast levels in mass 177-182 tungsten are shown. The trend in compression of the positive parity bands in the odd-A sequence reflects qualita- tively the Arl trend which is also found in the decoupling picture. It is expected that the even nuclei should follow the A-l trend more closely than the A+l behavior since the addition of a nucleon into a partly occupied orbital will induce less change in the position of the Fermi surface than the addition of an odd nucleon into a paired system. Only one exception to the observation that the even-even behavior can be predicted by the decoupling seen in the A-l neighbor has been noted, that of 17oYb. For the tungsten nuclei, then, it appears to be meaningful to discuss the even-even yrast behavior in terms of the {lg/2 neutron decoupling trend. The amount of hg/z proton involvement has not yet been determined. For the case of 18308, an experiment was performed which populated the positive parity band to spin (45/2) [Ne76]. Back— 'bending was detected in this band, clearly indicating the hg/Z proton :involvement. Such an experiment for 179W would be an important test of ‘the proton behavior in 180W. 104 comer.“ 8.8 111.2 m¥~.IIu= wk... [1.2 “an 1I1.Q .mmn111ua_ :93 54.»: 3N2 9 09 oo— 9N 8m 0... omw ..w 7...: [00 «aka loc— MKMN 0N— m=m 11-1.77: 281 a ||.~\m m: ..N\= 3N lo~\m— m; 1||loN\m_ 8w IIIIIoN\N— ...—o IIIIoN\w~ 07°” |0N\~N 2Q IIIoN\MN ”on" .Illlo~\m~ 80" I.~\m~ «EN |.~\m~ SN 1||1o~\~m «NON Illlo~\mm 38“ o Illoo Man 0N Nmm .3 000 I00 0m: Illow ...ww— Illloo— QMNN low" WNGN or— w—rm Iowa «No... ...IlloG— 3mm" a II N m rm ”N“: a! I11.~\m. 3w |..l.~\n_ mm: II..~\2 «nu ||.~\m. :8 1|.1.~\i~ 2: III.~\m~ {Nu 0N\fl~ mum. III.~\k~ «a. ..||.~\m~ 3mm“ a oo 02 low mrm or mam ow NT: 00 www— loo— ntNN low— mnON Io...— morm low— 2&1 O I|0N\K Km 0N\: MO” |0~\m— Nam |||19N\nn n77 |+N\Nn wnw +N\m~ KOO IlloN\—N Na: l+N\MN NmN— l0N\wN 070" I+N\KN N60“ 0N\fl~ rmNN |o~\_m r—tN IlloN\mm Figure 7-2. A plot of the yrast levels in tungsten nuclei mass 177—182. 105 Since the effects of Coriolis decoupling of a high-j particle are expected to be greatest for the low-Q orbitals, the location of the Fermi surface with respect to these orbitals is needed for an accurate determination of the matrix elements, and hence, of the Q-composition of the wavefunctions. The degree of backbending, then, is sensitive to the exact position of the Fermi surface with respect to the i13/2 orbitals [Ha73, Fa74] and in particular its nearness to the low-Q orbitals [St74] both of which depend on the hexadecapole deformation which may be increasing in this region [N169]. Thus, there remain questions on the detailed role of the i13/2 neutrons in the tungsten backbending-type behavior, although the prediction of the 180W yrast anomaly [Be76] is strongly suggested by the general trends observed in the odd-N positive parity bands. 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APPENDICES 111 APPENDIX A Gated Coincidence Spectra of Transitions in 178W The following background subtracted gated spectra were obtained from a coincidence experiment which was performed with two large volume - 82 and 102 - efficient detectors. The X—gates display spec- tra taken with low gain, and are used to show high energy coincidences. The Y-gates display the high-gain spectra, used for better identifica- tion of low energy coincidences. In general, the peaks which are not labeled in a gate belong to another rotational band, and are then labeled in the same gate shown in that band. The peaks which originate in contaminant nuclei, mainly 179W and 17811f, are labeled with a f. The top of each Y-axis is used as a limit, and overflows are not shown. Note that the X-scales are highly compressed so that in some cases statistical fluctuations in the background may appear as peaks. In the expanded gates, the distinction is easily made between peaks and background. 112 5000 1 , , 3 108 keV X-GATE 4000 ~ —~ 33 3000 a — 12 8 U 2000 2 .. :2 0‘ 1 O B N J A 33:31 1 '1 '" °‘ 1; 11 1 f f 237 keV Y-GATE 106 21] 448 352 keV Y-GATE 524 l 1088 237 106 HO! 01—1 NM 352 I l * ‘+‘+8 110V Y-GATE 0 500 Figure A—l. Gated spectra 1000 1500 2000 CHANNEL NUMBER of the first four ground band transitions. COUNTS 113 1500 , 1 I: N 524 keV Y-GATE- 1000 .. .. a; .. 500 :1 3- -‘ 70° 1 1 1 800 I: 579 keV Y-GATE- 500 E _ :2 .. . 2‘100 ‘3 g 5;; .. a a 0300 3 'l 200 g; ”E 4 h 1 1 1 3001- 3 814 keV X-GATE 1 a) m o EE:ZOO+. ' g ‘d :1 f. .‘1‘ CD m .n L) 1.01 g _ 200 1 l I l 830 116V X-GATE "3 1x 3‘. 5100 2 m .7 ... 3 o N .7 3 i .~ l l l 0 500 1000 1500 2000 CHANNEL NUMBER Figure Ar2. Gates on the high energy ground band transitions. 114 T r 182 keV X-GATE 106 1111111114 E m N? o T r 300 2 g a : 28‘+ keV Y-GATE‘ m P CI 52001- ~ g .1 100+ .1 800 1~ .1 I ‘ r F 250 33 380 keV X-GATE -1 00 200 N g ._ s 2 2 -" :3 150 i i 2 w m 8 100 " "‘ :2 g a. _ so °° 30° N 1 1 1 1 250 :1 L187 keV X-GATEd a) 200 .1 —1 5 8 .2 3 150 g g" A 8 100 ~ g - 50 3 :3 A 250 ‘1 1 1 200 . 5‘18 keV X-GATEJ $150 3 3 .. 1 8 10° 3 ”E 3 — so ._ _ l 1 0 500 1000 1500 2000 CHANNEL NUMBER Figure A-3. Gated spectra of crossover transitions from even-spin members of the K“=2"octupole band. 115 5° 1 F 1 1 “0 i 225 keV X-GATE: m —1 .... 2 .. :1 o a o h d m d 1 1 312 keV Y-GATE ‘ 9001- g .. 4 co '- H 3 ~ ‘ 52:3001- + 3 3 '- 3 m .. T T 388 keV X-GATE-« d 232 300 250 312 352 440 -4 .1 fi 961 l I 1 505 110V X-GATE 1001- _ co .— 2 N o a tab 2 00 i 8 :2 _ _ 1 1 l , 0 500 1000 1500 2000 CHANNEL NUMBER Figure A-4. Gated spectra of crossover transitions from odd-spin members of the K“=2‘ octupole band. 116 T 777 keV Y-GATE~ T 883 keV 1745111151 I T 938 keV X-GATEJ 226 284 ll .1 11 scone , 1 + 2501.. 1002 keV Y-GATE_ 1 l 11 l 0 500 1000 1500 zooc CHANNEL NUMBER Figure A-S. Gates on some interband transitions between the K"=2’ octupole band and the K“=O+ ground band. 117 2J7 T' 1 SH keV Y-GATE fl 350 g N 300 m A .— _ T r 7 I I 851 keV Y-GATE - 237 106 352 448 -p— 901 keV Y-GATE _ l r I 962 keV Y-GATE__ ‘0 200 ... E i *2 f g . :3 a CD m m _ U i l 1 l 0 $00 1000 1500 2000 CHANNEL NUMBER Figure A—6. Gates on the interband transitions from the higher energy levels of the octupole band to ground band levels. 118 1000 1 l l l E 73 110V X-GATE 750 - U) E 3 500 _ o .. S L) m m 250 " ...: _ 500 1000 100““ I“ ’M 0 T 300 I: 2 872 keV X"’GATE_1 . 232001- _ E .. o h .1 u " 0'1 100 2:: 5.: ME mom to — 90 11 ,3; E 1329 keV Y-GATE] 30 E : a U) E '4 3 0‘ ca 8200 ° 2 4 8° g z: :5; 1 1 , 500 1000 Figure A-7. CHANNEL NUMBER Gates on the interband transitions from the K"=6+ to ground band, and on the transition between the K"= (6,7) and K"-=6+ bands. 119 800 , j r 700 a ._ 800 171 keV Y GATE 1‘9 500 5 900 ”I 8 300 5:: 200 700 r 1 800 106 189 285 352 392 I121 446 65 72 4011] 111 1111111 r 188 keV Y-GATE 171 E 400 :3 8 300 200 1064. 204 05‘" 237 1 l1 l1 l1 l1uL1 900 r , 350 m 300 :1. r- 250 .. 5 200 .. .. _ 8 ~° m 150 100 1:. . T . - '1 350 217 keV X GATE q 33 300 . 3: .. gzso .. _ 8 200 _ 150 _. 100 .. 500 Jr 1 50 _ 11,, 229 keV Y-GATE _ e 350 .. 300 -. 3 250 23 8 200 150 100 l l l, 0 500 1000 1500 2000 CHANNEL NUMBER I 201‘ keV Y-GATE‘ 237 .J 105 150 1 l 392 171 106 2 106 13] it 352 q— 1 l l 284 Figure A-8. Gated spectra of cascade transitions in the Kfl=6+ band. 120 900 r r r 500 E 358 keV Y-GATE— 9‘00 E N 4 H h r T 300»- : ~ N 392 keV X-GATE1 93 r «“3» ‘ £3 ’ \ 3:: m g 4 T 4T I 300 E L+21 keV Y-GATE H 5 TV 4T ’r 300 q we keV Y-GATE- U) N ‘ *2- : ... 2200 "‘ E ”N q 53 3 n 100 300 : } IL r 2 L+87 keV X-GATE . ¢ug200 _ h' C 2 s ., —- ~ - 8 100 g a"; :d 0 500 1000 1500 2000 CHANNEL NUMBER Figure Ar9. Gated spectra of crossover transitions in the Kfl=6+ band. 121 we I I T 88 keV X-GATE 300 .. fl :5 4 500 ~ ~ ' r - .. 3 137 keV Y-GATE - two 2 - 3 H N, - E300 :3 + :2: - 53:20” 3 2 -# 100 800 h n I I I 500 a: 3 188 keV Y-GATE a 93W " .3" a 1 330° .. 3 z z; ... j 20° Q N M 3 2 E w a hr r T 300 3 21 13“} keV Y-GATE -+ 137 l l I r 219 keV x-GATEj .1 J 1 J 1 1 _ O 500 1000 1500 2000 CHANNEL NUMBER Figure A910. Gates on the cascade transitions in the K"=(6,7)- band. 122 30°F T I j L+57 keV Y-GATE+ 237 30% r . r L+98 keV Y-GATE _ 237 I 533 keV Y-GATE . 237 J 73 106 137 972 L I r 589 keV Y-GATE - a: c: :3 :TT 1?- COUNTS “0 c: c: fir 106 237 I l 1 4L 1 0 500 1000 1500 2000 CHANNEL NUMBER Figure A—ll. Gates on the crossover transitions in the K"=(6,7)- band. 123 APPENDIX B Angular Distribution Plots of 178W Transitions The angular distribution data shown here have been transposed to the 0—90° quadrant for plotting purposes. The data are fitted to the equation: W(9) = Z (cose) K=0,2,4 AKPK using the program GADFIT (written by R. A. Warner). The values of A2/Ao and Au/Ao obtained from these fits are listed in Table 5-1. INTENSITY 1m ENSITY 124 1.5. 13 .. H“ Eh!» f5 283 keV 386 keV 1.5. 1.9 . 3'3 {'3 fl 0 fl I E3 ~9- 224 keV 380 keV Figure B-l. ANGLE ANGLE o°Jeo‘wuésé'eo‘vd'eo‘sémo‘zo‘aJ'qd'séei'n“90396- Angular distributions of some crossover transitions in the K=2 octupole band. INTENSITY 125 306 keV 533 keV 226 keV 363 keV 7 53.5 0'1; 'ei'aozwd‘sd'ed'fieo‘so'o'm“25'303w6’so'6037o3803so" ANGLE ANGLE Figure B-2. Angular distributions of some crossover transitions in the K=2 octupole band. 126 143‘ 778 keV 1002 keV 1.3. 651 keV 883 keV fa: INTENSITY 3" d .8 '71 ' o'nol'zi'ao‘qd‘sé'efio“eo‘so‘o‘m‘éao‘fiso‘ed‘fieo‘so“ Am ANGLE Figure B—3. Angular distributions of some interband transitions between the K:2 octupole band and the ground band. 127 U . 137 keV 194 keV INTENSITY 3” 1.1. 171 keV 168 keV .BJ INTENSITY .‘l. .3- .2. .1. A J_ A ,o . . . . . 4 . r . . . . l . 0'10'20'30'H0‘50'60‘70'80'80'0 O’ZO’SO'QO'SO’SO’N'OO'SO' Am ANGLE. Figure B-é. Angular distributions of cascade transitions in the K"=(6,7)' band. 128 l J l I INTENSITY thbpgtfi l 291 keV INTENSITY s» .8 '6 901 keV 73 keV 44+}4’”+ 465 keV o-m32éao‘w6'sd'eo‘7éeo39o3o-m"zo‘ad'qd'sfi'eo3ro‘eo396' mu: 1mm Figure B-S. Angular distributions of various interband transitions and of the unassigned 291-keV transition. 129 APPENDIX C Gated Coincidence Spectra of Transitions in 177w The background subtracted gated coincidence spectra in this section were obtained in one of two coincidence experiments, the first performed with two large volume - 7 and 10% - efficient detectors, the second performed with the planar LEPS and the 8% detector. Gates labeled X' and Y' display the LEPS and 8% gated spectra respectively. Peaks which have a f above them are associated with contaminants. X- rays are not labeled nor are peaks which belong to another rotational band. The top of each Y-scale is used as a cutoff, with overflows not shown. COUNTS COUNTS 130 20' 81L I 79 keV X'-GATEn 7 2 262 98 220 l 197 keV X"GATE n 301 1 301 keV X-GATE - 198 393 I 382 keV X'-GATE - 198 301 .067 ll r L+67 keV Y'-GATE_ .... O M N 05 M C-1. 1 1 500 1000 1500 CHANNEL NUMBER Gated spectra of transitions in the 1/2-[521] band. 131 25 I F r n :3 + .. 95 keV X'-GATE c0200 1'3 o - .— .. r: :2: Z 00 l‘ U5 H N 3 ' :3 a .. 8 150 ~ .. ~ ..5 4.11111. 'MM \ 1.111111..1I.N1...1n l.‘11.-1 . «1.1.; 1T. 316 0'0 O 3' Q 4’ 593 208 keV X-GATE- .4 q q I I 316 keV X-GATE 209 J I I l+03 keV X-GATE 316 I085 5163 as 4. 1 1 1 3 489 keV Y-GATE 200 ~ - m 2 '2 :1 150 8 100 1 1 j_1 L o 250 $00 750 1000 Figure C—2. CHANNEL NUMBER Gated spectra of transitions in the 1/2-[521] band. 132 III 29E sec :92 -—— ozz __ ttz _' 991 IS! an! 5" — net 99 W8888 V) 3- 3' a) a: n; 01 —e SiNflOO Figure C—3. Gate se the 7/2 i 8 ‘O I I I CI. UJ '— 4: (D l . >< :> (D J T m E} O o D 10 0h?» 829’ 6501 ssn —~—~ sue 50‘! O 8 ° ° 8 ° 8 .. m g 13 .. SlNHOO on the 84-keV El interband transition from [633] to the 5/2‘[512]. 2000 :3 oz 0 U>.J "U1 :5 Z: ‘< J: t) O O O 1.4 133 2 : I I O J .— 150 2 63 keV X GATE _ m m E 7’ IN o N 3 1 .. 3 3 3 5 :2: ‘ 8 . m :2 5 -* 1 125 I I 3 i 1: 88 keV X'-GATE a) 200 2 . 3 ‘ [— o-o'so-c N N z .... ‘° : .. " :3 S: "’ 8 150 ‘° " "’ if} .. - q 350 3‘” 5 13% keV Y'-GATE- «3300 _ SE :oH 3250 m 2 3.3.2 — 8200 t 3 .. : N 1 150 " § "’ 3’ - ‘10 3 350 .3 3 127 keV Y'-GATE- 0:300 _ E :31250 g - 8200 3: 3. z: -1 150 33 13 2 3 ‘ 350 300 3° 211 keV Y'-GATE_J 33250 T § 5: n g 8200 _,_ _ 150 . "H z 3 ~ o 500 1000 1500 CHANNEL NUMBER Figure C-4. Gates on the cascade transitions in the 7/2+[633] band. 134 25' I I I I F 151 keV X'-GATE q (s: 0‘ HH MN m NN m 8‘. 262 I155 r I I I I 29"} he Y'-GATE 3 Q q 362 127 210 3‘10 (134 keV X-GATEL 362 O .1 a): mm m \ 1 ! é 1m-‘.1..HIL.J In 11.11.11! . 1'... II» ... J (127 keV X-GATEL 210 13‘. 362 609 (211 keV x-GATEL 25 :1. 2 a) H N .- g zoo - 8 w m N 150 ... S .J 0 250 500 750 1000 1250 CHANNEL NUMBER Figure C-S. Gates set on the cascade transitions in the 7/2+[633] band. 135 200 I I I 198 keV Y'-GATE 810 220 keV Y'-GATE- 127 1'“; C5 [N 1n 0" 339 I155 “LlJ'llI‘ . . 3 282 keV Y'-GATE_ ~55 sun I r 339 keV Y'-GATE‘ nus I Mitt-.1“ . . " 382 keV Y'-GATE‘ “55 5'90 .JJh“--1J“‘I1 I 500 1000 1500 CHANNEL NUMBER Figure C-6. Gates on the crossover transitions in the 7/2+[633] band. 136 I r I o z: 4 3° ; 362 keV Y'—GATE (03250 m m I; ‘- 5 ‘° 7" 3 gm ‘7: E z E 3 ‘ 150 “‘ .. 34 150 .. , ° ”(‘15 keV Y -GATE 33100 3 -+ § g: .. .. 3 so ' 2 :2 3; q 250 _. r r T 3° L1‘55 keV Y'-GATE 0:200 .. .... ‘ g 7° 2:: 8150 :3 ‘° g _ 200 :3 538 keV Y'-GATE U) y. 25 ‘— 3 8 . g 530 keV Y'-GATE zoo .. U) .— m z {D :l ; h: 0 .4 L) g m " I son 1000 1500 CHANNEL NUMBER Figure C—7. Gates on some crossover transitions in the 7/2+[633] band. 137 450 I «on g [220 keV X-GATEJ. 33350 3 m .. 5 "‘ :5: 8 300 :r :3 _ 250 ‘ ‘ aoo ..mMLJHL..n. “huh"; 2 E V - 250 N [26% k9 x GATE; 0) m l- : 3 g 2”” :2 c, -1 8 g a: 2 150 .p - 1 Lin “I‘J'IL‘-‘JLJI.P.H.!. 2°” _., [339 keV X-GAT c0150 ‘3 *3 . h- 3 g 100 8 50 300 I A J 250 o [362 keV X-BATE] U) N 3 l— N 3 8 t m E 150 ; J _ l . , I 250 H MMIJLLMLL‘LHJJ‘LLLIJuf .‘..l..llu .Ih ....JIL H55 keV X-GATE] a) 200 .4 h 0 2 :7, 3 a. U 150 3 _ O 500 1000 CHANNEL NUMBER Figure C-8. Gated spectra of crossover transitions in the 7/2+[633] band displaying high energy coincidences. 138 300 r I 2 , E 1% keV X'-GATE_ E! g E I: _ g; m 2 g + .Lll-“ And” “KI-uni]. .‘ ..l o a .. , L. . . .n . 250T =1 188 keV Y -GATE_ (0 o 52001— : "1 53 L_ E : 217 keV Y'-GATE zoo _ E! z :2 H :3 N E3 3 _ 2%2 keV Y'-GATE ur05 keV Y’-GATE 150+— _ luu COUNTS 810 13k soo ‘ 1ooo CHANNEL NUMBER Figure C-9. Gates on transitions associated with the possible three quasiparticle band. [39 Q I 117 keV X'-GATE 139 160 180 299 I COUNTS ..u»lt.lH th‘LJI'JII-JL.'H ..u L L . J 1. 139 keV Y'-GA TE 5 .... H - 160 101 Alumni; may ~. g 180 keV Y'-GATE" 250 g h { E, .4 Ho! L1H. ”U! I... ’ n 180 keV Y'-GATE z: 3 s; q r: 3 3 1’3 m d 21"} keV Y'-GATE 1‘ , I l-‘ 10”] ‘ ., ,f ‘ . 1' 7 . I 500 1000 CHANNEL NUMBER Figure C-lO. Gates on cascade transitions in the 7/2-[514] band. 140 210 l I 256 keV X°-GATE E3 0 3% ' 2 i H ‘ 8 "‘ 3 fl 35.1...1. - 28 keV X-GATE 377 117 180 ._ ....|.M filth.‘lnfl|lln. keV Y'-GATE.q to i a. F’ e~32 § 3 : " 8 15'1“ m" o 3 n 25. Ill-“1k."ll‘WILI l .. '- . ' . ., ‘ T m h 2 377 keV Y-GATE (1)2” : E + 1 ‘i :3 E; r “moo. “Hit.“UQLhmlm.Lam...“LL“. .. Ur11 keV Y'-GATE_ 117 139 COUNTS H O H to In N 299 3“!) ..ll‘libhc I IL - 1.. l . 1000 500 .. CHANNEL NUMBER Figure C-ll. Gates on some crossover transitions in the 7/2-[514] band. 141 m U5 N 377 I ”HI keV X-GATE 300 .. COUNTS I 471 keV Y'-GATE I" F‘ 0‘ .1 .4 m :2 ” § O d 1' 1' 377 I L*97 keV X-BATE ‘ uul I (”:72 keV X-GATE] N on O5 M u-o “ll L I 101 keV X'-GATE L I 130 160 139 0'0 m - M |\ .nJINLlnl ILLLIILIMIII I!” Lil .‘LIL ... ..; h. . . 0 500 1000 CHANNEL NLNBER Figure C-12. Gates on some crossover transitions in the 7/2'[514] band, and a gate on the 101-keV cascade transition in the 5/2'[512] band. 142 APPENDIX D Angular Distribution Plots of 177w Transitions The curves shown here represent fits of the data to the equation: w(e) = X P (c056) K=O,2,4 AK K using the program GADFIT (written by R. A. Warner for the MSU 2-7 comr puter). The data were taken in the 90-l80° quadrant. The values of A2/A0 and Au/Ao which were extracted from these fits are given in Table 3-1. 143 1.5. 209 keV 408 keV l.'+ . 1.3 . 1.2 . INTENSITY 1.1 . 1.0 .. 1.5. 79 keV 392 keV 1.9 .. 1.3 4 102 d INTENSITY 1.1 4 WW ..9 0'10 “20’ 30° 40' 50°60‘70' 80‘ so°o‘ 1o °20°30’wo'so°so°7o°so°so° ANGLE ANGLE Figure D-l. Some angular distributions of the transitions in the l/2'[521] band. The 79-keV transition is Ml/EZ, the others are E2. INTENSITY INTENSITY 144 1.1 . 1.0 . .s . .s . .7 . £5. .‘1 .4 .3 . .2 .. .1 . .0 127 keV 211 keV 1.1 . 1.0 . .3 1 J34 .7 . .8 . .5 .. .‘1’ T .3 4 .2 .. ‘1‘ 86 keV 134 keV .0 o‘ 10 ° 20' 30' so“ 50' 60° 70’ so“ so‘o‘ 10 ° 20‘ 30‘ 40’ 50' Go' 70' 80°90“ ANGLE ANGLE Figure D-2. Angular distributions of some cascade transitions in the 7/2+[633] band. INTENSITY INTENSITY 145 1.5 . 1.9 4 1.3 . 1.2 .. 1.1 '1 1.0 . .9 338 keV 454 keV 1.5 . 1.4 .. 1.3 . 1.2 d 1.1 d 1.0 .. 220 keV 362 keV Figure D-3. .9 ......L.. 21....... 0'10'20"30"'1’0'50"80°70'BO'SO‘O'lO"20'30"'+0"50°80'70'80.800 ANGLE ANGLE Angular distributions of the 7/2+[633] crossover transitions. INTENSITY INTENSITY 146 1.1. 1.0. .s. .8. .7. .G. .4. .3. .2. .1. .0 139 keV 214 keV L1 L0. .8. .7. .8. .5. .4. .3- .2. J. .0 116 keV 179 keV Figure D-4. o’ 10 ' 20' 30' Lto"'5o'Go"7o“ so“ so 0 ‘ 20' 30’ so“ 50360" 70" so" 90" ANGLE ANGLE Mixed multipolarity angular distributions of cascade transitions in the 7/2-[514] band. INTENSITY INTENSITY 147 1.1. .8. .8. .8q .5 . .‘1 . .3 . .2 . .1 . 188 keV 1.1. 1.1. 1.0. .8. .8. .7. .8. i=7 5" INTENSITY .. C (D 4 .1. 144 keV 84 keV ,0 . .. . . - . 4. . . . . J, . J . . .1 L O'lO'ZO'm'HO'SO'SO'flYBO'SO' o‘m'ao’ao'wo'so'so‘n’so’so‘ ANGLE ANGLE Figure D-S. Angular distributions of the interband 84-keV and l44-keV transitions, and of the l44-keV cascade member of the possible three quasiparticle band. 148 APPENDIX E Level Scheme of 18303 Levels in 13303 were populated in both the 185Re(p,3n) and 182W(a,3n) reactions. The usual techniques of in-beam gamma-ray spectroscopy - gamma-ray singles, angular distributions, excitation functions,gamma-time coincidence, and gamma-gamma-time coincidence - were employed to deduce the level scheme shown in Figure E—l. Transitions marked with an asterisk are components of closely spaced (