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Spectroscopy of 75Se studied with the 72Ge(α, nγ) reaction
~
NuclearPhysics A261 (1976) 93 -- 110; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
SPECTROSCOPY
O F 7SSe
S T U D I E D W I T H T H E 72Ge(~, n?) R E A C T I O N N. E. SANDERSONt and R. G. SUMMERS-GILL
McMaster University, Hamilton, Ontario, Canada Received 22 September 1975 (Revised 22 December 1975)
n)TSSe and a level scheme built up from the observed ~,-ray spectra. Gamma-ray angular distribution measurements have been analysed to yield spin assignments, mixing ratios and branching ratios. Comparison of the positive parity spectrum with the levels predicted by a Coriolis coupling calculation shows good agreement. In particular the model can successfully predict the occurrence of "anomalous" states with j~r = ~+ and 5 + which lie close to the ~+ state in this nucleus, and which are a general feature of many neighbouring nuclei. Calculated E2 and M 1 transition rates among these levels agree with available experimental data to within a factor of two. A strong case can therefore be made for regarding the low-lying levels in 7SSe as arising from an odd neutron coupled to a deformed prolate core.
Abstract: States in 75Se have been excited by the reaction 72Ge(u,
E
NUCLEAR REACTIONS 72Ge(tz,nT), E = 8.1, 10.0, 13.0 MeV; measured tr(E~,, 0), y),-coin. 75Se deduced levels, J, zt. Enriched target.
I
I
1. Introduction
I n a recent p a p e r 1) it was s h o w n t h a t a Coriolis c o u p l i n g m o d e l i n c o r p o r a t i n g a p a i r i n g residual i n t e r a c t i o n was c a p a b l e o f a c c o u n t i n g for the occurrence a n d overall b e h a v i o u r o f the ' a n o m a l o u s ' low-lying states w i t h d~ = ~+ a n d {+ w h i c h a p p e a r in the s p e c t r a o f m a n y lg~ nuclei. I n p a r t i c u l a r the p a p e r r e p o r t e d the results o f a 76Se(d ' t)75 Se transfer r e a c t i o n a n d showed t h a t the energies o f the f o u r lowest-lying positive p a r i t y states in 75Se [2~+, ( { + ) , ~+ a n d ½+ at 0, 112, 133, a n d 611 k e V respectively] c o u l d be r e m a r k a b l y well fitted b y this model. Theoretical spectroscopic factors were also in r e a s o n a b l e a g r e e m e n t with experiment. I t has been k n o w n f o r s o m e time t h a t a s t r a i g h t f o r w a r d q u a s i p a r t i c l e - p h o n o n c o u p l i n g m o d e l 2) c a n n o t a c c o u n t for such states, b u t m o r e recent calculations w h i c h include effects due t o static q u a d r u p o l e m o m e n t s a n d g r o u n d - s t a t e c o r r e l a t i o n s 3), a d d i t i o n a l p a r t i c l e - p l l o n o n interactions 4) o r t h r e e - q u a s i p a r t i c l e c o r r e l a t i o n s s) have h a d m o r e success. One feature o f all the m o d e l s m e n t i o n e d a b o v e is the p r e d i c t i o n o f a n u m b e r o f o t h e r positive p a r i t y states at a n e x c i t a t i o n o f 0.5-1.0 MeV, i n c l u d i n g h i g h e r spin levels with J~ = x2-A-~ + and ~+. Inevitably, further testing o f these m o d e l s is h a n d i c a p p e d by a l a c k o f e x p e r i m e n t a l i n f o r m a t i o n , b o t h o n a d d i t i o n a l p o s i t i v e p a r i t y levels and on the negative p a r i t y levels t Present Address: Physics Department, University of Birmingham, Birmingham, B15 2TT, England. 93
94
N.E. SANDERSON AND R. G. SUMMERS-GILL
arising from the 2p~, lf~ and 2p,~ single-particle orbits. For the case of 75Se, earlier r-decay 6) and (p, n) reaction 7) studies had been undertaken resulting in quite detailed level schemes but only two additional spin assignments to levels at 286.5 keV (~-) and 427.7 keV (~-). Such reactions would not of course populate the expected levels with J > ~, and indeed these have yet to be unambiguously identified in any oddneutron lg~ nucleus. This paper continues the investigation of the level structure of 758e by presenting results obtained using the 72Ge(ct, ny)75Se reaction. Two features of this reaction are pal ticularly attractive in this case. For energies reasonably close to threshold the high degree of alignment in the residual nucleus can be calculated, and angular distribution measurements of the de-excitation y-rays can lead to both spin assignments and y-ray mixing ratios. In addition, as the beam energy is increased, sumcient angular momentum can be brought into the system to populate higher spin states. In this way levels up to 1.5 MeV of excitation have been observed and the spins of many of these determined together with y-ray mixing and branching ratios. These results are compared with model predictions. Soon after a preliminary account of this experiment was given s), more experimental work on 7SSe was reported by two other groups in conference contributions. These groups have subsequently published their results. Agarwal et al. 9) using the 75As(p, ne-y) reaction give spin assignments and y-ray branching and mixing ratios for most levels below 748 keV. There is excellent agreement between their results and those presented in this paper. Protop et al. 10) have studied the 72Ge(a, ny) 75So and 7aGe(a, 2ny)TSSe reactions carried out at much higher beam energies than used in this work. Levels up to 3 MeV were observed including some which are suggested to show rotational band structure. Most recently another 75As(p, ne-y)TSSe study has been described in a paper by Sugimitsu ~~) in which levels up to 1.7 MeV were observed, but very few definite spin assignments made. A fuller discussion of these results will be given in later sections.
2. Experimental methods 2.1 TARGET PREPARATION The target consisted of a layer of 72Ge (isotopic purity 96.4 ~o) deposited by vacuum evaporation onto a pure gold backing. A target thickness of about 1 mg" cm-2 was obtained, which corresponds to a beam energy loss of 280 keV for 10 MeV a-particles. Gold of thickness 0.025 mm ensured that the beam was fully stopped in the backing, while at the same time minimising effects due to absorption of y-rays emerging from the back of the target. Coulomb excitation in gold. gives rise to a number of impurity lines in the y-ray spectrum, but these are well known 12) and readily identified. 2.2. ANGULARDISTRIBUTIONS For these measurements, the target was mounted at 45 ° to the beam axis in the
75Se
95
centre of a thin-walled (0.5 mm), cylindrically symmetric, aluminium chamber. A system of two 1.5 mm diameter gold apertures produced a well defined beam spot on the target. The y-ray spectra were recorded at six different angles between 0 ° and 90 ° using a 42 cm a Ge(Li) detector (resolution 2.5 keV F W H M at 1.3 MeV) set at a distance o f 8.5 cm from the target centre. The reaction yield was monitored with a 12 cm 3 Ge(Li) kept at a fixed angle. " D e a d " time corrections were monitored by counting the digitised output of the target current integrator simultaneously into three scalers; two of these were gated by the two ADC " b u s y " signals. These corrections were below 10 ~ at all times. The isotropy of the system was checked after the experiment by measuring the angular distribution of tb_e ~-rays following the r-decay of 75Se (T~ -- 120 d) which builds up during the bombardment. This activity produces strong y-rays of 121.1, 135.9, 264.6 and 279 keV [ref. 13)]. and these were found to be isotropic to within their statistical errors ( ~ 4 ~o). Peak areas were extracted from tbe spectra by fitting a straight line background to regions on either side of the peak and integrating the number of counts above it. Energies were extracted from the peak centroids, the spectrum having been first calibrated using the many accurately know y-rays from sources of 182Ta [ref. 14)] and 152gEu [ref. 15)]. These two sources were also used to determine the efficiency of the counter. 2.3. G A M M A - G A M M A C O I N C I D E N C E S
F o r these measurements the target was mounted in a small (2 cm diameter) chamber. Coincidences were recorded with the 42 cm a Ge(Li) and a 50 cm 3 Ge(Li) (resolution 2.9 keV F W H M at 1.3 MeV) both placed close to the target with 1 cm of lead shielding between them to prevent y-rays scattering from one counter to another. A system time resolution of 15 ns F W H M was achieved using constant fraction timing for the 50 cm a and extrapolated zero timing for the 42 cm a counters respectively. The true to random ratio was about 50 : 1. Each event consisting of a TAC output and two y-ray energy pulses was processed in a P D P 15 computer and stored on magnetic tape. Off-line analysis consisted of setting windows on the time peak and on those yrays of interest in one of the spectra. Background and random coincidences were subtracted by setting further windows below and above the y-ray peaks and also on the random part of the TAC spectrum.
3. Experimental results 3.1. G A M M A - R A Y S P E C T R A
Examples of the singles y-ray spectra obtained at beam energies of 8.1 and 10.0 MeV are shown in fig. 1. These energies correspond to 1.5 and 3.4 MeV above the reaction threshold. The yield at the lower bombarding energy is much reduced by the effect of the Coulomb barrio1, while at the higher energy the spectrum of y-rays is complex. The more prominent y-rays associated with 75Se have been marked with
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Fig. 2. Gamma-gamma coincidence spectra from the 7ZGe(~,nT)75Se reaction at a bombarding energy of 13.0 MeV. Peaks labelled (B) are due to background. their energies. Other ?-rays present in the spectrum include Coulomb excitation lines from the target and the gold backing, as well as ?-rays in 7Sms following the fl+ decay of 75Se. Examples of the sorted coincidence spectra, which were recorded at an energy of 13.0 Me¥, are shown in fig. 2. In the spectrum gated by the 132.8 keV 7-ray two background lines (labelled B) can be seen. These are present because the window overlaps with a 135.9 keV ?-ray (75As) and the tail of the intense 141.2 keV v-ray (?SSe). A complete list of ),-rays assigned to 7SSe is given in table 1, together with their coincidence relationships. Identification has been made on a combination o f the ),-), results, and previously reported ?-rays 6) and energy levels 1, 6). The energies for those ?-rays which are weak or unresolved in the singles spectra have been taken from the coincidence data, while the energies o f the 112.1, 132.8, 141.2 and 286.5 keV ),-rays have also been measured using a 1 cm a Ge(Li) detector (resolution = 0.6 keV F W H M at 122 keV). With the exception of a strong 596.3 keV y-ray observed at 8.1 MeV whose origin is not known, only a few weak ),-rays in the singles spectra remain unidentified.
N. E. S A N D E R S O N
98
A N D R. G. S U M M E R S - G I L L
TABLE 1 G a m m a rays associated with 75Se ),-ray (keV) 112.14-0.1 132.8- -0.1 141.2--0.1 191.3- -0.3 211.2--0.3 236.2- -0.3 286.5--0.1 293.0- -0.2 299.6- 0.3 315.8--0.2 319.8- -0.2 326.3- -0.3 330.9- -0.2 349.5 - -0.2 377.4- -0.2 404.2- -0.3 408.8- -0.3 428.0 -0.2 431.6- -0.2 461.2- -0.2 484.4- -0.3 487.5 - -0.3 490.6- -0.2 516.3z-0.2 573.04-0.2 596.1 + 0 . 3 608.44-0.4 611 ± 1 619.4±0.2 628.1 4-0.2 635.24-0.3 650.8±0.2 657.04-0.4 676.2±0.3 678 4-1 681 4-1 683.7- -0.3 701.8- -0.2 724.4- -0.4 734.0- -0.2 739.9- -0.3 754.1 -0.3 760.5- -0.4 767.8- -0.3 788.7- -0.4 801.3- -0.2 826.5- -0.3 841.3- -0.3
Coincidence gate 112.1
132.8
286.5
141.2
293.0
516.3
377.4
319.8
349.5
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7SSe
99
TASLE 1 (continued) y -ray (keV)
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293.0
516.3
377.4
319.8
349.5
650.8
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3.2. ENERGY LEVELS IN 7SSe Fig. 3 shows the proposed level scheme for 75Se and for comparison those levels reported in the (d, t) study 1). For convenience the level scheme has been separated into two parts. On the right are shown those levels which ~-decay predominantly to one or mole of the first three states (J~ = ~+, 5 + and $+). With one exception, these levels are not observed to be populated by fl-decay from the ground state (J~ = g2- or ~2-) of 75Br [ref. 6)]. It would appear then that most of these levels have high spin and/or positive parity. The existence of a 20.7 keV transition connecting the levels at 132.8 and 112.1 keV can be inferred from the fact that 7-rays of 628.1,801.3 and 954.0 keV are seen in coincidence with both 132.8 and 112.1 keV y-rays. Such a crossover transition connecting the two states has now been directly observed by Agarwal et al. 9). Because of this transition, pairs of ?-rays differing by about 20.7 keV have been assigned to the decay of levels at 789.9, 813.6 and 1086.9 keV. The existence of ground-state decays from levels at 628.4 and 953.4 keV cannot be conclusively established because they overlap in energy with ~-rays of 628.1 and 954.0 keV which feed the 132.8 keV (-~+) level. However their presence in the singles spectrum taken at 8.1 MeV argues for their inclusion. The 747 keV level observed in the (d, t) study 1) was one of two levels whose differential cross sections could only be fitted by mixed lvalues of different parities. The decay mode of the 747.7 keV level appears to be well established 6, 9), but a 635.2 keV y-ray observed in this experiment has not been reported by other workers. Consequently we suggest the possibility that this ~-ray represents the decay of a new level at 747.3 keV to the 112.1 k e y level. Many of the levels shown on the left of fig. 3 are populated by the fl-decay of 7 SBr and comparison with the (d, t) spectrum shows that they have negative parity. The presence of a level at 293.2 keV with a lifetime of 30 ns has been recently established by Agarwal et al. 9). A list of the energy levels and spin assignments (to be discussed later) in 75Se is given in table 2. Also given is a summary of the energy levels reported in a wide range of other studies. The levels proposed by Coban et al. 6) and by Sugimitsu 11) have been corrected for the presence of the 286.5-293.2 keV doublet which was not known
100
N.E. SANDERSON AND R. G. SUMMERS-GILL
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TABL~ 2 Energy levels in 75Se (in keV) (p, n) a)
fl-decay b)
(13, n~) c. d)
(~, xn~') c)
0 115
0 112.1
286
286.5
425 584 610 627 660
427.7 586.0
0 112 132 287 293 428 586
663.8
0 112.1 133.0 286.7 293.2 428.1 586.1 611.0 628.2 664.1
745
747.4
748.0
779
777.0
777.3 789.6
749 761 778
629 664
(d, t) 0 112 133 287 427 586 611 629 664 747* 777
814 832 852 890
859.4 895.4
840.1 859.3 895.9
859 895 934
958 996 1010 1044 1072
1020.4 1073.7
962.6 1003.9 1020.6 1047.4 1073.8
1048
963 1004 1021 1048 1074
1080 1087 1143
1144.5
1144.7 1162
1190
1250 1302 1378
1184.3
1184.7
1198.5 1245.5
1198.9 1245.3 1301.9 1375.8
1374.8 1380.5
1407 1441
0 112.1 132.8 286.5 293.0 427.9 586.1 611 628.4 664.0 (747.3) 747.7 760.9 777.2 789.9 813.6 839.6 859.5 894.9 934.1 953.4 962.3 1020.5 1047.2 1073.7 1078.7 1086.9 1144.9 1162.0 1181.9 1182.7 1199.0
1246
1490
1556 1561.0
1561.1 1588.2 1630 1666.6
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3½-, 3 ~+ ~3 +, 3 + ½-, ~ ~-, 9-
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1490.6 1550.2
1650 1668 1733
This work
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N. E. SANDERSON A N D R. G. SUMMERS-GILL
102
TABLE 2 (continued) (p, n) a)
fl-decay b)
(p, ny) c. a)
1764
(~t, xny) *)
(d, t) f)
jTr
1744 1803.1 1905.2
1907 1912 2395 2768 3021 a) b) c) a) c) f)
This work
Ref. 7). Coban et aL 6) level scheme corrected. Levels below 748 keV, Agarwal et aL 9). Levels above 748 keV, Sugimitsu et aL 11), level scheme corrected. Protop et a L l o ) , levels at 761 and 1087 keV altered. Ref. 1) levels marked with an asterisk are doublets. TABLE 3 Gamma-ray branching ratios in 7SSe
?'-rays (keV)
Initial level (keV)
20.7 132.8 141.2 315.8 428.0 293.0 299.6 586.1 495.4 516.3 628.3 236.2 377.4 551.7 663.8 191.3 319.8 461.2 349.5 484.4 490.6
132.8 427.9
586.1
628.4
664.0
747.7
777.2
Final level, j~r (keV) 112.1, g.s., 286.5, 112.1, g.s., 293.0, 286.5, g.s., 132.8, 112.1, g.s., 428.0, 286.5, 112.1, g.s., 586.1, 428.0, 286.5, 428.0, 293.0, 286.5,
~+ ~+ -~{~+ ½~.~+ ~+ {-+ ~+ ~:{{-+ ~-+ ~-~~-~-½3-
Rel. a) int. 70 30 65 5 30 89 11
Rel. b) int.
59 5 38 86 8 6
25 75
15 77 6 2
79 29 30 35 35
46 54 22 36 42
Rel. ¢) int. 55 45 58 7 35 84 11 5 9 70 22 10 78 6 69 23
a) This work. b) Coban et aL 6). ¢) Agarwal et aL 9). t o t h o s e a u t h o r s . I t is t h o u g h t t h a t levels at 741 a n d 1067 k e V r e p o r t e d b y P r o t o p et al. l o ) h a v e b e e n m i s p l a c e d a n d s h o u l d in f a c t be at 761 a n d 1087 k e V r e s p e c t i v e l y w i t h t h e d e - e x c i t a t i o n r a y s f e e d i n g t h e 132.8 k e V level. T h e i m p r e s s i v e o v e r l a p a n d
7$Se
103
agreement obtained from such a wide variety of reactions makes it probable that a rather complete picture o f the energy levels in this nucleus up to about 1200 keV of excitation now exists. Branching ratios have also been extracted from the singles data, although the complexity of the spectra restricted the number of y-rays for which this could be done. The results are given in table 3, and compared with a selection of the ratios reported by other groups. The ratio for the 20.7 : 132.8 keV branch has been taken from the coincidence data and is possibly subject to angular correlation effects. As can be seen from the table, the overall agreement is basically good. 3.3. GAMMA-RAY ANGULAR DISTRIBUTIONS At 8.1 MeV bombarding energy, distributions have been obtained for those v-rays indicated in fig. 1, with the exception of the 608.4+611 keV doublet, and the 628.1 and 954.0 keV y-rays which are thought to be possible doublets. The complexity of the spectra recorded at 10.0 MeV restricted the number o f y-rays for which reliable areas could be extracted. In addition, for reasons discussed below, useful spectroscopic information has only been obtained from these distributions in a few cases. A list of measured angular distributions is given in table 4, where the necessary solid angle correction factors (Q2 and Q4) have been taken from Camp and Van Lehn 26). In order to derive spin assignments and mixing ratios from these angular distributions, it is necessary to estimate the magnetic substate populations produced by the (0~, n) reaction. This has been done using the statistical compound nucleus programme M A N D Y ~7). The statistical nature of the reaction is ensured by an effective target "thickness" of about 300 keV, which corresponds to averaging over a few TABLE 4
Gamma-ray angular distributions Transition (keV)
A2/A o
A4/Ao
Reduced Z2
(a) Measured at E~ ~ 8.1 M e V
112.1 286.5 428.0 141.2 293.0 377.4 431.6 962.3 734.0
--0.404-0.02 --0.054-0.02 + 0.22 + 0.04 --0.41 :k0.03 --0.08 4-0.03 --0.614-0.05 --0.20-}-0.06 --0.14±0.02 --0.024-0.03
0.03 4-0.02 0.074-0.04
0.9 0.6 1.0 1.0 0.7 1.7 1.6 0.5 0.8
(b) Measured at E~ = 10.0 M e V
319.8 461.2 349.5 801.3
--0.59±0.01 +0.39 4-0.04 +0.214-0.03 +0.544-0.07
--0.13 ±0.04 --0.41 4-0.07
0.5 0.7 0.4 0.6
104
N.E. SANDERSON AND R. G. SUMMERS-GILL
hundred states in the compound nucleus 18). Transmission coefficients for the neutrons have been calculated from the energy dependent optical potential of Wilmore and Hodgson 19). For the ~-particles, the potential derived by Satchler 20) from the elastic scattering of 25 MeV alphas on germanium has been used, although its validity at the energies used here is open to question. Consequently, these calculations have been checked at E~ = 8.1 MeV for the case of the 428.0 keV y-ray which decays from the 427.9 keV level [J= = -~-, refs. 1, 6)] to the ~+ ground state. A fit to this angular distribution was carried out for a pure E1 transition allowing the substate populations to vary without restraint. A best fit (reduced Z2 = 1.3) was obtained with populations of P(m = ½) = 0.52, P(~-) = 0.38 and P(-~) = 0.10, which correspond reasonably well with the theoretical predictions of 0.58, 0.30 and 0.12 respectively. Therefore for the analysis of distributions recorded at this energy, the population parameters have been allowed to vary within _+30 ~ of the predicted values. As the bombarding energy is raised to 10 MeV, not only is the initial alignment further reduced by the increased contribution of higher/-wave neutrons, but there can be an increasing conlribution to the population of the observed low-lying levels by ),-ray cascade feeding from higher levels. In these circumstances the populations have been allowed to vary freely, subject only to the reasonable condition that P(rn = ½) > P($) > P(~z)> P(~) and with P(m > ~) 2 = 0. This increased uncertainty has resulted in much more ambiguity in the analysis of the 10 MeV data. The procedure followed is that for a given spin sequence and mixing ratio (fi), a grid search is carried out over the allowed range of population parameters to find the minimum value of $(2. Where appropriate this search is repeated from arctan (6) = - 9 0 ° to +90 ° in 5 ° steps. The phase convention is that of Rose and Brink 21). Rejection of a spin hypothesis is based on the 0.1 ~o confidence level, the prescription used for determining both this and the errors on 6 being the one given by James et al. 22). In selecting trial spins, the (d, t) results 1) have been used to restrict the possibilities. In addition Weisskopf single-particle estimates 23) indicate that the only mixed transitions which need be considered are E2/M1. Consequently a non-zero mixing ratio for a transition means no change in parity between initial and final states. Some examples of this analysis are shown in fig. 4 and a complete summary is given in table 5. It is interesting to note that the angular distribution of the 801.3 keV y-ray corresponds to the maximum possible anisotropy for a-~a- ~ 29_transition, i.e. complete alignment of the initial state. This in turn means that the transition must be E2, since an M2 transition would have a lifetime in excess of 10 ns which is sufficiently long for the initial alignment to be severely reduced by extra-nuclear effects. 3.4. SPIN AND PARITY ASSIGNMENTS Levels at 112.1,664.0, 859.5 and 962.3 keV can be assigned spins 27-+,~-, ~:- and ~r- on the basis of the angular distribution analysis in the last section. Both Agarwal et aL 9) and Sugimitsu 11) give spins for the first two of these levels which are irt
75Se
105
112.1 keY J = 912"1' " ~ =1177
801.3 keY 934.1~
/
J : 5/2
J= 712 • J= 1112
.....
132.8.---~-- 912 +
J=712
- - '
J
J= 912
10( •
•
/
50 ,,
•
..
/
2010
"x
5
I
+'
ji
--~'.OJ % lev ,~
I
I
1
I
- - 4 0 j % level
~l J
~;
I
I
I
I
-,X--J = 1312
I
J =
-
I
I
712"~'X ~ • 1049
!
I
J=712 + X = = 7 6 8
J=512
J • 512
-
I
377.4 keY
1/.1.2 keV
!
I J=512
]
T
20 --*OJ % I~I
"--* 0.1% level
10-
I I -90-EO
I -30
I 0
I +30
I .60
1 .gO
I -90
arctan
I -60
I -30
I 0 arctan
I *30
I °60
I *90
Fig. 4. Analysis of angular distributions for some of the 7-rays observed in the 72Ge(c¢,n~')7SSe reaction.
agreement with this. The level at 934.1 keV can have either J~ = 3 + or ~3_+ on the basis of fits to the 801.3 keV y-ray distribution. In order to resolve this uncertainty, the intensity of this and other y-rays has been measured at a higher beam energy (12 MeV). These y-ray yields have been normalised to the yields measured at 10 MeV and are presented in table 6 as a function of the spin of their associated levels. The smooth and pronounced increase of the relative yields with spin makes for a strong argument that the 934.1 keV level has J= = t_~+. The differential cross section for neutron pickup 1) to a level at 747 keV could only be fitted by a mixture of l-values (l = 1 + 4 or less probably I = 3 + 4 ) . Fig. 3 shows a level at 747.7 keV which decays to two levels with J~ = ~r- and { - , thereby suggesting an initial spin between J~ = ½ and ~. The angulal distribution analysis for the 319.8 and 461.2 keV y-rays shows fits for J~ = ~ - (40 % confidence level) and J~ = ~:- ( 1 % confidence level for 461.2 keV y-ray). An assignment o f J ~ = ½- is preferred
N. E. SANDERSON AND R. G. SUMMERS-GILL
106
TABLE 5
Angular distribution analysis Transition Initial
Trial
(keV)
level (keY)
j~r
112.1
112.1
.~+ {-+ 6{,~6½{~~½6½-
141.2
427.9
293.0
586.1
377.4
664,0
431.6
859.5
962.3
962.3
319.8
Final jlr
6+ "~½-
~+
Minimum Z2
Allowed j~r
1177 3.6 19.0 199 3.1 2.5 8.5 767 5.4 6.2 21 8.2 21
747.7
{~
1.8 61
747,7
½ {
971 2.1 2.8
Mixing ratio ~ (E2/M1)
~-+
+0.25±0.13or + 2 . 1 i 0 . 4
~-~½-
+0.19±0.10or+1.6~0.2 --0.12±0.08or+2.5±0.6
6~-
+0.73±0.45 --0.3 ~0.3 o r ~ 2 . 9
~,~-
+0.16<6<
+1.5
- - 0 . 6 3 ± 0 . 2 o r - - 4 . 3 ~ 6 ~ --0.87 461.2
801.3
934.1
½ 4} 42t ~~-
9+
~
86 5.6 21 5.3 20 20
~-
+ 1 . 5 ~ 6 ~ +7.1 --5.6 ~ 6 ~ +0.09
4f-+ 9+
~
--0.9 ±0.3
TABLE 6
Relative yields ofT-rays at E~ ~ 12 and 10 MeV y-ray (keV) Energy level (keV) j~r Relative yielda)
516.3 628.4 ~+ 0.6
112. l 112.1 -~-+ 1.0
132.8 132.8 ~+ 1.3
801.3 934.1 ~+ or a#+ 4.4
~) Normalised to 112.1 keV level.
for this level a n d this is also the spin given by Agarwal et al. 9), presumably o n the basis of a n E2 m u l t i p o l a r i t y for the 461.2 keV transition. F u r t h e r progress i n assigning spins can be m a d e by considering the available ),-ray b r a n c h i n g data i n table 3. A level at 777.2 keV with J~ = { - or ½- [ref. i)] c a n n o t i n fact have J~ = ~-- as tl'te ?-decay mode w o u l d t h e n require a n M3 transition competing with M1 a n d E2 transitions. The same a r g u m e n t c a n be applied to show that the
758e
107
628.4 keV level must have J~ = ~+ and not ~+. Finally, an assignment of J~ = ½for the 586.1 keV level would mean M2 : M1 ratios in the 7-decay branches which are about one thousand times larger than indicated by Weisskopf estimates 23). An assignment of J~ = ~ - is therefore preferred for this level, this also corresponds to the assignment of Agarwal et aL 9). A list of spin assignments for levels in 755e has been given in table 2. Levels at 132.8, 286.5, 427.9 and 611 keV had spin assignments prior to this study 1, 6) and have not been discussed in this section, while the 293.0 keV level is the recently found ½- level 9). The list has been restricted to cases where the possible spins are at most two, although it is possible to put limits on the range of spins of many of the other levels. 4. Discussion A comparison of the level scheme for 75Se with the predictions of the Coriolis coupling model is shown in fig. 5. Details of this calculation and the resulting wave functions for the positive parity states have been given in ref. 1). The theoretical energy spectrum results from strong mixing between rotational bands built on states key ,/
ool
:,12.
O.al
S'2"
0
13/2"
O
"~' 11/2.
I • • / /
/
1200
3~. s , ¢ - ~ - - - ?12"
0
1000
~
--D/d--a//"
3v~, s'/'
o..
13r,'--~- " o - " (" 6~'2~ - -
,
'
t~O0
o.~
1, f 3 n "
a~
~v i -
~ I
O.29 712"
I I
O.33
I I
600
0.12
I
5/2312-
%
5r/' ,~ 0.1S 1/2" "
O.C~
%.
t 512"
138
0.0~
v2"
o_~;
5/2"
~ ~ .11 l&
400
512"
t 3/2"
1,1
. . . .
~
/112<1.?
"3/2"
200
9/2'-._ 11i
THEORY
EXP.
?/2" "
o.oe
~ ,.
5/2"
0.19 EXP
d
%"
0.04 7/2" THEORY
Fig. 5. Comparison of levels in 75Se with the predictions of a Coriolis coupling calculation i). Spectroscopic factors for neutron pickup are indicated by each energy level.
108
N . E . SANDERSON AND R. G. SUMMERS-GILL
arising from the 1g~ orbital. Agreement with the four lowest-lying experimental levels is good, and the J~ = 1_~_+state at 934.0 keV also lies close to a predicted level with the same spin. Further correspondence between levels with J~ = ]+, ~+ and ~+ can be suggested on the basis of spectroscopic factors. Additional levels observed above 600 keV may well originate from configurations such as (gt_)3. Comparison of the negative parity spectrum with theory shows that a correspondence can be found for the lowest-lying ~-, 2 :~-, ½- and -2 z- states, but the situation is not so clearly defined because of the number of levels observed with low spin throughout this range of excitation. It is worth pointing cut that the negative parity states are not such a good test of the model as the positive parity states. This is because the bands being mixed originate from the lf~, 2p~ and 2p~. orbitals and consequently the final energy spectrum is much more sensitive to the single particle parameters in the Nilsson calculation. Theoretical y-ray transition rates among the lower lying positive parity states have been calculated using the wave functions of ref. 1). The expression for M1 transitions is given by B(MI, I ~ I ' )
(- eh ~- 2 3 = \2Me/ iG
[
Z
Ki=Kd+ I , K j
C' C" K, rs
x { +bM16r, ' ~firj,} ( - 1) r+k I"yKIKj la ]2 x } "-'tat -ijJ ,
where the C~x are the amplitudes of the wave functions for the level with spin I, and the quantities bm and GMt depend on the orbital, spin and collective #-factors as well as the expansion coefficients in the Nilsson wave functions. For the collective 9TABLE 7 Experimental and theoretical transition rates in 7 SSe Transition (keV)
Quantity
Measured a)
Predicted a)
112.1, ~+ ~ 9 +
B(M1) B(E2) 6(E2/M 1) B(E2) B(MI)
0.024-0.004 125 4-25 +0.25 4-0.13 344-6 0.03+0.006
0.03 130 +0.2 52 0.056
132.8, ~+ --~ 9 + 20.7, ~+ --~ ~+
a) Reduced transition rates expressed in W.u.
factor the value Z / A has been used, and the flee neutron value for the spin g-factor. Finally the quantity P~i allows for the effect of pairing and has been taken as
e,= u, %+v,v~, where U 2 and V2 are the quasiparticle level emptiness and occupation probabilities
758e
109
respectively. For E2 transitions where in-band transitions dominate, the expression simplifies to B(E2, I --, I ' ) = ~ 16n
e2O 2 [ ~, C~, cr'j (IK~201I' Kj)] 2. K, = r j
The intrinsic quadrupole moment of the core (Q0) has in this case been derived from the measured quadrupole moment of the ground state 24). The results of these calculations are presented in table 7 together with the experimental values. These experimental values have been derived from the lifetime measurements of Agarwal et aL 9), the ~-ray branching and mixing ratios given in tables 3 and 5 of this paper, and where necessary the theoretical internal electron conversion coefficients of Hager and Seltzel 25). The agreement in all cases is within a factor of two, which is remarkably good. The highly collective nature of the 112.1 keV (~+ ~ ~+) and 132.8 keV (~ ~+) transitions is evident from their large B(E2) values. The results of this work appear to confirm the argument advanced in ref. 1), namely that the positive parity low-excitation spectrum of 75Se can be adequately described by considering a single neutron coupled to a deformed prolate core. As pointed out for example by Stephens et aL 26), a general feature of situations where Coriolis coupling is strong, is the development of rotationally aligned band structure. Consequently we also note with interest the report by Protop et aL 27) that candidates for such bands have been found in some of the odd-proton nuclei in this mass region. We wish to thank the staff of McMaster University Tandem Accelerator Laborat ory and the other members of the research group for their assistance during these experiments. The work was supported financially by the National Research Council o f Canada.
References 1) N. E. Sanderson, Nucl. Phys. A216 (1973) 173 2) L. S. Kisslinger and R. A. Sorensen, Rev. Mod. Phys. 35 (1963) 853; L. S. Kisslinger and R. Kumar, Phys. Rev. Lett. 19 (1967) 1239 3) A. Goswami and O. Nalcio~lu, Phys. Lett. 26B (1968) 353 4) A. Goswami, D. K. McDaniels and O. Nalcio~lu, Phys. Rev. C7 (1973) 1263 5) A. Kuriyama, T. Marumori and K. Matsuyanagi, Prog. Theor. Phys. 45 (1971) 784; 47 (1972) 498; J. Phys. Soc. Jap. Suppl. 34 (1973) 407 6) I. Ladenbauer-Bellis and H. Bakhru, Phys. Rev. 178 (1969) 2019; S. Ray, J. N. Mo, S. Muszynski and S. K. Mark, Nucl. Phys. A138 (1969) 49; B. C. Dzhelepov, A. G. Dmitriev, N. N. Zhukovski, L. N. Moskvin and Y. U. Penionzhkevich, Bull. Acad. Sci USSR (phys. ser.) 33 (1969) 1513; A. Coban, J. C. Willmott, J. C. Lisle and G. Murray, Nucl. Phys. A182 (1972) 385 7) K. Way and H. Ikegami, Nucl. Dat. B1-6(1966) 80; F. W. Richter, J. Schutt and D. Wieglandt, Z. Phys. 217 (1968) 1; E. Finckh, U. Jahnke, B. Sachreiber and A. Wiedinger. Nucl. Phys. A144 (1970) 67 8) N. E. Sanderson and R. G. Summers-Gill, Bull. Am. Phys. Soc. 18 (1973) 721 9) Y. K. Agarwal, S. M. Bharathi, S. K. Bhattacherjee, B. Lal, B. Sahai and C. V. K. Baba, Proc. Int. Conf. on nuclear physics, Munich 1973, ed. J. De Boer and H. J. Mang (North-Holland,
110
10)
11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27)
N. E. SANDERSON A N D R. G. S U M M E R S - G I L L Amsterdam, 1973) p. 288; Y. K. Agarwal, C. V. Baba, S. M. Bharathi, S. K. Bhattacherjee, B. Lal and B. Sahai, Pramana 3 (1974) 243 C. Protop, K. O. Zell, H. G. Friedericks, B. Heits and P. V. Brentano, Proc. Int. Conf. on nuclear physics, Munich 1973, ed. J. de Boer and H. J. Mang (North-Holland, Amsterdam, 1973) p. 216; K. O. Zell, H. G. Friedericks, B. Heits, P. V. Brentano and C. Protop, Z. Phys. A272 (1975) 27 T. Sugimitsu, Nucl. Phys. A224 (1974) 199 F. K. McGowan, W. T. Milner, R. L. Robinson and P. H. Stelson, Ann. of Phys. 63 (1971) 549 K. Way and H. Ikegami, Nucl. Data B1-6 (1966) D. H. White, R. E. Birkett and T. Thomson, Nucl. Instr. 77 (1970) 261 G. Aubin, J. Barrette and S. Monaro, Nucl. Instr. 76 (1969) 93 D. C. Camp and A. L. van Lehn, Nucl. Instr. 76 (1969) 19 E. Sheldon and P. Gantenbein, J. Appl. Maths. Phys. 18 (1967) 397; E. Sheldon and R. M. Strang, Comp. Phys. Commun. 1 (1969) 35 C. C. Lu., L. C. Vaz and J. R. Huizinga, Nucl. Phys. A190 (1972) 229 D. Wilmore and P. E. Hodgson, Nucl. Phys. 55 (1964) 673 L. McFadden and G. R. Satchler, Nucl. Phys. 84 (1966) 177 H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306 A. N. James, P. J. Twin and P. A. Butler, Nucl. Instr. 115 (1974) 105 A. H. Wapstra, G. J. Nijgh and R. van Lieshout, Nuclear spectroscopy tables (North-Holland, Amsterdam, 1959) p. 71 L. C. Aadomt and P. C. Fletcher, Phys. Rev. 98 (1955) 1224 P. S. Hager and E. C. Seltzer, Nucl. Data A4 (1968) 26 F. S. Stephens, R. M. Diamond and S. G. Nilsson, Phys. Lett. 1144 (1973) 429 C. Protop, B. Heits, H. G. Friedericks, K. O. Zell and P. von Brentano, Z. Phys. 271 (1974) 65
NuclearPhysics A261 (1976) 93 -- 110; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
SPECTROSCOPY
O F 7SSe
S T U D I E D W I T H T H E 72Ge(~, n?) R E A C T I O N N. E. SANDERSONt and R. G. SUMMERS-GILL
McMaster University, Hamilton, Ontario, Canada Received 22 September 1975 (Revised 22 December 1975)
n)TSSe and a level scheme built up from the observed ~,-ray spectra. Gamma-ray angular distribution measurements have been analysed to yield spin assignments, mixing ratios and branching ratios. Comparison of the positive parity spectrum with the levels predicted by a Coriolis coupling calculation shows good agreement. In particular the model can successfully predict the occurrence of "anomalous" states with j~r = ~+ and 5 + which lie close to the ~+ state in this nucleus, and which are a general feature of many neighbouring nuclei. Calculated E2 and M 1 transition rates among these levels agree with available experimental data to within a factor of two. A strong case can therefore be made for regarding the low-lying levels in 7SSe as arising from an odd neutron coupled to a deformed prolate core.
Abstract: States in 75Se have been excited by the reaction 72Ge(u,
E
NUCLEAR REACTIONS 72Ge(tz,nT), E = 8.1, 10.0, 13.0 MeV; measured tr(E~,, 0), y),-coin. 75Se deduced levels, J, zt. Enriched target.
I
I
1. Introduction
I n a recent p a p e r 1) it was s h o w n t h a t a Coriolis c o u p l i n g m o d e l i n c o r p o r a t i n g a p a i r i n g residual i n t e r a c t i o n was c a p a b l e o f a c c o u n t i n g for the occurrence a n d overall b e h a v i o u r o f the ' a n o m a l o u s ' low-lying states w i t h d~ = ~+ a n d {+ w h i c h a p p e a r in the s p e c t r a o f m a n y lg~ nuclei. I n p a r t i c u l a r the p a p e r r e p o r t e d the results o f a 76Se(d ' t)75 Se transfer r e a c t i o n a n d showed t h a t the energies o f the f o u r lowest-lying positive p a r i t y states in 75Se [2~+, ( { + ) , ~+ a n d ½+ at 0, 112, 133, a n d 611 k e V respectively] c o u l d be r e m a r k a b l y well fitted b y this model. Theoretical spectroscopic factors were also in r e a s o n a b l e a g r e e m e n t with experiment. I t has been k n o w n f o r s o m e time t h a t a s t r a i g h t f o r w a r d q u a s i p a r t i c l e - p h o n o n c o u p l i n g m o d e l 2) c a n n o t a c c o u n t for such states, b u t m o r e recent calculations w h i c h include effects due t o static q u a d r u p o l e m o m e n t s a n d g r o u n d - s t a t e c o r r e l a t i o n s 3), a d d i t i o n a l p a r t i c l e - p l l o n o n interactions 4) o r t h r e e - q u a s i p a r t i c l e c o r r e l a t i o n s s) have h a d m o r e success. One feature o f all the m o d e l s m e n t i o n e d a b o v e is the p r e d i c t i o n o f a n u m b e r o f o t h e r positive p a r i t y states at a n e x c i t a t i o n o f 0.5-1.0 MeV, i n c l u d i n g h i g h e r spin levels with J~ = x2-A-~ + and ~+. Inevitably, further testing o f these m o d e l s is h a n d i c a p p e d by a l a c k o f e x p e r i m e n t a l i n f o r m a t i o n , b o t h o n a d d i t i o n a l p o s i t i v e p a r i t y levels and on the negative p a r i t y levels t Present Address: Physics Department, University of Birmingham, Birmingham, B15 2TT, England. 93
94
N.E. SANDERSON AND R. G. SUMMERS-GILL
arising from the 2p~, lf~ and 2p,~ single-particle orbits. For the case of 75Se, earlier r-decay 6) and (p, n) reaction 7) studies had been undertaken resulting in quite detailed level schemes but only two additional spin assignments to levels at 286.5 keV (~-) and 427.7 keV (~-). Such reactions would not of course populate the expected levels with J > ~, and indeed these have yet to be unambiguously identified in any oddneutron lg~ nucleus. This paper continues the investigation of the level structure of 758e by presenting results obtained using the 72Ge(ct, ny)75Se reaction. Two features of this reaction are pal ticularly attractive in this case. For energies reasonably close to threshold the high degree of alignment in the residual nucleus can be calculated, and angular distribution measurements of the de-excitation y-rays can lead to both spin assignments and y-ray mixing ratios. In addition, as the beam energy is increased, sumcient angular momentum can be brought into the system to populate higher spin states. In this way levels up to 1.5 MeV of excitation have been observed and the spins of many of these determined together with y-ray mixing and branching ratios. These results are compared with model predictions. Soon after a preliminary account of this experiment was given s), more experimental work on 7SSe was reported by two other groups in conference contributions. These groups have subsequently published their results. Agarwal et al. 9) using the 75As(p, ne-y) reaction give spin assignments and y-ray branching and mixing ratios for most levels below 748 keV. There is excellent agreement between their results and those presented in this paper. Protop et al. 10) have studied the 72Ge(a, ny) 75So and 7aGe(a, 2ny)TSSe reactions carried out at much higher beam energies than used in this work. Levels up to 3 MeV were observed including some which are suggested to show rotational band structure. Most recently another 75As(p, ne-y)TSSe study has been described in a paper by Sugimitsu ~~) in which levels up to 1.7 MeV were observed, but very few definite spin assignments made. A fuller discussion of these results will be given in later sections.
2. Experimental methods 2.1 TARGET PREPARATION The target consisted of a layer of 72Ge (isotopic purity 96.4 ~o) deposited by vacuum evaporation onto a pure gold backing. A target thickness of about 1 mg" cm-2 was obtained, which corresponds to a beam energy loss of 280 keV for 10 MeV a-particles. Gold of thickness 0.025 mm ensured that the beam was fully stopped in the backing, while at the same time minimising effects due to absorption of y-rays emerging from the back of the target. Coulomb excitation in gold. gives rise to a number of impurity lines in the y-ray spectrum, but these are well known 12) and readily identified. 2.2. ANGULARDISTRIBUTIONS For these measurements, the target was mounted at 45 ° to the beam axis in the
75Se
95
centre of a thin-walled (0.5 mm), cylindrically symmetric, aluminium chamber. A system of two 1.5 mm diameter gold apertures produced a well defined beam spot on the target. The y-ray spectra were recorded at six different angles between 0 ° and 90 ° using a 42 cm a Ge(Li) detector (resolution 2.5 keV F W H M at 1.3 MeV) set at a distance o f 8.5 cm from the target centre. The reaction yield was monitored with a 12 cm 3 Ge(Li) kept at a fixed angle. " D e a d " time corrections were monitored by counting the digitised output of the target current integrator simultaneously into three scalers; two of these were gated by the two ADC " b u s y " signals. These corrections were below 10 ~ at all times. The isotropy of the system was checked after the experiment by measuring the angular distribution of tb_e ~-rays following the r-decay of 75Se (T~ -- 120 d) which builds up during the bombardment. This activity produces strong y-rays of 121.1, 135.9, 264.6 and 279 keV [ref. 13)]. and these were found to be isotropic to within their statistical errors ( ~ 4 ~o). Peak areas were extracted from tbe spectra by fitting a straight line background to regions on either side of the peak and integrating the number of counts above it. Energies were extracted from the peak centroids, the spectrum having been first calibrated using the many accurately know y-rays from sources of 182Ta [ref. 14)] and 152gEu [ref. 15)]. These two sources were also used to determine the efficiency of the counter. 2.3. G A M M A - G A M M A C O I N C I D E N C E S
F o r these measurements the target was mounted in a small (2 cm diameter) chamber. Coincidences were recorded with the 42 cm a Ge(Li) and a 50 cm 3 Ge(Li) (resolution 2.9 keV F W H M at 1.3 MeV) both placed close to the target with 1 cm of lead shielding between them to prevent y-rays scattering from one counter to another. A system time resolution of 15 ns F W H M was achieved using constant fraction timing for the 50 cm a and extrapolated zero timing for the 42 cm a counters respectively. The true to random ratio was about 50 : 1. Each event consisting of a TAC output and two y-ray energy pulses was processed in a P D P 15 computer and stored on magnetic tape. Off-line analysis consisted of setting windows on the time peak and on those yrays of interest in one of the spectra. Background and random coincidences were subtracted by setting further windows below and above the y-ray peaks and also on the random part of the TAC spectrum.
3. Experimental results 3.1. G A M M A - R A Y S P E C T R A
Examples of the singles y-ray spectra obtained at beam energies of 8.1 and 10.0 MeV are shown in fig. 1. These energies correspond to 1.5 and 3.4 MeV above the reaction threshold. The yield at the lower bombarding energy is much reduced by the effect of the Coulomb barrio1, while at the higher energy the spectrum of y-rays is complex. The more prominent y-rays associated with 75Se have been marked with
COUNTS PER CHANNEL~>
COUNTS PER CHANNEL . ~
,
,<
~,,=:
(-
L2!
m .,:-,
112.1
112.1
'<
132.8
,c
141.2
~
Au
Au
Au
c}
I
.1~1.2
211.2 <
236,2
~__=Au
~ , - - AJ f
'~
I=
286.5 293.0
,,,Au
r
299.8 293.0.c
286.5
.~ 315.6 319.8 330.9 3&9.5 l<
P=
--
377.&
(
/
428.0
<
377.4
(
&28.0
""431.6
~-~-&31.6
461.2
0
~48&.&
-"'490.6
.> ~::~==~,--,- (5111
516.3
516.3
573.0
=::l
( 608.4.611 ~[ 619o4 628.1
628
(.~
~-..-850.8 *"557.0
f
$=
681+683.1776"2÷ 6~ 701.6
0 I=1 <
73&.0
734.0
0 788.7
Ge
F
0 oo l=
~
841.3
<
912.5
801.3 Ge
~'e~
/"954.0
954 962.3
_ . (.n ~ .~"
~
"~" 962,3
m
m II <
.<
1050
0
b
"IIID-S~I~IIAIIAIflS"D "H Q N V
NOS~I3GNVS
"~I "N
96
7~Se
97
c~
72
~' =,
0
~
;~
=
=.
~. =.
75
]
Ge(~.n) S e I ~'-~" Coincidences I Energies in keY I
112,1
l
100O w z z
0
111111
i I
I
I~1.2
0
~
0-
s60
CH,,,EL 1~ ~UMBER
lSb0
20N
Fig. 2. Gamma-gamma coincidence spectra from the 7ZGe(~,nT)75Se reaction at a bombarding energy of 13.0 MeV. Peaks labelled (B) are due to background. their energies. Other ?-rays present in the spectrum include Coulomb excitation lines from the target and the gold backing, as well as ?-rays in 7Sms following the fl+ decay of 75Se. Examples of the sorted coincidence spectra, which were recorded at an energy of 13.0 Me¥, are shown in fig. 2. In the spectrum gated by the 132.8 keV 7-ray two background lines (labelled B) can be seen. These are present because the window overlaps with a 135.9 keV ?-ray (75As) and the tail of the intense 141.2 keV v-ray (?SSe). A complete list of ),-rays assigned to 7SSe is given in table 1, together with their coincidence relationships. Identification has been made on a combination o f the ),-), results, and previously reported ?-rays 6) and energy levels 1, 6). The energies for those ?-rays which are weak or unresolved in the singles spectra have been taken from the coincidence data, while the energies o f the 112.1, 132.8, 141.2 and 286.5 keV ),-rays have also been measured using a 1 cm a Ge(Li) detector (resolution = 0.6 keV F W H M at 122 keV). With the exception of a strong 596.3 keV y-ray observed at 8.1 MeV whose origin is not known, only a few weak ),-rays in the singles spectra remain unidentified.
N. E. S A N D E R S O N
98
A N D R. G. S U M M E R S - G I L L
TABLE 1 G a m m a rays associated with 75Se ),-ray (keV) 112.14-0.1 132.8- -0.1 141.2--0.1 191.3- -0.3 211.2--0.3 236.2- -0.3 286.5--0.1 293.0- -0.2 299.6- 0.3 315.8--0.2 319.8- -0.2 326.3- -0.3 330.9- -0.2 349.5 - -0.2 377.4- -0.2 404.2- -0.3 408.8- -0.3 428.0 -0.2 431.6- -0.2 461.2- -0.2 484.4- -0.3 487.5 - -0.3 490.6- -0.2 516.3z-0.2 573.04-0.2 596.1 + 0 . 3 608.44-0.4 611 ± 1 619.4±0.2 628.1 4-0.2 635.24-0.3 650.8±0.2 657.04-0.4 676.2±0.3 678 4-1 681 4-1 683.7- -0.3 701.8- -0.2 724.4- -0.4 734.0- -0.2 739.9- -0.3 754.1 -0.3 760.5- -0.4 767.8- -0.3 788.7- -0.4 801.3- -0.2 826.5- -0.3 841.3- -0.3
Coincidence gate 112.1
132.8
286.5
141.2
293.0
516.3
377.4
319.8
349.5
650.8
x X X
X
X
x
X
X
X
X
X
X X
X
X
X X
X X
X
X X X X
X
X
X x X x X X
X x
x
X x
x
x x
x
x
x
x x X
X x
X
x
X
7SSe
99
TASLE 1 (continued) y -ray (keV)
C o i n c i d e n c e gate 112.1
132.8
286.5
141.2
>( )<
>(
868.3 :~0.6
872 4-1 912.54-0.4 954.04-0.2 961.5±0.5 962.3±0.2 974.9±0.3 1049.9-4-0.3 1144.9±0.2
293.0
516.3
377.4
319.8
349.5
650.8
X
X X
3.2. ENERGY LEVELS IN 7SSe Fig. 3 shows the proposed level scheme for 75Se and for comparison those levels reported in the (d, t) study 1). For convenience the level scheme has been separated into two parts. On the right are shown those levels which ~-decay predominantly to one or mole of the first three states (J~ = ~+, 5 + and $+). With one exception, these levels are not observed to be populated by fl-decay from the ground state (J~ = g2- or ~2-) of 75Br [ref. 6)]. It would appear then that most of these levels have high spin and/or positive parity. The existence of a 20.7 keV transition connecting the levels at 132.8 and 112.1 keV can be inferred from the fact that 7-rays of 628.1,801.3 and 954.0 keV are seen in coincidence with both 132.8 and 112.1 keV y-rays. Such a crossover transition connecting the two states has now been directly observed by Agarwal et al. 9). Because of this transition, pairs of ?-rays differing by about 20.7 keV have been assigned to the decay of levels at 789.9, 813.6 and 1086.9 keV. The existence of ground-state decays from levels at 628.4 and 953.4 keV cannot be conclusively established because they overlap in energy with ~-rays of 628.1 and 954.0 keV which feed the 132.8 keV (-~+) level. However their presence in the singles spectrum taken at 8.1 MeV argues for their inclusion. The 747 keV level observed in the (d, t) study 1) was one of two levels whose differential cross sections could only be fitted by mixed lvalues of different parities. The decay mode of the 747.7 keV level appears to be well established 6, 9), but a 635.2 keV y-ray observed in this experiment has not been reported by other workers. Consequently we suggest the possibility that this ~-ray represents the decay of a new level at 747.3 keV to the 112.1 k e y level. Many of the levels shown on the left of fig. 3 are populated by the fl-decay of 7 SBr and comparison with the (d, t) spectrum shows that they have negative parity. The presence of a level at 293.2 keV with a lifetime of 30 ns has been recently established by Agarwal et al. 9). A list of the energy levels and spin assignments (to be discussed later) in 75Se is given in table 2. Also given is a summary of the energy levels reported in a wide range of other studies. The levels proposed by Coban et al. 6) and by Sugimitsu 11) have been corrected for the presence of the 286.5-293.2 keV doublet which was not known
100
N.E. SANDERSON AND R. G. SUMMERS-GILL
---_.-_--- -_-_-_-_-'-.+ @
u3
;>
6"77Lt,I. _ 6°?L6 O"/56
CK 0
Z k--.I
C
u'}
u')
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._.1
LU
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LU
0 C
._1
<.,.;
0
LU
II
I
il
+eq+I
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r jt
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o e.,
d O3
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S'9i;~
~
75Se
101
TABL~ 2 Energy levels in 75Se (in keV) (p, n) a)
fl-decay b)
(13, n~) c. d)
(~, xn~') c)
0 115
0 112.1
286
286.5
425 584 610 627 660
427.7 586.0
0 112 132 287 293 428 586
663.8
0 112.1 133.0 286.7 293.2 428.1 586.1 611.0 628.2 664.1
745
747.4
748.0
779
777.0
777.3 789.6
749 761 778
629 664
(d, t) 0 112 133 287 427 586 611 629 664 747* 777
814 832 852 890
859.4 895.4
840.1 859.3 895.9
859 895 934
958 996 1010 1044 1072
1020.4 1073.7
962.6 1003.9 1020.6 1047.4 1073.8
1048
963 1004 1021 1048 1074
1080 1087 1143
1144.5
1144.7 1162
1190
1250 1302 1378
1184.3
1184.7
1198.5 1245.5
1198.9 1245.3 1301.9 1375.8
1374.8 1380.5
1407 1441
0 112.1 132.8 286.5 293.0 427.9 586.1 611 628.4 664.0 (747.3) 747.7 760.9 777.2 789.9 813.6 839.6 859.5 894.9 934.1 953.4 962.3 1020.5 1047.2 1073.7 1078.7 1086.9 1144.9 1162.0 1181.9 1182.7 1199.0
1246
1490
1556 1561.0
1561.1 1588.2 1630 1666.6
jrr ~+ ~+ 3+ 3½~~-,(3-) ½+ ]+ ~½-,(3-) ]-
3½-, 3 ~+ ~3 +, 3 + ½-, ~ ~-, 9-
3+, 3 +
½-,31300 1374.8
1490.6 1550.2
1650 1668 1733
This work
1411.3
1480
1592
1145 1161 1183"
r)
1431.6 1454.4 1487.6
N. E. SANDERSON A N D R. G. SUMMERS-GILL
102
TABLE 2 (continued) (p, n) a)
fl-decay b)
(p, ny) c. a)
1764
(~t, xny) *)
(d, t) f)
jTr
1744 1803.1 1905.2
1907 1912 2395 2768 3021 a) b) c) a) c) f)
This work
Ref. 7). Coban et aL 6) level scheme corrected. Levels below 748 keV, Agarwal et aL 9). Levels above 748 keV, Sugimitsu et aL 11), level scheme corrected. Protop et a L l o ) , levels at 761 and 1087 keV altered. Ref. 1) levels marked with an asterisk are doublets. TABLE 3 Gamma-ray branching ratios in 7SSe
?'-rays (keV)
Initial level (keV)
20.7 132.8 141.2 315.8 428.0 293.0 299.6 586.1 495.4 516.3 628.3 236.2 377.4 551.7 663.8 191.3 319.8 461.2 349.5 484.4 490.6
132.8 427.9
586.1
628.4
664.0
747.7
777.2
Final level, j~r (keV) 112.1, g.s., 286.5, 112.1, g.s., 293.0, 286.5, g.s., 132.8, 112.1, g.s., 428.0, 286.5, 112.1, g.s., 586.1, 428.0, 286.5, 428.0, 293.0, 286.5,
~+ ~+ -~{~+ ½~.~+ ~+ {-+ ~+ ~:{{-+ ~-+ ~-~~-~-½3-
Rel. a) int. 70 30 65 5 30 89 11
Rel. b) int.
59 5 38 86 8 6
25 75
15 77 6 2
79 29 30 35 35
46 54 22 36 42
Rel. ¢) int. 55 45 58 7 35 84 11 5 9 70 22 10 78 6 69 23
a) This work. b) Coban et aL 6). ¢) Agarwal et aL 9). t o t h o s e a u t h o r s . I t is t h o u g h t t h a t levels at 741 a n d 1067 k e V r e p o r t e d b y P r o t o p et al. l o ) h a v e b e e n m i s p l a c e d a n d s h o u l d in f a c t be at 761 a n d 1087 k e V r e s p e c t i v e l y w i t h t h e d e - e x c i t a t i o n r a y s f e e d i n g t h e 132.8 k e V level. T h e i m p r e s s i v e o v e r l a p a n d
7$Se
103
agreement obtained from such a wide variety of reactions makes it probable that a rather complete picture o f the energy levels in this nucleus up to about 1200 keV of excitation now exists. Branching ratios have also been extracted from the singles data, although the complexity of the spectra restricted the number of y-rays for which this could be done. The results are given in table 3, and compared with a selection of the ratios reported by other groups. The ratio for the 20.7 : 132.8 keV branch has been taken from the coincidence data and is possibly subject to angular correlation effects. As can be seen from the table, the overall agreement is basically good. 3.3. GAMMA-RAY ANGULAR DISTRIBUTIONS At 8.1 MeV bombarding energy, distributions have been obtained for those v-rays indicated in fig. 1, with the exception of the 608.4+611 keV doublet, and the 628.1 and 954.0 keV y-rays which are thought to be possible doublets. The complexity of the spectra recorded at 10.0 MeV restricted the number o f y-rays for which reliable areas could be extracted. In addition, for reasons discussed below, useful spectroscopic information has only been obtained from these distributions in a few cases. A list of measured angular distributions is given in table 4, where the necessary solid angle correction factors (Q2 and Q4) have been taken from Camp and Van Lehn 26). In order to derive spin assignments and mixing ratios from these angular distributions, it is necessary to estimate the magnetic substate populations produced by the (0~, n) reaction. This has been done using the statistical compound nucleus programme M A N D Y ~7). The statistical nature of the reaction is ensured by an effective target "thickness" of about 300 keV, which corresponds to averaging over a few TABLE 4
Gamma-ray angular distributions Transition (keV)
A2/A o
A4/Ao
Reduced Z2
(a) Measured at E~ ~ 8.1 M e V
112.1 286.5 428.0 141.2 293.0 377.4 431.6 962.3 734.0
--0.404-0.02 --0.054-0.02 + 0.22 + 0.04 --0.41 :k0.03 --0.08 4-0.03 --0.614-0.05 --0.20-}-0.06 --0.14±0.02 --0.024-0.03
0.03 4-0.02 0.074-0.04
0.9 0.6 1.0 1.0 0.7 1.7 1.6 0.5 0.8
(b) Measured at E~ = 10.0 M e V
319.8 461.2 349.5 801.3
--0.59±0.01 +0.39 4-0.04 +0.214-0.03 +0.544-0.07
--0.13 ±0.04 --0.41 4-0.07
0.5 0.7 0.4 0.6
104
N.E. SANDERSON AND R. G. SUMMERS-GILL
hundred states in the compound nucleus 18). Transmission coefficients for the neutrons have been calculated from the energy dependent optical potential of Wilmore and Hodgson 19). For the ~-particles, the potential derived by Satchler 20) from the elastic scattering of 25 MeV alphas on germanium has been used, although its validity at the energies used here is open to question. Consequently, these calculations have been checked at E~ = 8.1 MeV for the case of the 428.0 keV y-ray which decays from the 427.9 keV level [J= = -~-, refs. 1, 6)] to the ~+ ground state. A fit to this angular distribution was carried out for a pure E1 transition allowing the substate populations to vary without restraint. A best fit (reduced Z2 = 1.3) was obtained with populations of P(m = ½) = 0.52, P(~-) = 0.38 and P(-~) = 0.10, which correspond reasonably well with the theoretical predictions of 0.58, 0.30 and 0.12 respectively. Therefore for the analysis of distributions recorded at this energy, the population parameters have been allowed to vary within _+30 ~ of the predicted values. As the bombarding energy is raised to 10 MeV, not only is the initial alignment further reduced by the increased contribution of higher/-wave neutrons, but there can be an increasing conlribution to the population of the observed low-lying levels by ),-ray cascade feeding from higher levels. In these circumstances the populations have been allowed to vary freely, subject only to the reasonable condition that P(rn = ½) > P($) > P(~z)> P(~) and with P(m > ~) 2 = 0. This increased uncertainty has resulted in much more ambiguity in the analysis of the 10 MeV data. The procedure followed is that for a given spin sequence and mixing ratio (fi), a grid search is carried out over the allowed range of population parameters to find the minimum value of $(2. Where appropriate this search is repeated from arctan (6) = - 9 0 ° to +90 ° in 5 ° steps. The phase convention is that of Rose and Brink 21). Rejection of a spin hypothesis is based on the 0.1 ~o confidence level, the prescription used for determining both this and the errors on 6 being the one given by James et al. 22). In selecting trial spins, the (d, t) results 1) have been used to restrict the possibilities. In addition Weisskopf single-particle estimates 23) indicate that the only mixed transitions which need be considered are E2/M1. Consequently a non-zero mixing ratio for a transition means no change in parity between initial and final states. Some examples of this analysis are shown in fig. 4 and a complete summary is given in table 5. It is interesting to note that the angular distribution of the 801.3 keV y-ray corresponds to the maximum possible anisotropy for a-~a- ~ 29_transition, i.e. complete alignment of the initial state. This in turn means that the transition must be E2, since an M2 transition would have a lifetime in excess of 10 ns which is sufficiently long for the initial alignment to be severely reduced by extra-nuclear effects. 3.4. SPIN AND PARITY ASSIGNMENTS Levels at 112.1,664.0, 859.5 and 962.3 keV can be assigned spins 27-+,~-, ~:- and ~r- on the basis of the angular distribution analysis in the last section. Both Agarwal et aL 9) and Sugimitsu 11) give spins for the first two of these levels which are irt
75Se
105
112.1 keY J = 912"1' " ~ =1177
801.3 keY 934.1~
/
J : 5/2
J= 712 • J= 1112
.....
132.8.---~-- 912 +
J=712
- - '
J
J= 912
10( •
•
/
50 ,,
•
..
/
2010
"x
5
I
+'
ji
--~'.OJ % lev ,~
I
I
1
I
- - 4 0 j % level
~l J
~;
I
I
I
I
-,X--J = 1312
I
J =
-
I
I
712"~'X ~ • 1049
!
I
J=712 + X = = 7 6 8
J=512
J • 512
-
I
377.4 keY
1/.1.2 keV
!
I J=512
]
T
20 --*OJ % I~I
"--* 0.1% level
10-
I I -90-EO
I -30
I 0
I +30
I .60
1 .gO
I -90
arctan
I -60
I -30
I 0 arctan
I *30
I °60
I *90
Fig. 4. Analysis of angular distributions for some of the 7-rays observed in the 72Ge(c¢,n~')7SSe reaction.
agreement with this. The level at 934.1 keV can have either J~ = 3 + or ~3_+ on the basis of fits to the 801.3 keV y-ray distribution. In order to resolve this uncertainty, the intensity of this and other y-rays has been measured at a higher beam energy (12 MeV). These y-ray yields have been normalised to the yields measured at 10 MeV and are presented in table 6 as a function of the spin of their associated levels. The smooth and pronounced increase of the relative yields with spin makes for a strong argument that the 934.1 keV level has J= = t_~+. The differential cross section for neutron pickup 1) to a level at 747 keV could only be fitted by a mixture of l-values (l = 1 + 4 or less probably I = 3 + 4 ) . Fig. 3 shows a level at 747.7 keV which decays to two levels with J~ = ~r- and { - , thereby suggesting an initial spin between J~ = ½ and ~. The angulal distribution analysis for the 319.8 and 461.2 keV y-rays shows fits for J~ = ~ - (40 % confidence level) and J~ = ~:- ( 1 % confidence level for 461.2 keV y-ray). An assignment o f J ~ = ½- is preferred
N. E. SANDERSON AND R. G. SUMMERS-GILL
106
TABLE 5
Angular distribution analysis Transition Initial
Trial
(keV)
level (keY)
j~r
112.1
112.1
.~+ {-+ 6{,~6½{~~½6½-
141.2
427.9
293.0
586.1
377.4
664,0
431.6
859.5
962.3
962.3
319.8
Final jlr
6+ "~½-
~+
Minimum Z2
Allowed j~r
1177 3.6 19.0 199 3.1 2.5 8.5 767 5.4 6.2 21 8.2 21
747.7
{~
1.8 61
747,7
½ {
971 2.1 2.8
Mixing ratio ~ (E2/M1)
~-+
+0.25±0.13or + 2 . 1 i 0 . 4
~-~½-
+0.19±0.10or+1.6~0.2 --0.12±0.08or+2.5±0.6
6~-
+0.73±0.45 --0.3 ~0.3 o r ~ 2 . 9
~,~-
+0.16<6<
+1.5
- - 0 . 6 3 ± 0 . 2 o r - - 4 . 3 ~ 6 ~ --0.87 461.2
801.3
934.1
½ 4} 42t ~~-
9+
~
86 5.6 21 5.3 20 20
~-
+ 1 . 5 ~ 6 ~ +7.1 --5.6 ~ 6 ~ +0.09
4f-+ 9+
~
--0.9 ±0.3
TABLE 6
Relative yields ofT-rays at E~ ~ 12 and 10 MeV y-ray (keV) Energy level (keV) j~r Relative yielda)
516.3 628.4 ~+ 0.6
112. l 112.1 -~-+ 1.0
132.8 132.8 ~+ 1.3
801.3 934.1 ~+ or a#+ 4.4
~) Normalised to 112.1 keV level.
for this level a n d this is also the spin given by Agarwal et al. 9), presumably o n the basis of a n E2 m u l t i p o l a r i t y for the 461.2 keV transition. F u r t h e r progress i n assigning spins can be m a d e by considering the available ),-ray b r a n c h i n g data i n table 3. A level at 777.2 keV with J~ = { - or ½- [ref. i)] c a n n o t i n fact have J~ = ~-- as tl'te ?-decay mode w o u l d t h e n require a n M3 transition competing with M1 a n d E2 transitions. The same a r g u m e n t c a n be applied to show that the
758e
107
628.4 keV level must have J~ = ~+ and not ~+. Finally, an assignment of J~ = ½for the 586.1 keV level would mean M2 : M1 ratios in the 7-decay branches which are about one thousand times larger than indicated by Weisskopf estimates 23). An assignment of J~ = ~ - is therefore preferred for this level, this also corresponds to the assignment of Agarwal et aL 9). A list of spin assignments for levels in 755e has been given in table 2. Levels at 132.8, 286.5, 427.9 and 611 keV had spin assignments prior to this study 1, 6) and have not been discussed in this section, while the 293.0 keV level is the recently found ½- level 9). The list has been restricted to cases where the possible spins are at most two, although it is possible to put limits on the range of spins of many of the other levels. 4. Discussion A comparison of the level scheme for 75Se with the predictions of the Coriolis coupling model is shown in fig. 5. Details of this calculation and the resulting wave functions for the positive parity states have been given in ref. 1). The theoretical energy spectrum results from strong mixing between rotational bands built on states key ,/
ool
:,12.
O.al
S'2"
0
13/2"
O
"~' 11/2.
I • • / /
/
1200
3~. s , ¢ - ~ - - - ?12"
0
1000
~
--D/d--a//"
3v~, s'/'
o..
13r,'--~- " o - " (" 6~'2~ - -
,
'
t~O0
o.~
1, f 3 n "
a~
~v i -
~ I
O.29 712"
I I
O.33
I I
600
0.12
I
5/2312-
%
5r/' ,~ 0.1S 1/2" "
O.C~
%.
t 512"
138
0.0~
v2"
o_~;
5/2"
~ ~ .11 l&
400
512"
t 3/2"
1,1
. . . .
~
/112<1.?
"3/2"
200
9/2'-._ 11i
THEORY
EXP.
?/2" "
o.oe
~ ,.
5/2"
0.19 EXP
d
%"
0.04 7/2" THEORY
Fig. 5. Comparison of levels in 75Se with the predictions of a Coriolis coupling calculation i). Spectroscopic factors for neutron pickup are indicated by each energy level.
108
N . E . SANDERSON AND R. G. SUMMERS-GILL
arising from the 1g~ orbital. Agreement with the four lowest-lying experimental levels is good, and the J~ = 1_~_+state at 934.0 keV also lies close to a predicted level with the same spin. Further correspondence between levels with J~ = ]+, ~+ and ~+ can be suggested on the basis of spectroscopic factors. Additional levels observed above 600 keV may well originate from configurations such as (gt_)3. Comparison of the negative parity spectrum with theory shows that a correspondence can be found for the lowest-lying ~-, 2 :~-, ½- and -2 z- states, but the situation is not so clearly defined because of the number of levels observed with low spin throughout this range of excitation. It is worth pointing cut that the negative parity states are not such a good test of the model as the positive parity states. This is because the bands being mixed originate from the lf~, 2p~ and 2p~. orbitals and consequently the final energy spectrum is much more sensitive to the single particle parameters in the Nilsson calculation. Theoretical y-ray transition rates among the lower lying positive parity states have been calculated using the wave functions of ref. 1). The expression for M1 transitions is given by B(MI, I ~ I ' )
(- eh ~- 2 3 = \2Me/ iG
[
Z
Ki=Kd+ I , K j
C' C" K, rs
x {
where the C~x are the amplitudes of the wave functions for the level with spin I, and the quantities bm and GMt depend on the orbital, spin and collective #-factors as well as the expansion coefficients in the Nilsson wave functions. For the collective 9TABLE 7 Experimental and theoretical transition rates in 7 SSe Transition (keV)
Quantity
Measured a)
Predicted a)
112.1, ~+ ~ 9 +
B(M1) B(E2) 6(E2/M 1) B(E2) B(MI)
0.024-0.004 125 4-25 +0.25 4-0.13 344-6 0.03+0.006
0.03 130 +0.2 52 0.056
132.8, ~+ --~ 9 + 20.7, ~+ --~ ~+
a) Reduced transition rates expressed in W.u.
factor the value Z / A has been used, and the flee neutron value for the spin g-factor. Finally the quantity P~i allows for the effect of pairing and has been taken as
e,= u, %+v,v~, where U 2 and V2 are the quasiparticle level emptiness and occupation probabilities
758e
109
respectively. For E2 transitions where in-band transitions dominate, the expression simplifies to B(E2, I --, I ' ) = ~ 16n
e2O 2 [ ~, C~, cr'j (IK~201I' Kj)] 2. K, = r j
The intrinsic quadrupole moment of the core (Q0) has in this case been derived from the measured quadrupole moment of the ground state 24). The results of these calculations are presented in table 7 together with the experimental values. These experimental values have been derived from the lifetime measurements of Agarwal et aL 9), the ~-ray branching and mixing ratios given in tables 3 and 5 of this paper, and where necessary the theoretical internal electron conversion coefficients of Hager and Seltzel 25). The agreement in all cases is within a factor of two, which is remarkably good. The highly collective nature of the 112.1 keV (~+ ~ ~+) and 132.8 keV (~ ~+) transitions is evident from their large B(E2) values. The results of this work appear to confirm the argument advanced in ref. 1), namely that the positive parity low-excitation spectrum of 75Se can be adequately described by considering a single neutron coupled to a deformed prolate core. As pointed out for example by Stephens et aL 26), a general feature of situations where Coriolis coupling is strong, is the development of rotationally aligned band structure. Consequently we also note with interest the report by Protop et aL 27) that candidates for such bands have been found in some of the odd-proton nuclei in this mass region. We wish to thank the staff of McMaster University Tandem Accelerator Laborat ory and the other members of the research group for their assistance during these experiments. The work was supported financially by the National Research Council o f Canada.
References 1) N. E. Sanderson, Nucl. Phys. A216 (1973) 173 2) L. S. Kisslinger and R. A. Sorensen, Rev. Mod. Phys. 35 (1963) 853; L. S. Kisslinger and R. Kumar, Phys. Rev. Lett. 19 (1967) 1239 3) A. Goswami and O. Nalcio~lu, Phys. Lett. 26B (1968) 353 4) A. Goswami, D. K. McDaniels and O. Nalcio~lu, Phys. Rev. C7 (1973) 1263 5) A. Kuriyama, T. Marumori and K. Matsuyanagi, Prog. Theor. Phys. 45 (1971) 784; 47 (1972) 498; J. Phys. Soc. Jap. Suppl. 34 (1973) 407 6) I. Ladenbauer-Bellis and H. Bakhru, Phys. Rev. 178 (1969) 2019; S. Ray, J. N. Mo, S. Muszynski and S. K. Mark, Nucl. Phys. A138 (1969) 49; B. C. Dzhelepov, A. G. Dmitriev, N. N. Zhukovski, L. N. Moskvin and Y. U. Penionzhkevich, Bull. Acad. Sci USSR (phys. ser.) 33 (1969) 1513; A. Coban, J. C. Willmott, J. C. Lisle and G. Murray, Nucl. Phys. A182 (1972) 385 7) K. Way and H. Ikegami, Nucl. Dat. B1-6(1966) 80; F. W. Richter, J. Schutt and D. Wieglandt, Z. Phys. 217 (1968) 1; E. Finckh, U. Jahnke, B. Sachreiber and A. Wiedinger. Nucl. Phys. A144 (1970) 67 8) N. E. Sanderson and R. G. Summers-Gill, Bull. Am. Phys. Soc. 18 (1973) 721 9) Y. K. Agarwal, S. M. Bharathi, S. K. Bhattacherjee, B. Lal, B. Sahai and C. V. K. Baba, Proc. Int. Conf. on nuclear physics, Munich 1973, ed. J. De Boer and H. J. Mang (North-Holland,
110
10)
11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27)
N. E. SANDERSON A N D R. G. S U M M E R S - G I L L Amsterdam, 1973) p. 288; Y. K. Agarwal, C. V. Baba, S. M. Bharathi, S. K. Bhattacherjee, B. Lal and B. Sahai, Pramana 3 (1974) 243 C. Protop, K. O. Zell, H. G. Friedericks, B. Heits and P. V. Brentano, Proc. Int. Conf. on nuclear physics, Munich 1973, ed. J. de Boer and H. J. Mang (North-Holland, Amsterdam, 1973) p. 216; K. O. Zell, H. G. Friedericks, B. Heits, P. V. Brentano and C. Protop, Z. Phys. A272 (1975) 27 T. Sugimitsu, Nucl. Phys. A224 (1974) 199 F. K. McGowan, W. T. Milner, R. L. Robinson and P. H. Stelson, Ann. of Phys. 63 (1971) 549 K. Way and H. Ikegami, Nucl. Data B1-6 (1966) D. H. White, R. E. Birkett and T. Thomson, Nucl. Instr. 77 (1970) 261 G. Aubin, J. Barrette and S. Monaro, Nucl. Instr. 76 (1969) 93 D. C. Camp and A. L. van Lehn, Nucl. Instr. 76 (1969) 19 E. Sheldon and P. Gantenbein, J. Appl. Maths. Phys. 18 (1967) 397; E. Sheldon and R. M. Strang, Comp. Phys. Commun. 1 (1969) 35 C. C. Lu., L. C. Vaz and J. R. Huizinga, Nucl. Phys. A190 (1972) 229 D. Wilmore and P. E. Hodgson, Nucl. Phys. 55 (1964) 673 L. McFadden and G. R. Satchler, Nucl. Phys. 84 (1966) 177 H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306 A. N. James, P. J. Twin and P. A. Butler, Nucl. Instr. 115 (1974) 105 A. H. Wapstra, G. J. Nijgh and R. van Lieshout, Nuclear spectroscopy tables (North-Holland, Amsterdam, 1959) p. 71 L. C. Aadomt and P. C. Fletcher, Phys. Rev. 98 (1955) 1224 P. S. Hager and E. C. Seltzer, Nucl. Data A4 (1968) 26 F. S. Stephens, R. M. Diamond and S. G. Nilsson, Phys. Lett. 1144 (1973) 429 C. Protop, B. Heits, H. G. Friedericks, K. O. Zell and P. von Brentano, Z. Phys. 271 (1974) 65