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High-spin states in the odd-odd nucleus 82Y
NUCLEAR PHYSICSA
Nuclear Physics A568 (1994) 202-220 North-Holland
High-spin states in the odd-odd
nucleus 82Y
J. Mukai *, A. Odahara, H. Tomura, S. Suematsu, S. Mitarai, T. Kuroyanagi Department of Physics, Kyushu Uniuersity, Fukuoka 812, Japan D. Jerrestam Uppsala University, NFL, Studsuik, S-611 82 Nykijping, Sweden
J. Nyberg 2, G. Sletten, A. Atac 3 Niels Bohr Institute, DK-4000 Roskilde, Denmark
S.E. Arnell, H.A. Roth, 6. Skeppstedt Department of Physics, Chalmers University of Technology, S-412 96 GGteborg, Sweden
Received 23 February 1993 (Revised 5 July 1993)
Abstract
High-spin states in 82Y have been studied by the 5*Nl‘(*%,3pn) reaction at 128 MeV. Low-lying states were investigated by the same reaction but at a lower bombarding energy and the band heads of the high-spin sequences have been characterized. Four rotational bands forming two sets of signature partners were established. The yrast band was observed up to J” = 27” and shows large signature splitting, while a negative-parity yrare band, observed up to spin 22 shows a much smaller splitting. The yrast band structure was very similar to the g,,, proton band in 79Rb.
Key words: NUCLEAR REACTIONS 58Ni(28Si,n3p), E = 100, 102, 128 MeV; measured E,, I,,, Z,(O), (particle)y-, yy-coin. **Y deduced levels, J, rr. Enriched target, Ge detector array, particle-multiplicity filter.
1. Introduction
Neutron-deficient nuclei in the A N 80 region have been shown to be strongly deformed, and theoretical calculations [l] indicate the existence of a deformed ’ Present address: Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan. 2 Present address: The Svedberg Laboratory, Uppsala University, Box 533, S-751 21 Uppsala, Sweden. 3 Present address: Department of Radiation Sciences, Uppsala University, Box 535, S-751 21 Uppsala, Sweden. 0375-9474/94/$07.~ 0 1994 - Eisevier Science B.V. All rights reserved SSDI 037S-9474(93)E0415-5
J. Mukai et al. / High spin states
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shell gap at nucleon number 38. Experimental data show a large deformation of the 2 _ 38 nuclei such as 79Rb (ref. 1211,77-80Sr (refs. [3,4]), 83Y (ref. [5]) and 83Zr (ref. [6]), while a transition from collective to single-particle motion has been observed around N = 44 (refs. [7-101). The orbital with largest angular momentum near the Fermi surface is g,,, for both protons and neutrons, and many g,,, bands have been established in odd-A nuclei as the yrast bands [2-151. From these experimental data the core-polarization effect of an odd nucleon has been investigated. This effect has been observed on soft cores of 76Kr (ref. [12]), 80Sr (refs. [9,16]) and 82Zr (ref. [61), and is known to depend on the geometrical configuration of the odd nucleon. Therefore it would be interesting to study the competing effects of the two nucleons in an odd-odd nucleus. Very little experimental data have been published for high-spin states in odd-odd nuclei in this mass region. Two bromine isotopes 74Br (ref. [17]) and 76Br (ref. [18]) have been well studied. In both nuclei the yrast band is based on a low-lying isomeric state with 1” = 4+, with the configuration assignment rg,,2 @ vg9,2. Regular rotational structure starts at J = 9 in 74Br and at J = 11 in 76Br, and at lower spin an inversion of the signature splitting has been observed. The authors of ref. [171 have suggested that at small angular momentum the total spin can be increased by both collective rotation and realignment of the intrinsic spins, causing a deviation from regular collective structure. Measurements of transition quadrupole moments have, however, shown that 74Br and 76Br have a large deformation both at low and high spins [17,18]. For 78Rb, the yrast band up to J = 15 has been reported [19], and a similar change from less regular structure to rigid rotation has been observed around spin 8. For the next odd-Z element, yttrium, no data had been published on high-spin states of the even-A isotopes until very recently. A new paper [20] has reported on the identification of a rotational structure in 84Y built on a 6+ isomeric state extending up to 21+. The excitation energy of the isomeric state is estimated to be in the range 0 N 500 keV. A large signature splitting in the band is observed and signature inversion happens for J < 11. There has been no data on lighter yttrium isotopes, which are especially interesting because both the unpaired proton and the neutron are expected to stay in the g,,, shell and can affect the core with similar strength. Although a dominance of single-particle structures is foreseen in the heavier isotopes of yttrium, 82Y with N = 43 is still expected to show collective features and is predicted as a good example to investigate the deviation from a simple rotor caused by two particles. In this work excited states in 82Y were identified and rotational structures were established up to spins 27+ and 22-. Four rotational bands were identified as two pairs of signature partners. These pairs are built on distinct isomeric band heads, the excitation energies of which were determined without ambiguity. The experimental data were analyzed in terms of the cranking model.
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J. Mukai et al. / High spin states
2. Experimental procedure The nucleus ‘*Y was produced in the 58Ni(28Si,3pn) reaction at a beam energy of 128 MeV for the high-spin studies. The 58Ni target, enriched to 97%, consisted of two stacked self-supporting foils each with a thickness of 350 kg/cm*. The 28Si beam was provided by the tandem and booster accelerator at the Niels Bohr Institute. The fusion-evaporation residues were stopped in a gold foil placed 2 cm downstream from the target. Gamma rays were detected by twenty Compton-suppressed Ge detectors in the NORDBALL array [21]. Five Ge detectors were placed in each of the four rings at 37”, 79”, 101” and 143” relative to the beam direction. Charged particles were detected by the Si Ball [22], a 47r array of silicon detectors, which was mounted at the center of NORDBALL. It consists of seventeen AE detectors of 170 urn thick silicon surrounding the target, and the total detection efficiencies for the protons and a-particles were 80% and 65%, respectively. Details are described in a separate paper [22]. The evaporated neutrons were detected by six NE213 liquid scintillators [23]. One detector was placed at 0” to the beam direction, and the others at 63”. For an event to be accepted it was required that at least one charged particle and at least two y-rays were detected in the Si Ball and in the Ge detectors, respectively. In this experiment a total of 230 million events were accumulated. In the off-line analysis the 0.7 million events with 3 protons and 1 neutron were Doppler-corrected and sorted into a two-dimensional E, versus E,, matrix. An angular correlation matrix of y-rays detected at 37” or 143” versus the ones detected at 79” or 101” was also created using the same 3pln gate. In order to remove y-rays from the contaminating 4pn reaction channel cglSr), which is the strongest impurity in the 3pln matrix, the 4pln matrix was produced in the same way and subtracted from the 3pln matrix with a proper multiplying factor. These “cleaned” matrices were used in the analysis as well as the “original” matrices. To establish the low-lying structure of 82Y, further experiments were performed at the Kyushu University Tandem Accelerator Laboratory. The same combination of target and beam was used and a lower bombarding energy was selected to suppress other reaction channels. Single y and yy coincidence measurements were performed with a selection on the number and type of evaporated particles. Two pure Ge detectors with a thin beryllium window were placed at _t90” to the beam direction. An NE213 liquid scintillator placed at 0” was used as a neutron detector, and PID (particle identification) signals for charged particles were provided by the Si Ball. A 58Ni target enriched to 99.76% was bombarded with a 28Si beam at energies of 100 and 102 MeV. The 0.9 mg/cm* thick target had a gold backing with a thickness of 11 mg/cm* which was thick enough to stop the beam and the evaporation residues,
J. Mukai et al. / High spin states
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but allowed most of the protons and a-particles to pass through. A yy coincidence gate width of 2 l.~swas set to observe delayed y-rays. An angular distribution measurement was performed with a pure Ge detector at 30”, 45”, 60”, 75” and 90” relative to the beam direction in the horizontal plane. Another Ge(Li) detector was fixed at -90” to monitor the beam intensity by measuring the Coulomb excitation lines of 58Ni. An NE213 liquid scintillator was placed at 0” for detection of neutrons. In this measurement the target was 2 mg/cm2 thick with 20 mg/cm2 thick gold backing. The beam energy was 100 MeV in the angular distribution measurement.
3. Results 3.1. High-spin states Table 1 is a list of y rays assigned to 82Y in the NORDBALL experiment. Energies and relative intensities were determined mainly from the projection of the original 3pln matrix, while peaks overlapped by lines from the 4pn channel were analyzed by use of the cleaned matrix. For the doublets and very weak lines, spectra gated by coincident -y-rays were also used when determining the -y-ray energies and intensities. For the intensities of inseparable peaks, only upper limits are shown. The y-rays with energies of 109.7 keV and 166.7 keV are overlapped by the delayed (and therefore broadened due to Doppler correction) 106.4 keV and 171.4 keV -y-rays, respectively. From coincidence relations these -y-rays were classified into four groups, and summed spectra gated on strong lines in each group are shown in Fig. 1. Fig. 2 shows the level scheme of 82Y deduced from this experiment. The 32.6 keV transition indicated by the dotted line was not observed in this experiment because of the energy threshold, but it was confirmed in other experiments as described in the next subsection. Excitation energies, spins, parities and half lives of the band heads will also be discussed there. Delayed y-rays were only very weakly observed in this experiment, since the maximum allowed time between two y-rays was set to about 120 ns. It was difficult to gate on the 1337 keV and 1369 keV transitions in band 3 because of their weak intensities and nearby stronger peaks (1346 keV in band 2 and 1363 keV in band 4). Their cascade relation is hence rather tentative especially as for their ordering, although they were undoubtedly confirmed to be in coincidence with low-lying transitions in the band. The multipolarity of the y-rays was investigated by directional correlation of oriented nuclei (DCO) [24]. In this experiment the DC0 ratio is defined as I, at 37” gated by yG at 79” R
DCo = Z, at 79” gated by yG at 37” ’
J. Mukai et al. / High spin states
206
Table 1 Gamma-ray energies, intensities, excitation energies of initial states, DC0 ratios, deduced spin changes and band assignments determined from data obtained in the NORDBALL experiment. Intensities are normalized to the 243.9 keV transition.
E, (keV) 109.7 (1) 166.7 (8) 211.3 (1) 243.9 (1) 276.1 (5) 278.2 (6) 320.3 (4) 370.2 (1) 395.5 (1) 442.6 (2) 445.1 (3) 448.9 (5) 594.3 (1) 730.8 (1) 789.3 (1) 813.2 (1) 838.2 (1) 914.4 (1) 964.6 (3) 1010.5 (3) 1061.5 (1) 1072.8 (1) 1124.0 (1) 1171.8 (1) 1211.0 (3) 1252.8 (1) 1264.4 (2) 1313.6 (3) 1336.7 (3) 1346.0 (2) 1362.8 (2) 1368.5 (8) 1410.3 (4) 1422.1 (4) 1458.2 (3) 1492.3 (8) 1522.0 (3) 1601.3 (2) 1666.8 (4) 1751.4 (3) 1851.8 (8) 1952.1(4) 2072.7 (4) 2196.8 (8)
a
b b b
b b b
b b
b
b
b
IY
E, (keV)
R DC0
AJ
Band
< 73 < 62 67.6 (6) 100.0 < 43 < 43 16 (3) b 51.0 (6) 63.8 (7) ll(2) b < 15 <8 37.9 (7) 30.6 (7) 40.6 (7) 52.5 (8) 98.7 (11) 42.3 (8) 28 (3) b 30 (4) b 41.5 (9) 25.5 (7) 20.5 (7) 58.9 (10) 24 (3) b 31.0 (9) 17 (3) b 43.1 (10) 12.1 (25) 15.0 (7)
511.9 (2) 678.8 (6) 718.7 (3) 751.5 (2) 678.8 (6) 957.0 (5) 2970.8 (8) 1960.3 (5) 1147.1 (4) 1589.7 (3) 957.0 (5) 957.0 (5) 1273.1 (7) 1687.8 (6) 2062.4 (8) 1960.3 (5) 1589.7 (3) 2602.2 (7) 3027 (1) 2970.8 (8) 2651.2 (4) 3675.0 (8) 4151(l) 4142.6 (9) 4886 (1) 3904.0 (5) 5415 (1) 5456 (1) 6223 (1) 5250.0 (7) 6778 (2) 7591(2) 8189 (2) 6672 (1) 6914 (2) 9681 (3) 8194 (1) 8516 (2) 9861(2) 10267 (2) 11713 (3) 12219 (2) 13785 (3) 14416 (3)
0.77 (16)
(1)
3 4-3 l-2 2 4 3-4 l-t2 1+2 1 2-l 3 3+2 4 3 4 1 2 3 4 1 2 3 4 1 3 2 4 1 3 2 4 3 4 2 1 4 2 1 2 1 2 1 2 1
9 (2) b 12 (4) b 5 (2) b 14.0 (8) 32 (2) b 3.9 (9) 9.1 (7) 16.5 (9) 7.0 (7) 12.2 (8) 5.7 (8) 5.8 (6) 3.6 (13) b 4.0 (4)
0.50 0.95 0.88 0.68 0.65 0.56 0.43 0.38 1.06
(6) (7) (20) (22) (11) (6) (4) (10) (16)
1.01 0.96 1.02 0.88 1.08 1.13 0.91 0.97 1.11 0.82 1.11 1.07 1.17 1.08 1.01 1.10 1.25 1.04
(13) (14) (13) (15) (14) (18) (18) (12) (18) (17) (24) (15) (52) (26) (36) (22) (80) (29)
1 & (1) 1 1 1 1 2 2 2 & 2 2 2 2 & 2 & 2 2 2 (2) 2
0.91 (32) 1.01 (33)
(2) (2)
0.92 (34) 0.75 (25) 1.15 (44)
(2) (2) (2)
a Calculated from the energy difference between two levels. b Determined from gated spectra.
J. Mukai et al. / High spin states
207
counts
400 300 200
100 0 (c) band 3
0
Fig. 1. Summed
0.4
spectra
gated
0.8
1.6
2.0
on the y-rays in band 1 (a), 2 @I, 3 Cc) and 4 Cd). The gating indicated by a filled circle.
2.4
y-rays
are
208
J. Mukai et al. / High spin states
where 2, is the intensity of the -y-ray of interest and yG is an immediately higher-lying transition assumed to be an E2. The angles 143” and 101” are treated as equivalent to 37” and 79”, respectively. The ratio is 1 for pure E2 transitions. Ratios for dipole transitions depend both on the mixing ratio and the degree of nuclear alignment, but would be = 0.6 for most Ml/E2 transitions near the yrast line. The results are listed in Table 1. Each band is confirmed to consist of AJ = 2 transitions as expected for a rotational-like structure. For the highest-lying transitions in all the bands (1751.4, 1952.1, 2196.8 in band 1; 1851.8, 2072.7 in band 2; 1368.5 in band 3; 1362.8, 1410.3 and 1492.3 keV in band 4) the multipolarities could not be determined experimentally but they were assumed to be stretched E2 transitions in the spin-parity assignments in the level scheme. Band 1 and 2 are the yrast sequences with odd and even spin, respectively, and have larger intensities than band 3 and 4. In the high-spin region the levels in band 1 are pushed down compared to band 2, suggesting that band 1 is the favored signature. These two bands are connected by several AJ = 1 inter-band transitions. Transitions from the favored band 1 to the unfavored band 2 are stronger than those in the opposite direction. This non-symmetric pattern has also been observed in the yrast band of the odd-odd nucleus 74Br (ref. [17]). No interband transitions were observed beyond the J = 14 level. Band 3 and 4 also have AJ = 2 in-band and AJ = 1 inter-band transitions, although it was difficult to determine the DC0 ratios for the low-lying transitions in these bands. Band 3 and 4 are considered to be yrare sequences with odd and even spins. Both signatures have nearly the same intensities, but band 4 seems to be slightly more favored and extends up to a higher spin than band 3. The strength of the inter-band transitions in these bands could not be determined because of many overlapping peaks. The 448.9 keV y-ray which is the transition from the 957.0 keV level in band 3 to the lowest level in band 2 was observed, but no other transitions connecting band 3 and 4 with band 1 and 2 were found. This indicates that the yrast and yrare states have rather different configurations. 3.2. Low-spin states Fig. 3 is a spectrum of y-rays observed at the beam energy of 102 MeV in coincidence with three protons and one neutron, and is an almost pure spectrum of 82Y. Energies a nd relative intensities of y-rays assigned to *‘Y are given in Table 2, and a level scheme was constructed as shown in Fig. 4. A cascade consisting of the 32.6 keV and 211.1 keV transitions competes with the 243.8 keV transition from the 751.4 keV to the 507.6 keV level. The 32.6 keV y-ray was weak due to the large probability of internal conversion, and was observed only in gated spectra. Although the relative ordering of the cascade is an important point in the evaluation of band 1 and 2, it could not be determined in the present experiments.
.I. Mukai et al. / High spin states
209
band 1 G7+1 band 2 13785
--I--
(26’)
2193.8
(25’)
122 9
,“,“y,, -i
1952.1 1851.8 c23+1
l&67
band 4 9861
I
(22’)
---I-
1751.4
I
1666.8
1452.3
(21’)
856 --I
(22-I
9681
I
m-)
8189
band 3
-I-
1801.3 1522.0 (19’)
6914
(18+)
+
14k.2
(l-T+)
5456 -+
=-i-
1313.6
1368.5
I
1362.8
1422.1
---I5250.0
(16’)
1346.0
---I1171.8
---I3904.0
1+8
(14’)
1124.0 3021
1072.8
1
(12-I
I
96f.6 x62.4 1687.8 J.
(9-I
F.8
Fig. 2. Level scheme of 82Y. See also Fig. 4.
1
(10-I
ti.3 1213.1 4
(8-I
.I. Mukai et al. / High spin states
210
gate:3pln i
400
600
channel
800
1000
1200
number
Fig. 3. G~ma-ray spectrum in coincidence with three protons and one neutron at a beam energy of 102 MeV. Delayed y-rays are slightly reduced in this spectrum because of the 500 ns wide (charged particle-)y coincidence requirement.
Table 2 Gamma-ray energies, intensities, excitation energies of initial states, A, coefficients and deduced spin changes determined from data obtained in the lower beam energy experiments. E, (keW 32.6 (3) 63.7 (3) 64.3 (3) 65.7 (2) 87.5 (1) 88.9 (2) 106.4 (1) 107.9 (2) 109.2 (1) 142.3 (1) 166.5 (2) 171.4 (1) 194.6 (1) 211.1(2) 243.8 (2) 250.2 (1) 276.6 (3) 278.7 (3) 313.7 (1) 337.1 (2) 395.2 (2) 443.0 (5) 445.0 (3) 449.6 (3) 813.1 (6) 837.9 (5)
E, (keW
G a
b b b b
7 (2) 23 (9) 17 (9) 21(Z) 55 (2) 16 (1) 48 (2) 8 (1) 20 (1) 100 4 (1) 50 (2) 51(Z) 35 (4) 40 (5) 27 (2) 3 (1) 4 (1) 43 (3) 25 (3) 29 (3) 6 (2) 10 (2) 10 (3) 13 (6) 28 (7)
a
b b
751.4 (5) 313.7 (1) 401.3 (2) 402.7 (3) 401.3 (2) 402.7 (3) 507.6 (3) 250.2 (1) 511.9 (5) 142.3 (1)
A,
Af
0.14 (4)
2
- 0.05 (3)
1
313.7 (1) 337.1 (2) 718.7 (5) 751.4 (5) 250.2 (1)
- 0.10 (5)
313.7 (1) 337.1 (2) 1146.6 (7)
0.13 (7) 0.13 (10) - 0.59 (21)
- 0.23 (5) -0.38 (9) ’ 0.20 (8) ’ -0.19 (13)
b b
a Determined from spectra gated by coincident y-rays. b Determined from a spectrum gated by the PID of 3pn. ’ Overlapped by a mixed dipole y-ray in 83Zr.
2 2 1
J. Mukai et al. / High spin states
751.4
(8+)
718.7
(7+)
507.6
”
211
137Go)nPtf 106.4
..,,,&C4+1 337.1 313.7
87.5
i
J 63.7
250.2
(2)
194.6
107.9
337.1 ”
142.3
171.4 313.7
”
(2+) 250.2 142.3
0
W
”
” 82
39
”
1+
Y 43
Fig. 4. Lower portion of the level scheme of *‘Y. Measured half-lives of three isomeric states at 401.3, 402.7 and 507.6 keV are given in the figure.
New data communicated to us by ref. 1251 establish the 33 keV y-ray as the higher-lying transition and the 211 keV as the lower one. This level ordering is adopted in Fig. 4 and the intermediate state lies at 718.7 keV. Half-lives of the levels at 401.3 keV, 402.7 keV and 507.6 keV were extracted from time distributions of the deexciting y-rays in the ny and yy coincidence measurements. All other states in the scheme were found to have a shorter lifetime than the detection limit in this setup, that is about a few ns. The spin-parity of the ground state of 82Y has been investigated through its p-decay by Lister et al. [26] and by Della Negra et al. [27]. In those references, allowed p-transitions to the ground O+, first 2+, second 2+ and excited O+ states in 82Sr have been reported, and the ground state has been determined to have a spin and parity of 1+. The J” assignments of the excited states were obtained by measuring the angular distribution of the y-rays. In some cases, measured lifetimes
212
J. Mukai et al. / High spin states
and conversion coefficients derived from the intensity balance of -y-rays were also needed. The angular distributions were fitted to the polynomial expression: w(e)
=A,[1
+A,P,(cos
8) +A,P,(cos
e>] 7
where Pk are Legendre functions of kth order. In the present analysis, A, was set to zero because it rapidly decreases as the spin alignment is attenuated [28]. In fact, the anisotropy of y-rays below the isomeric states was small, indicating an attenuation of the alignment. Fitted values of A, together with deduced spin changes are tabulated in Table 2. Although the A, coefficients only are insufficient to determine transition multipolarity, their signs are expected to be positive for stretched quadrupole (AJ = 2) and non-stretched dipole (AJ = 0) transitions, and to be negative for pure dipole and most of the mixed AJ = 1 transitions. The 250.2 keV transition is assigned to AJ = 1 by the negative A,, although the experimental uncertainty is large. The spin value of the initial state is thus limited to 0 or 2 as the final state has J” = 1+. The observed anisotropy of this y-ray excludes an initial spin of 0, therefore J = 2 is proposed for the 250.2 keV level. A cross-over transition from the 313.7 keV level to the ground state competes with the cascade of two AJ = 1 transitions with energies of 171.4 keV and 142.3 keV. Since the 313.7 keV y-ray is a transition with AJ = 0 or 2, the multipolarity of the cross-over and the cascade transitions are strongly suggested to be E2 and Ml(/E2), respectively. The most probable assignment of the spin and parity is 2+ for the 142.3 keV level and 3+ for the 313.7 keV level. A similar argument can be applied for the 337.1 keV cross-over and the 194.6 keV and 142.3 keV cascade transitions. Therefore the 337.1 keV level is also assigned to have J” = 3+. It was difficult to extract reliable angular distributions for the y-rays deexciting the close-lying levels at 401.3 keV and 402.7 keV due to their closeness in energy. In this case, conversion coefficients were taken into account. The theoretical conversion coefficients [29] for a 65 keV y-ray are 0.38, 0.67 and 5.4 for El, Ml and E2 multipolarities, respectively. These values for a 88 keV -y-ray are 0.16, 0.67 and 1.5. The intensity balance between feeding and deexciting y-rays of the 401.3 keV level requires Ml multipolarity for the 64.3 keV and 87.5 keV transitions. The partial half-lives of 106 ns for the 64.3 keV y-ray and 33 ns for the 87.5 keV y-ray also indicate an Ml/E2 nature considering the theoretical values [29] which are as follows: 79 ps (Ml; 65 keV), 22 l~,s(E2; 65 keV), 32 ps (Ml; 88 keV) and 4.7 ~J.LS (E2; 88 keV). By considering that the y-rays feeding into the 3+ states are Ml/E2 mixed transitions, the spin and parity of the 401.3 keV level is proposed to be 4+. The 65.7 keV and the 88.9 keV y-rays are shown to be dipoles from the intensity balance with the 109.2 keV y-ray. In addition, the long lifetime observed for the 402.7 keV level suggests an El multipolarity which is often known to be hindered by lop2 N 10e6 (ref. [30]). The spin and parity of the 402.7 keV level is therefore restricted to be 2-, 3- or 4- considering the final states have J” = 3+. A
J. Mukai et al. / High spin states
213
4- assignment is most plausible since neither transitions feeding the 2+ state at 142.3 keV nor the l+ ground state are observed. The 402.7 keV level is the band head of the yrare sequence observed in the NORDBALL experiment and its spin value is expected to be similar to the band-head spin of the yrast sequence (assigned to be 6 in the following), because of the considerable intensities of band 3 and 4. A spin value of 4 is therefore reasonable for this state. The 106.4 keV y-ray deexciting the 507.6 keV level is considered to be a stretched quadrupole transition, according to the positive A, coefficient and the long lifetime of the level. The intensity balance with the direct feeding y-rays with energies of 211.1 keV and 243.8 keV requires a conversion coefficient of about 1 for the 106.4 keV y-ray, which agrees with the theoretical value [29] of 0.91 for an E2 transition. Hence, the 106.4 keV transition is probably an E2 with a strength of 14 Weisskopf units [29]. The collectivity of this transition is small and it may not be proper to include it as a band member although it is a stretched E2. The 507.6 keV level, which is the band head of the yrast sequence of the NORDBALL experiment, is thus assigned to have J” = 6+. The 211.1 keV and 243.8 keV y-rays feed the 507.6 keV level. These peaks are contaminated by the dipole transitions at 209.7 keV and 243.2 keV in 83Zr (ref. [S]), which contribute by about 30% of total peak areas. In spite of these contaminations, the angular distributions show a multipolarity of Ml/E2 for the 211.1 keV and E2 for the 243.8 keV y-rays, which is consistent with the results of the DC0 analysis previously described. The 718.7 keV and 751.4 keV levels are thus assigned to have J” = 7+ and 8+, respectively. The 32.6 keV transition from the 751.4 keV to the 718.7 keV level is therefore assigned to the Ml multipolarity. A conversion coefficient 1291 of about 5 for a pure Ml transition is sufficient to explain the weakness of the 32.6 keV -y-ray which has an intensity of 20% of the 211.1 keV -y-ray. The angular distribution of the 395.2 keV y-ray shows dipole multipolarity, which is also consistent with the DC0 analysis. Higher-lying transitions were only very weakly populated and angular distributions were not obtained.
4. Discussion 4.1. Configurations at low excitation Single-particle 2P l/2 and lf,,* 2d 5,2 neutron There is a nuclei near N first excitation
levels around nucleon number 39 and 43 are from the lg,,,, shells [l]. At large deformation the 2p,,, proton orbitals and the orbitals should also be considered. lot of data for low-lying states of odd-A yttrium isotopes. In the = 50 the ~r,~ shell-model state is lowest and the g,,, state of the is at 909 keV in 89Y, 381 keV in 87Y and 20 keV in 85Y (ref. [311). In
214
J. Mukai et al. / High spin states
83Y (ref. [5]) the spin-parity of the ground state is + ’ and it has been assigned to the K= $ state in the g,,, shell. The first excited state at 62 keV has been assigned to f,,,[3011~. In ‘lY (ref. [lo]) and 79Y (refs. [34,351) the ground state has been assigned to + + from the g,,, shell. The first excited state at 113 keV in ‘lY has been proposed to be 5 - or $-, coming from the f5,* shell. In addition to the proton levels, various single-neutron states at low excitation energy have been observed in N = 43 isotones with odd mass. In 83Zr, ‘lSr and 79Kr the spin-parity of the ground state is $- and has been assigned to the p,,,[301]~orbital [6-9,131. In those nuclei a J” = I’ state based on the g,,,[422]+ ’ (or [4131; ‘> h as b een observed at about 100 keV excitation energy. The f,,,[301]~- state has been observed at 53 keV in 83Zr and at 384 keV in 79Kr, while the f,,,[303]$state appears at 79 keV in ‘lSr and at 147 keV in 79Kr. The J” = i(+) state at 120 keV in “Sr has been proposed to have the ds,J431]~+ configuration. Such a variety of single-particle orbitals may sufficiently reproduce spin-parities of the complex low-lying states in 82Y. The most probable candidate of the configuration of the J” = 1+ ground state is rg,,2[422]$+@ vg,,,[413]5+ or 7rf,,2[301]$ -@ vp,,,[3011~ -. 4.2. Band I and 2 The band head configuration of band 1 and 2 is most likely rrg,,, @ vg9,2 or =g,/, Q vdg,z since other combinations of orbitals in consideration would fail to compose a J” = 6+ state. The last proton occupies an orbital in the middle of the g,,, shell while the neutron is in the upper half of the g,,, or at the bottom of the d 5,2. As the angular momentum of the d5,2 neutron is more or less opposite to that of the g 9,2 proton, it is difficult to form the total spin of 6. On the other hand, two g,,, nucleons can easily make a J = 6 state, e.g. a proton in the R = $ orbital and a neutron in L! = 5. In the neighboring isotones the g,,, band has been observed as the yrast band [7-9,131, thus it is natural to assume that the unpaired neutron in the yrast band of 82Y occupies a g,,, orbital as well as the unpaired proton. In the paper about 74Br (ref. [17]) it is described that rigid rotation is not expected below the spin of j, + j, because energies of low-lying states are shifted by realignment of the intrinsic spins. In fact, a transition from non-collective to collective phase has been observed at J = 9 in 74Br (ref. 1171)and at J = 11 in 76Br (ref. [181), for which nuclei of both the unpaired proton and the neutron are considered to occupy a g9,2 orbital and hence j, + j, = 9. For the yrast states in 82Y a typical rotational band is constructed above J = 8, which is close to j, +>, = 9. Since band 1 and 2 are connected by A J = 1 inter-band transitions, these bands are probably signature partners. In this case, the odd-spin (a = 1) sequence is
215
J. Mukai et al. / High spin states
-3
0
0.5
1.0
1.5
tiw( MeV) Fig. 5. Kinematic (top) and dynamic ~middIe~ moments of inertia and experimental routhian (bottoms of the yrast band. Reference parameters in the routhian plot are taken as J, = 20.0 h2 MeV-’ and J, = 0.
expected to be energetically favored because the favored signature of a g9,* nucleon should be + 3 in the cranking model, and in fact, the positive signatures of g9,2 band behave as favored sequences in both odd-2 and odd-N nuclei in this mass region [2-111. Indeed, band 1 composed from odd-spin states is lowered relative to band 2 above the 8+ state. Signature inversion is seen at the 7+ state, which is a lower spin value than those of the inverting points in the odd-odd neighbors [17-201. Fig. 5 shows f O), kinematical moments of inertia, J(*), d~amical moments of inertia, and e’, experimental routhians, for band 1 and 2. To calculate these values the K quantum number is assumed to be the same as the band-head spin, that is, 6. The selection of K does not give any serious effect in high-spin region, especially to relative values such as signature splitting. Reference parameters of J, = 20.0 h* MeV-* and J, = 0 are chosen only to emphasize the splitting, and do
216
J. Mukai et al. / High spin states
not represent a reasonable vacuum configuration. The Jo) in band 2 has a sharp rise starting at hw = 0.6 MeV, in contrast to the gradual increase in band 1 at the same frequency. These rises correspond to the sharp and broad peaks around hw = 0.65 MeV in the J(‘) plots for band 2 and 1, respectively. After this rise, Jo) of band 2 closely approaches to that of the band 1 and almost degenerates. On the other hand, the splitting of the routhian increases as the rotational frequency increases in the region below 0.6 MeV, and above this point shows a nearly constant value of = 500 keV. In the 2 = 37 nucleus 79Rb, moments of inertia and routhians for both signatures of the yrast rg9,2 band have very similar behavior to those of band 1 and 2, as shown in Figs. 8 and 10 of ref. [14]. The signature splitting between band 1 and 2 is hence suggested to be caused by the unpaired proton in the same orbital as in the 79Rb case. The configurations of band 1 and 2 are considered to be rg9,*, CY= + + CSyg9,z, (Y= + i and rrg9,2, (Y= - ; @ ugg,*, (Y= + i, respectively. The
0.5
1.0
J 1.5
Aw( MeV) Fig. 6. Same as Fig. 5 but for the yrare band.
J. Mukui et al. / High spin states
217
property of the yrast band in 79Rb has been theoretically investigated in ref. 1341. In this ref. the irregular point observed in moments of inertia and routhians in both signatures is interpreted to correspond to the first crossing caused by an alignment of g9,2 neutron pair. Total routhian surface (TRS) calculations [34] have shown a stable prolate shape of p = 0.33 in 79Rb at low spin. In the calculations this shape is conserved at higher spin in the favored band, while a clear change to a nearly oblate shape has been shown at the band crossing in the unfavored band. The crossing at fro = 0.65 MeV observed in the yrast bands in 82Y is probably caused by an alignment of g9,2 neutrons, as in 79Rb, although the nuclear shape has not been determined for 82Y. The unpaired neutron in a g,,,, orbital is expected to block the first alignment of g,,, neutrons. It is not clearly understood why the alignment occurs in “Y at nearly the same frequency as in a non-blocked system 79Rb. This may be explained as a shift of the crossing frequency by different shape in the two nuclei. Another possibility is that the aligning neutrons of both nuclei are not in a g,,, orbital but in ds,z, which has been proposed as the lowest neutron state in a N = 42 system at p2 = 0.35, y = - 7” as given in Fig. 18 of ref. 111. As the unpaired neutron in a g,,,, orbital does not block d,,,, neutron alignments, the first crossing in ‘*Y may occur at the same frequency as in N = 42 79Rb. However, calculations of theoretical routhians are necessary to pursue these explanations. The signature splitting between the band 1 and 2, which is considered to arise from the unpaired g 9,2 proton, can be compared to that of rg9,* bands in 2 = 39 isotopes. In 83Y the splitting in energy has been observed to be about 500 keV up to hw = 0.8 MeV (ref. [35]), which is very close to that of 82Y. In “Y the unfavored band has been established only at lower spin region (ho = 0.4 MeV), and the splitting is about 250 keV (ref. [lo]). 4.3. Biznd 3 and 4 Band 3 and 4 are considered to be the signature partners of a yrare band. Fig. 6 shows J(l), JC2)and e’ for them. The signature splitting is much smaller than that of the yrast band, about 100 keV. Such a small energy splitting can not be considered resulting from g9,2 nucleon, because g,,,* bands show large signature splitting of several hundreds keV for both odd-proton and odd-neutron systems in this mass region [5-101. It is very probable that one unpaired nucleon occupies a negative-parity orbital with small j (therefore small signature splitting), and its anguiar momentum couples to that of another odd nucleon in a g,,, orbital to compose the K” = 4- band head. In .7(i) for both signatures there is an abrupt increase which gives a sharp peak in 3”’ around ho = 0.65 MeV, nearly the same as the crossing frequency in the yrast band. Such a rapid increase of Jo’ in both signatures has not been reported in neighboring nuclei. However, a number of levels could be identified in “Y tarp
218
J. Mukai et al. / High spin states
channel) in the present data [36], and it was found that the first alignment occurs at hw = 0.67 MeV in the favored signature of the yrast band, giving a rapid increase in Jo) similarly to the 82Y case. The alignment in band 3 and 4 of 82Y may be due to g,,, neutrons as same as in "Y . It may be considered that the unpaired neutron occupies a negative-parity orbital and hence does not block the g,,, neutron alignment. In ‘lSr (ref. [9]> and 83Zr (ref. [7,8]) the yrare band is built on a J” = $- state coming from the f5,2 shell. In these K" = $- bands the LY= - i sequence is slightly favored, and the magnitude of the signature splitting is about 60 keV in ‘lSr (ref. [9]) and 150 keV in s3Zr (ref. [7]). Combined to the favored signature of + i for a g,,, proton, the f5,2 neutron will make the LY= 0 sequence as a favored band in 82Y. Indeed, band 4 of the even-spin sequence was observed to be favored relative to band 3. The most probable configurations for band 3 and 4 are rgg,2, (Y= ++f cr = + $ and rrg9,2, (Y=+i@)Vf 5/27 a = - $, respectively. S/2) These assignments of the negative-parity states indicate only the main components as they are not pure states due to the level mixing.
5. Summary Excited states in 82Y were investigated through two types of experiments. Delayed coincidence measurements of particle-y and yy were effective to construct the low-lying level structure including the band heads of the high-spin bands. On the other hand, high-spin structures were established by a prompt coincidence measurement with higher incident energy. Four rotational bands were observed up to the highest spin among odd-odd nuclei in this mass region. Two of the bands were identified as signature partners and they are the yrast states. The magnitudes of moments of of m,/, Q %9/2, inertia are similar to those of neighboring nuclei. Large signature splitting was observed likewise in g,,, bands of the odd-A neighbor. Signature inversion at low spin, which is a rather common feature in odd-odd nuclei [17-20,371, was observed only for the lowest state of the yrast band. A band crossing of very similar behavior with 79Rb was observed at nearly the same rotational frequency in the 79Rb case for both signatures. It is not clear yet whether this is the non-blocked first crossing or the second crossing shifted to a lower frequency. Two other bands were considered to be signature partners, probably with negative parity. There is a small signature splitting between them, which is similar to the negative-parity bands in odd-A neighbors. An onset of band crossing was seen at the highest spin observed for both signatures. For the comparison with theoretical predictions it is important to determine the nuclear shape experimentally, because the properties of a quasi-particle diagram such as crossing frequencies predicted by calculations strongly depend on the
J. Mukai et al. / High spin states
deformation parameters. necessary.
Further experiments including lifetime measurements
219
are
We would Iike to thank Dr. W. Nazarewicz for helpful discussions and the Niels Bohr Institute for its hospitali~. We gratefully ac~owledge Prof. S.L. Tabor (FSU) for access to his unpublished data on “Y (ref. [2.5]) and the Nuclear Physics referees for pointing out their existence. This work was partly supported by the Japanese government (grant numbers: 01044037 and 024520271, the Danish Natural Science Research Council and the Swedish Natural Science Research Council. One of us (S.M.) was also supported by the Yamada Science Foundation.
References [I] W. Nazarewicz, J. Dudek, R. Bengtsson and I. Ragnarsson, Nucl. Phys. A435 (1985) 397 [2] J. Panqueva, H.P. Hellmeister, L. Liihmann, F.J. Bergmeister, K.P. Lieb and T. Otsuka, Nucl. Phys. A389 (1982) 424 [3] C.J. Lister, B.J. Varley, H.G. Price and J.W. Olness, Phys. Rev. Lett. 49 (1982) 308 [4] J. Heese, K.P. Lieb, S. Ulbig, B. Wormann, J. Billowes, A.A. Chishti, W. Gelletly, C.J. Lister and B.J. Varley, Phys. Rev. C43 (1990) 603 [S] C.J. Lister, B.J. Varley, W. Fieber, J. Heese, K.P. Lieb, E.K. Warburton and J.W. Olness, Z. Phys. A329 (1988) 413 [6] W. Fieber, K. Bharuth-Ram, J. Heese, F. Cristancho, C.J. Gross, K.P. Lieb, S. Skoda and J. Eberth, Z. Phys. A332 (1989) 363 [7] U.J. Hiittmeier, C.J. Gross, D.M. Headly, E.F. Moore, S.L. Tabor, T.M. Cormier, P.M. Stwertka and W. Nazarewicz, Phys. Rev. C37 (1988) 118 [8] S. Suematsu, Y. Haruta, B.J. Mitt, K. Heiguchi, Y. Ishikawa, S. Mitarai, T. Kuroyanagi and Y. Onizuka, Nucl. Phys. A485 (1988) 304 [9] E.F. Moore, P.D. Cottle, C.J. Gross, D.M. Headly, U.J. Hiittmeier, S.L. Tabor and W. Nazarewicz, Phys. Rev. C38 (1988) 696 [lo] C.J. Lister, R. Moscrop, B.J. Varley, H.G. Price, E.K. Warburton, J.W. Olness and J.A. Becker, J. of Phys. Gil (1985) 969 [II] A.A. Chishti, W. Gelletly, C.J. Lister, J.H. McNeill, B.J. Varley, D.J.G. Love and 6. Skeppstedt, Nucl. Phys. A501 (1989) 568 [12] C.J. Gross, P.D. Cottle, D.M. Headly, U.J. Hiittmeier, E.F. Moore, S.L. Tabor and W. Nazarewicz, Phys. Rev. C36 (1987) 2601 1131 R. Schwengner, J. Doring, L. Funke, G. Winter, A. Johnson and W. Nazarewicz, Nucl. Phys. A509 (1990) 550 [14] (i. Skeppstedt, C.J. Lister, A.A. Chishti, B.J. Varley, W. Gelletly, U. Lenz, R. Moscrop and L. Goettig, Nucl. Phys. A511 (1990) 137 [15] A.A. Chishti, W. Gelletly, C.J. Lister, B.J. Varley and 8. Skeppstedt, J. of Phys. G16 (1990) 481 [16] E.F. Moore, P.D. Cottle, C.J. Gross, D.M. Headly, U.J. Hiittmeier, S.L. Tabor and W. Nazarewicz, Phys. Lett. B211 (1988) 14 [17] J.W. Holcomb, T.D. Johnson, PC. Womble, P.D. Cottle, S.L. Tabor, F.E. Durham and S.G. Buccino, Phys. Rev. C43 (1991) 470 [18] S.G. Buccino, F.E. Durham, J.W. Holcomb, T.D. Johnson, P.D. Cottle and S.L. Tabor, Phys. Rev. C41 (1990) 2056 [19] G.C. Hicks, C.J. Gross, U.J. Hiittmeier, Xi-Ting Lu, G. Neuschaefer and S.L. Tabor, Phys. Rev. c30 (1984) 549
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H.C. Jain, J.A. Sheikh, Y.K. Agarwal and M.L. Jhingan, Phys. Rev. C47 (1993)
[21] E Moszyhski, J.H. Bjerregard, J.J. Gaardhoje, B. Herskind, P. Knudsen and G. Sletten, Nucl. Instr. Meth. A280 (1989) 73 [22] T. Kuroyanagi, S. Mitarai, S. Suematsu, B.J. Min, H. Tomura, J. Mukai, T. Maeda, R. Nakatani, G. Sletten, J. Nyberg and D. Jerrestam, Nucl. Instr. Meth. A316 (1992) 289 [23] S.E. Arnell, H.A. Roth, 6. Skeppstedt, J. Biatkowski, M. Moszynski, D. Wolski and J. Nyberg, Nucl. Instr. Meth. A300 (1991) 303 [24] KS. Krane, R.M. Steffen and R.M. Wheeler, Nucl. Data Tables 11 (1973) 351 [25] P.C. Womble, J. Doring, T. Glasmacher, J.W. Holcomb, G.D. Johns, T.D. Johnson, T.J. Petters, M.A. Riley, V.A. Wood and S.L. Tabor, Phys. Rev. C47 (1993) 2546 [26] C.J. Lister, P.E. Haustein, D.E. Alburger and J.W. Olness, Phys. Rev. C24 (1981) 260 [27] S. Della Negra, H. Gauvin, D. Jacquet and Y. Le Beyec, Z. Phys. A307 (1982) 305 [28] T. Yamazaki, Nucl. Data A3 (1967) 1 [29] E. Browne, J.M. Dairiki, R.E. Doebler, A.A. Shihab-Eldin, L.J. Jardine, J.K. Tuli and A.B. Buyrn, in Table of Isotopes, eds. CM. Lederer and V.S. Shirley, 7th ed. (Wiley, New York, 1978) Appendix V [30] P.M. Endt, At. Data Nucl. Data Tables 23 (1979) 547 [31] E. Browne, J.M. Dairiki, R.E. Doebler, A.A. Shihab-Eldin, L.J. Jardine, J.K. Tuli, A.B. Buyrn, in Table of Isotopes, eds. C.M. Lederer, V.S. Shirley, 7th ed. (Wiley, New York, 1978) [32] H. Grawel, P. Hoff, J.P. Omtvedt, K. Steffensen, R. Eder, H. Haas and H. Ravn, Z. Phys. A341 (19921 247 [33] J. Mukai, A. Odahara, R. Nakatani, Y. Haruta, H. Tomura, B.J. Min, K. Heiguchi, S. Suematsu, S. Mitarai and T. Kuroyanagi, Z. Phys. A342 (1992) 393 [34] R. Bengtsson, W. Nazarewicz, 6. Skeppstedt and R. Wyss, Nucl. Phys. A528 (1991) 215 [35] F. Cristancho, C.J. Gross, K.P. Lieb, D. Rudlph, 6. Skeppstedt, M.A. Bentley, W. Gelletly, H.G. Price, J. Simpson, J.L. Durell, B.J. Varley and S. Rastikerdar, Nucl. Phys. A540 (1992) 307 [36] S. Mitarai, T. Kuroyanagi, A. Odahara, J. Mukai, H. Tomura, S. Suematsu, T. Morikawa, D. Jerrestam, J. Nyberg, G. Sletten, A. Atac, S.E. Arnell, H. Roth and 6. Skeppstedt, Proc. 21st INS Int. Symp. on rapidly rotating nuclei, Tokyo, 1992, Nucl. Phys. A557 (1993) 381~ [37] T. Komatsubara, K. Furuno, T. Hosoda, J. Mukai, T. Hayakawa, T. Morikawa, Y. Iwata, N. Kato, J. Espino, J. Gascon, N. Gjorup, G.B. Hagemann, H.J. Jensen, D. Jerrestam, J. Nyberg, G. Sletten, B. Cederwall and P.O. Tjom, Proc. 21st INS Int. Symp. on rapidly rotating nuclei, Tokyo, 1992, Nucl. Phys. A557 (1993) 419~ and references therein
Nuclear Physics A568 (1994) 202-220 North-Holland
High-spin states in the odd-odd
nucleus 82Y
J. Mukai *, A. Odahara, H. Tomura, S. Suematsu, S. Mitarai, T. Kuroyanagi Department of Physics, Kyushu Uniuersity, Fukuoka 812, Japan D. Jerrestam Uppsala University, NFL, Studsuik, S-611 82 Nykijping, Sweden
J. Nyberg 2, G. Sletten, A. Atac 3 Niels Bohr Institute, DK-4000 Roskilde, Denmark
S.E. Arnell, H.A. Roth, 6. Skeppstedt Department of Physics, Chalmers University of Technology, S-412 96 GGteborg, Sweden
Received 23 February 1993 (Revised 5 July 1993)
Abstract
High-spin states in 82Y have been studied by the 5*Nl‘(*%,3pn) reaction at 128 MeV. Low-lying states were investigated by the same reaction but at a lower bombarding energy and the band heads of the high-spin sequences have been characterized. Four rotational bands forming two sets of signature partners were established. The yrast band was observed up to J” = 27” and shows large signature splitting, while a negative-parity yrare band, observed up to spin 22 shows a much smaller splitting. The yrast band structure was very similar to the g,,, proton band in 79Rb.
Key words: NUCLEAR REACTIONS 58Ni(28Si,n3p), E = 100, 102, 128 MeV; measured E,, I,,, Z,(O), (particle)y-, yy-coin. **Y deduced levels, J, rr. Enriched target, Ge detector array, particle-multiplicity filter.
1. Introduction
Neutron-deficient nuclei in the A N 80 region have been shown to be strongly deformed, and theoretical calculations [l] indicate the existence of a deformed ’ Present address: Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan. 2 Present address: The Svedberg Laboratory, Uppsala University, Box 533, S-751 21 Uppsala, Sweden. 3 Present address: Department of Radiation Sciences, Uppsala University, Box 535, S-751 21 Uppsala, Sweden. 0375-9474/94/$07.~ 0 1994 - Eisevier Science B.V. All rights reserved SSDI 037S-9474(93)E0415-5
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shell gap at nucleon number 38. Experimental data show a large deformation of the 2 _ 38 nuclei such as 79Rb (ref. 1211,77-80Sr (refs. [3,4]), 83Y (ref. [5]) and 83Zr (ref. [6]), while a transition from collective to single-particle motion has been observed around N = 44 (refs. [7-101). The orbital with largest angular momentum near the Fermi surface is g,,, for both protons and neutrons, and many g,,, bands have been established in odd-A nuclei as the yrast bands [2-151. From these experimental data the core-polarization effect of an odd nucleon has been investigated. This effect has been observed on soft cores of 76Kr (ref. [12]), 80Sr (refs. [9,16]) and 82Zr (ref. [61), and is known to depend on the geometrical configuration of the odd nucleon. Therefore it would be interesting to study the competing effects of the two nucleons in an odd-odd nucleus. Very little experimental data have been published for high-spin states in odd-odd nuclei in this mass region. Two bromine isotopes 74Br (ref. [17]) and 76Br (ref. [18]) have been well studied. In both nuclei the yrast band is based on a low-lying isomeric state with 1” = 4+, with the configuration assignment rg,,2 @ vg9,2. Regular rotational structure starts at J = 9 in 74Br and at J = 11 in 76Br, and at lower spin an inversion of the signature splitting has been observed. The authors of ref. [171 have suggested that at small angular momentum the total spin can be increased by both collective rotation and realignment of the intrinsic spins, causing a deviation from regular collective structure. Measurements of transition quadrupole moments have, however, shown that 74Br and 76Br have a large deformation both at low and high spins [17,18]. For 78Rb, the yrast band up to J = 15 has been reported [19], and a similar change from less regular structure to rigid rotation has been observed around spin 8. For the next odd-Z element, yttrium, no data had been published on high-spin states of the even-A isotopes until very recently. A new paper [20] has reported on the identification of a rotational structure in 84Y built on a 6+ isomeric state extending up to 21+. The excitation energy of the isomeric state is estimated to be in the range 0 N 500 keV. A large signature splitting in the band is observed and signature inversion happens for J < 11. There has been no data on lighter yttrium isotopes, which are especially interesting because both the unpaired proton and the neutron are expected to stay in the g,,, shell and can affect the core with similar strength. Although a dominance of single-particle structures is foreseen in the heavier isotopes of yttrium, 82Y with N = 43 is still expected to show collective features and is predicted as a good example to investigate the deviation from a simple rotor caused by two particles. In this work excited states in 82Y were identified and rotational structures were established up to spins 27+ and 22-. Four rotational bands were identified as two pairs of signature partners. These pairs are built on distinct isomeric band heads, the excitation energies of which were determined without ambiguity. The experimental data were analyzed in terms of the cranking model.
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2. Experimental procedure The nucleus ‘*Y was produced in the 58Ni(28Si,3pn) reaction at a beam energy of 128 MeV for the high-spin studies. The 58Ni target, enriched to 97%, consisted of two stacked self-supporting foils each with a thickness of 350 kg/cm*. The 28Si beam was provided by the tandem and booster accelerator at the Niels Bohr Institute. The fusion-evaporation residues were stopped in a gold foil placed 2 cm downstream from the target. Gamma rays were detected by twenty Compton-suppressed Ge detectors in the NORDBALL array [21]. Five Ge detectors were placed in each of the four rings at 37”, 79”, 101” and 143” relative to the beam direction. Charged particles were detected by the Si Ball [22], a 47r array of silicon detectors, which was mounted at the center of NORDBALL. It consists of seventeen AE detectors of 170 urn thick silicon surrounding the target, and the total detection efficiencies for the protons and a-particles were 80% and 65%, respectively. Details are described in a separate paper [22]. The evaporated neutrons were detected by six NE213 liquid scintillators [23]. One detector was placed at 0” to the beam direction, and the others at 63”. For an event to be accepted it was required that at least one charged particle and at least two y-rays were detected in the Si Ball and in the Ge detectors, respectively. In this experiment a total of 230 million events were accumulated. In the off-line analysis the 0.7 million events with 3 protons and 1 neutron were Doppler-corrected and sorted into a two-dimensional E, versus E,, matrix. An angular correlation matrix of y-rays detected at 37” or 143” versus the ones detected at 79” or 101” was also created using the same 3pln gate. In order to remove y-rays from the contaminating 4pn reaction channel cglSr), which is the strongest impurity in the 3pln matrix, the 4pln matrix was produced in the same way and subtracted from the 3pln matrix with a proper multiplying factor. These “cleaned” matrices were used in the analysis as well as the “original” matrices. To establish the low-lying structure of 82Y, further experiments were performed at the Kyushu University Tandem Accelerator Laboratory. The same combination of target and beam was used and a lower bombarding energy was selected to suppress other reaction channels. Single y and yy coincidence measurements were performed with a selection on the number and type of evaporated particles. Two pure Ge detectors with a thin beryllium window were placed at _t90” to the beam direction. An NE213 liquid scintillator placed at 0” was used as a neutron detector, and PID (particle identification) signals for charged particles were provided by the Si Ball. A 58Ni target enriched to 99.76% was bombarded with a 28Si beam at energies of 100 and 102 MeV. The 0.9 mg/cm* thick target had a gold backing with a thickness of 11 mg/cm* which was thick enough to stop the beam and the evaporation residues,
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but allowed most of the protons and a-particles to pass through. A yy coincidence gate width of 2 l.~swas set to observe delayed y-rays. An angular distribution measurement was performed with a pure Ge detector at 30”, 45”, 60”, 75” and 90” relative to the beam direction in the horizontal plane. Another Ge(Li) detector was fixed at -90” to monitor the beam intensity by measuring the Coulomb excitation lines of 58Ni. An NE213 liquid scintillator was placed at 0” for detection of neutrons. In this measurement the target was 2 mg/cm2 thick with 20 mg/cm2 thick gold backing. The beam energy was 100 MeV in the angular distribution measurement.
3. Results 3.1. High-spin states Table 1 is a list of y rays assigned to 82Y in the NORDBALL experiment. Energies and relative intensities were determined mainly from the projection of the original 3pln matrix, while peaks overlapped by lines from the 4pn channel were analyzed by use of the cleaned matrix. For the doublets and very weak lines, spectra gated by coincident -y-rays were also used when determining the -y-ray energies and intensities. For the intensities of inseparable peaks, only upper limits are shown. The y-rays with energies of 109.7 keV and 166.7 keV are overlapped by the delayed (and therefore broadened due to Doppler correction) 106.4 keV and 171.4 keV -y-rays, respectively. From coincidence relations these -y-rays were classified into four groups, and summed spectra gated on strong lines in each group are shown in Fig. 1. Fig. 2 shows the level scheme of 82Y deduced from this experiment. The 32.6 keV transition indicated by the dotted line was not observed in this experiment because of the energy threshold, but it was confirmed in other experiments as described in the next subsection. Excitation energies, spins, parities and half lives of the band heads will also be discussed there. Delayed y-rays were only very weakly observed in this experiment, since the maximum allowed time between two y-rays was set to about 120 ns. It was difficult to gate on the 1337 keV and 1369 keV transitions in band 3 because of their weak intensities and nearby stronger peaks (1346 keV in band 2 and 1363 keV in band 4). Their cascade relation is hence rather tentative especially as for their ordering, although they were undoubtedly confirmed to be in coincidence with low-lying transitions in the band. The multipolarity of the y-rays was investigated by directional correlation of oriented nuclei (DCO) [24]. In this experiment the DC0 ratio is defined as I, at 37” gated by yG at 79” R
DCo = Z, at 79” gated by yG at 37” ’
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206
Table 1 Gamma-ray energies, intensities, excitation energies of initial states, DC0 ratios, deduced spin changes and band assignments determined from data obtained in the NORDBALL experiment. Intensities are normalized to the 243.9 keV transition.
E, (keV) 109.7 (1) 166.7 (8) 211.3 (1) 243.9 (1) 276.1 (5) 278.2 (6) 320.3 (4) 370.2 (1) 395.5 (1) 442.6 (2) 445.1 (3) 448.9 (5) 594.3 (1) 730.8 (1) 789.3 (1) 813.2 (1) 838.2 (1) 914.4 (1) 964.6 (3) 1010.5 (3) 1061.5 (1) 1072.8 (1) 1124.0 (1) 1171.8 (1) 1211.0 (3) 1252.8 (1) 1264.4 (2) 1313.6 (3) 1336.7 (3) 1346.0 (2) 1362.8 (2) 1368.5 (8) 1410.3 (4) 1422.1 (4) 1458.2 (3) 1492.3 (8) 1522.0 (3) 1601.3 (2) 1666.8 (4) 1751.4 (3) 1851.8 (8) 1952.1(4) 2072.7 (4) 2196.8 (8)
a
b b b
b b b
b b
b
b
b
IY
E, (keV)
R DC0
AJ
Band
< 73 < 62 67.6 (6) 100.0 < 43 < 43 16 (3) b 51.0 (6) 63.8 (7) ll(2) b < 15 <8 37.9 (7) 30.6 (7) 40.6 (7) 52.5 (8) 98.7 (11) 42.3 (8) 28 (3) b 30 (4) b 41.5 (9) 25.5 (7) 20.5 (7) 58.9 (10) 24 (3) b 31.0 (9) 17 (3) b 43.1 (10) 12.1 (25) 15.0 (7)
511.9 (2) 678.8 (6) 718.7 (3) 751.5 (2) 678.8 (6) 957.0 (5) 2970.8 (8) 1960.3 (5) 1147.1 (4) 1589.7 (3) 957.0 (5) 957.0 (5) 1273.1 (7) 1687.8 (6) 2062.4 (8) 1960.3 (5) 1589.7 (3) 2602.2 (7) 3027 (1) 2970.8 (8) 2651.2 (4) 3675.0 (8) 4151(l) 4142.6 (9) 4886 (1) 3904.0 (5) 5415 (1) 5456 (1) 6223 (1) 5250.0 (7) 6778 (2) 7591(2) 8189 (2) 6672 (1) 6914 (2) 9681 (3) 8194 (1) 8516 (2) 9861(2) 10267 (2) 11713 (3) 12219 (2) 13785 (3) 14416 (3)
0.77 (16)
(1)
3 4-3 l-2 2 4 3-4 l-t2 1+2 1 2-l 3 3+2 4 3 4 1 2 3 4 1 2 3 4 1 3 2 4 1 3 2 4 3 4 2 1 4 2 1 2 1 2 1 2 1
9 (2) b 12 (4) b 5 (2) b 14.0 (8) 32 (2) b 3.9 (9) 9.1 (7) 16.5 (9) 7.0 (7) 12.2 (8) 5.7 (8) 5.8 (6) 3.6 (13) b 4.0 (4)
0.50 0.95 0.88 0.68 0.65 0.56 0.43 0.38 1.06
(6) (7) (20) (22) (11) (6) (4) (10) (16)
1.01 0.96 1.02 0.88 1.08 1.13 0.91 0.97 1.11 0.82 1.11 1.07 1.17 1.08 1.01 1.10 1.25 1.04
(13) (14) (13) (15) (14) (18) (18) (12) (18) (17) (24) (15) (52) (26) (36) (22) (80) (29)
1 & (1) 1 1 1 1 2 2 2 & 2 2 2 2 & 2 & 2 2 2 (2) 2
0.91 (32) 1.01 (33)
(2) (2)
0.92 (34) 0.75 (25) 1.15 (44)
(2) (2) (2)
a Calculated from the energy difference between two levels. b Determined from gated spectra.
J. Mukai et al. / High spin states
207
counts
400 300 200
100 0 (c) band 3
0
Fig. 1. Summed
0.4
spectra
gated
0.8
1.6
2.0
on the y-rays in band 1 (a), 2 @I, 3 Cc) and 4 Cd). The gating indicated by a filled circle.
2.4
y-rays
are
208
J. Mukai et al. / High spin states
where 2, is the intensity of the -y-ray of interest and yG is an immediately higher-lying transition assumed to be an E2. The angles 143” and 101” are treated as equivalent to 37” and 79”, respectively. The ratio is 1 for pure E2 transitions. Ratios for dipole transitions depend both on the mixing ratio and the degree of nuclear alignment, but would be = 0.6 for most Ml/E2 transitions near the yrast line. The results are listed in Table 1. Each band is confirmed to consist of AJ = 2 transitions as expected for a rotational-like structure. For the highest-lying transitions in all the bands (1751.4, 1952.1, 2196.8 in band 1; 1851.8, 2072.7 in band 2; 1368.5 in band 3; 1362.8, 1410.3 and 1492.3 keV in band 4) the multipolarities could not be determined experimentally but they were assumed to be stretched E2 transitions in the spin-parity assignments in the level scheme. Band 1 and 2 are the yrast sequences with odd and even spin, respectively, and have larger intensities than band 3 and 4. In the high-spin region the levels in band 1 are pushed down compared to band 2, suggesting that band 1 is the favored signature. These two bands are connected by several AJ = 1 inter-band transitions. Transitions from the favored band 1 to the unfavored band 2 are stronger than those in the opposite direction. This non-symmetric pattern has also been observed in the yrast band of the odd-odd nucleus 74Br (ref. [17]). No interband transitions were observed beyond the J = 14 level. Band 3 and 4 also have AJ = 2 in-band and AJ = 1 inter-band transitions, although it was difficult to determine the DC0 ratios for the low-lying transitions in these bands. Band 3 and 4 are considered to be yrare sequences with odd and even spins. Both signatures have nearly the same intensities, but band 4 seems to be slightly more favored and extends up to a higher spin than band 3. The strength of the inter-band transitions in these bands could not be determined because of many overlapping peaks. The 448.9 keV y-ray which is the transition from the 957.0 keV level in band 3 to the lowest level in band 2 was observed, but no other transitions connecting band 3 and 4 with band 1 and 2 were found. This indicates that the yrast and yrare states have rather different configurations. 3.2. Low-spin states Fig. 3 is a spectrum of y-rays observed at the beam energy of 102 MeV in coincidence with three protons and one neutron, and is an almost pure spectrum of 82Y. Energies a nd relative intensities of y-rays assigned to *‘Y are given in Table 2, and a level scheme was constructed as shown in Fig. 4. A cascade consisting of the 32.6 keV and 211.1 keV transitions competes with the 243.8 keV transition from the 751.4 keV to the 507.6 keV level. The 32.6 keV y-ray was weak due to the large probability of internal conversion, and was observed only in gated spectra. Although the relative ordering of the cascade is an important point in the evaluation of band 1 and 2, it could not be determined in the present experiments.
.I. Mukai et al. / High spin states
209
band 1 G7+1 band 2 13785
--I--
(26’)
2193.8
(25’)
122 9
,“,“y,, -i
1952.1 1851.8 c23+1
l&67
band 4 9861
I
(22’)
---I-
1751.4
I
1666.8
1452.3
(21’)
856 --I
(22-I
9681
I
m-)
8189
band 3
-I-
1801.3 1522.0 (19’)
6914
(18+)
+
14k.2
(l-T+)
5456 -+
=-i-
1313.6
1368.5
I
1362.8
1422.1
---I5250.0
(16’)
1346.0
---I1171.8
---I3904.0
1+8
(14’)
1124.0 3021
1072.8
1
(12-I
I
96f.6 x62.4 1687.8 J.
(9-I
F.8
Fig. 2. Level scheme of 82Y. See also Fig. 4.
1
(10-I
ti.3 1213.1 4
(8-I
.I. Mukai et al. / High spin states
210
gate:3pln i
400
600
channel
800
1000
1200
number
Fig. 3. G~ma-ray spectrum in coincidence with three protons and one neutron at a beam energy of 102 MeV. Delayed y-rays are slightly reduced in this spectrum because of the 500 ns wide (charged particle-)y coincidence requirement.
Table 2 Gamma-ray energies, intensities, excitation energies of initial states, A, coefficients and deduced spin changes determined from data obtained in the lower beam energy experiments. E, (keW 32.6 (3) 63.7 (3) 64.3 (3) 65.7 (2) 87.5 (1) 88.9 (2) 106.4 (1) 107.9 (2) 109.2 (1) 142.3 (1) 166.5 (2) 171.4 (1) 194.6 (1) 211.1(2) 243.8 (2) 250.2 (1) 276.6 (3) 278.7 (3) 313.7 (1) 337.1 (2) 395.2 (2) 443.0 (5) 445.0 (3) 449.6 (3) 813.1 (6) 837.9 (5)
E, (keW
G a
b b b b
7 (2) 23 (9) 17 (9) 21(Z) 55 (2) 16 (1) 48 (2) 8 (1) 20 (1) 100 4 (1) 50 (2) 51(Z) 35 (4) 40 (5) 27 (2) 3 (1) 4 (1) 43 (3) 25 (3) 29 (3) 6 (2) 10 (2) 10 (3) 13 (6) 28 (7)
a
b b
751.4 (5) 313.7 (1) 401.3 (2) 402.7 (3) 401.3 (2) 402.7 (3) 507.6 (3) 250.2 (1) 511.9 (5) 142.3 (1)
A,
Af
0.14 (4)
2
- 0.05 (3)
1
313.7 (1) 337.1 (2) 718.7 (5) 751.4 (5) 250.2 (1)
- 0.10 (5)
313.7 (1) 337.1 (2) 1146.6 (7)
0.13 (7) 0.13 (10) - 0.59 (21)
- 0.23 (5) -0.38 (9) ’ 0.20 (8) ’ -0.19 (13)
b b
a Determined from spectra gated by coincident y-rays. b Determined from a spectrum gated by the PID of 3pn. ’ Overlapped by a mixed dipole y-ray in 83Zr.
2 2 1
J. Mukai et al. / High spin states
751.4
(8+)
718.7
(7+)
507.6
”
211
137Go)nPtf 106.4
..,,,&C4+1 337.1 313.7
87.5
i
J 63.7
250.2
(2)
194.6
107.9
337.1 ”
142.3
171.4 313.7
”
(2+) 250.2 142.3
0
W
”
” 82
39
”
1+
Y 43
Fig. 4. Lower portion of the level scheme of *‘Y. Measured half-lives of three isomeric states at 401.3, 402.7 and 507.6 keV are given in the figure.
New data communicated to us by ref. 1251 establish the 33 keV y-ray as the higher-lying transition and the 211 keV as the lower one. This level ordering is adopted in Fig. 4 and the intermediate state lies at 718.7 keV. Half-lives of the levels at 401.3 keV, 402.7 keV and 507.6 keV were extracted from time distributions of the deexciting y-rays in the ny and yy coincidence measurements. All other states in the scheme were found to have a shorter lifetime than the detection limit in this setup, that is about a few ns. The spin-parity of the ground state of 82Y has been investigated through its p-decay by Lister et al. [26] and by Della Negra et al. [27]. In those references, allowed p-transitions to the ground O+, first 2+, second 2+ and excited O+ states in 82Sr have been reported, and the ground state has been determined to have a spin and parity of 1+. The J” assignments of the excited states were obtained by measuring the angular distribution of the y-rays. In some cases, measured lifetimes
212
J. Mukai et al. / High spin states
and conversion coefficients derived from the intensity balance of -y-rays were also needed. The angular distributions were fitted to the polynomial expression: w(e)
=A,[1
+A,P,(cos
8) +A,P,(cos
e>] 7
where Pk are Legendre functions of kth order. In the present analysis, A, was set to zero because it rapidly decreases as the spin alignment is attenuated [28]. In fact, the anisotropy of y-rays below the isomeric states was small, indicating an attenuation of the alignment. Fitted values of A, together with deduced spin changes are tabulated in Table 2. Although the A, coefficients only are insufficient to determine transition multipolarity, their signs are expected to be positive for stretched quadrupole (AJ = 2) and non-stretched dipole (AJ = 0) transitions, and to be negative for pure dipole and most of the mixed AJ = 1 transitions. The 250.2 keV transition is assigned to AJ = 1 by the negative A,, although the experimental uncertainty is large. The spin value of the initial state is thus limited to 0 or 2 as the final state has J” = 1+. The observed anisotropy of this y-ray excludes an initial spin of 0, therefore J = 2 is proposed for the 250.2 keV level. A cross-over transition from the 313.7 keV level to the ground state competes with the cascade of two AJ = 1 transitions with energies of 171.4 keV and 142.3 keV. Since the 313.7 keV y-ray is a transition with AJ = 0 or 2, the multipolarity of the cross-over and the cascade transitions are strongly suggested to be E2 and Ml(/E2), respectively. The most probable assignment of the spin and parity is 2+ for the 142.3 keV level and 3+ for the 313.7 keV level. A similar argument can be applied for the 337.1 keV cross-over and the 194.6 keV and 142.3 keV cascade transitions. Therefore the 337.1 keV level is also assigned to have J” = 3+. It was difficult to extract reliable angular distributions for the y-rays deexciting the close-lying levels at 401.3 keV and 402.7 keV due to their closeness in energy. In this case, conversion coefficients were taken into account. The theoretical conversion coefficients [29] for a 65 keV y-ray are 0.38, 0.67 and 5.4 for El, Ml and E2 multipolarities, respectively. These values for a 88 keV -y-ray are 0.16, 0.67 and 1.5. The intensity balance between feeding and deexciting y-rays of the 401.3 keV level requires Ml multipolarity for the 64.3 keV and 87.5 keV transitions. The partial half-lives of 106 ns for the 64.3 keV y-ray and 33 ns for the 87.5 keV y-ray also indicate an Ml/E2 nature considering the theoretical values [29] which are as follows: 79 ps (Ml; 65 keV), 22 l~,s(E2; 65 keV), 32 ps (Ml; 88 keV) and 4.7 ~J.LS (E2; 88 keV). By considering that the y-rays feeding into the 3+ states are Ml/E2 mixed transitions, the spin and parity of the 401.3 keV level is proposed to be 4+. The 65.7 keV and the 88.9 keV y-rays are shown to be dipoles from the intensity balance with the 109.2 keV y-ray. In addition, the long lifetime observed for the 402.7 keV level suggests an El multipolarity which is often known to be hindered by lop2 N 10e6 (ref. [30]). The spin and parity of the 402.7 keV level is therefore restricted to be 2-, 3- or 4- considering the final states have J” = 3+. A
J. Mukai et al. / High spin states
213
4- assignment is most plausible since neither transitions feeding the 2+ state at 142.3 keV nor the l+ ground state are observed. The 402.7 keV level is the band head of the yrare sequence observed in the NORDBALL experiment and its spin value is expected to be similar to the band-head spin of the yrast sequence (assigned to be 6 in the following), because of the considerable intensities of band 3 and 4. A spin value of 4 is therefore reasonable for this state. The 106.4 keV y-ray deexciting the 507.6 keV level is considered to be a stretched quadrupole transition, according to the positive A, coefficient and the long lifetime of the level. The intensity balance with the direct feeding y-rays with energies of 211.1 keV and 243.8 keV requires a conversion coefficient of about 1 for the 106.4 keV y-ray, which agrees with the theoretical value [29] of 0.91 for an E2 transition. Hence, the 106.4 keV transition is probably an E2 with a strength of 14 Weisskopf units [29]. The collectivity of this transition is small and it may not be proper to include it as a band member although it is a stretched E2. The 507.6 keV level, which is the band head of the yrast sequence of the NORDBALL experiment, is thus assigned to have J” = 6+. The 211.1 keV and 243.8 keV y-rays feed the 507.6 keV level. These peaks are contaminated by the dipole transitions at 209.7 keV and 243.2 keV in 83Zr (ref. [S]), which contribute by about 30% of total peak areas. In spite of these contaminations, the angular distributions show a multipolarity of Ml/E2 for the 211.1 keV and E2 for the 243.8 keV y-rays, which is consistent with the results of the DC0 analysis previously described. The 718.7 keV and 751.4 keV levels are thus assigned to have J” = 7+ and 8+, respectively. The 32.6 keV transition from the 751.4 keV to the 718.7 keV level is therefore assigned to the Ml multipolarity. A conversion coefficient 1291 of about 5 for a pure Ml transition is sufficient to explain the weakness of the 32.6 keV -y-ray which has an intensity of 20% of the 211.1 keV -y-ray. The angular distribution of the 395.2 keV y-ray shows dipole multipolarity, which is also consistent with the DC0 analysis. Higher-lying transitions were only very weakly populated and angular distributions were not obtained.
4. Discussion 4.1. Configurations at low excitation Single-particle 2P l/2 and lf,,* 2d 5,2 neutron There is a nuclei near N first excitation
levels around nucleon number 39 and 43 are from the lg,,,, shells [l]. At large deformation the 2p,,, proton orbitals and the orbitals should also be considered. lot of data for low-lying states of odd-A yttrium isotopes. In the = 50 the ~r,~ shell-model state is lowest and the g,,, state of the is at 909 keV in 89Y, 381 keV in 87Y and 20 keV in 85Y (ref. [311). In
214
J. Mukai et al. / High spin states
83Y (ref. [5]) the spin-parity of the ground state is + ’ and it has been assigned to the K= $ state in the g,,, shell. The first excited state at 62 keV has been assigned to f,,,[3011~. In ‘lY (ref. [lo]) and 79Y (refs. [34,351) the ground state has been assigned to + + from the g,,, shell. The first excited state at 113 keV in ‘lY has been proposed to be 5 - or $-, coming from the f5,* shell. In addition to the proton levels, various single-neutron states at low excitation energy have been observed in N = 43 isotones with odd mass. In 83Zr, ‘lSr and 79Kr the spin-parity of the ground state is $- and has been assigned to the p,,,[301]~orbital [6-9,131. In those nuclei a J” = I’ state based on the g,,,[422]+ ’ (or [4131; ‘> h as b een observed at about 100 keV excitation energy. The f,,,[301]~- state has been observed at 53 keV in 83Zr and at 384 keV in 79Kr, while the f,,,[303]$state appears at 79 keV in ‘lSr and at 147 keV in 79Kr. The J” = i(+) state at 120 keV in “Sr has been proposed to have the ds,J431]~+ configuration. Such a variety of single-particle orbitals may sufficiently reproduce spin-parities of the complex low-lying states in 82Y. The most probable candidate of the configuration of the J” = 1+ ground state is rg,,2[422]$+@ vg,,,[413]5+ or 7rf,,2[301]$ -@ vp,,,[3011~ -. 4.2. Band I and 2 The band head configuration of band 1 and 2 is most likely rrg,,, @ vg9,2 or =g,/, Q vdg,z since other combinations of orbitals in consideration would fail to compose a J” = 6+ state. The last proton occupies an orbital in the middle of the g,,, shell while the neutron is in the upper half of the g,,, or at the bottom of the d 5,2. As the angular momentum of the d5,2 neutron is more or less opposite to that of the g 9,2 proton, it is difficult to form the total spin of 6. On the other hand, two g,,, nucleons can easily make a J = 6 state, e.g. a proton in the R = $ orbital and a neutron in L! = 5. In the neighboring isotones the g,,, band has been observed as the yrast band [7-9,131, thus it is natural to assume that the unpaired neutron in the yrast band of 82Y occupies a g,,, orbital as well as the unpaired proton. In the paper about 74Br (ref. [17]) it is described that rigid rotation is not expected below the spin of j, + j, because energies of low-lying states are shifted by realignment of the intrinsic spins. In fact, a transition from non-collective to collective phase has been observed at J = 9 in 74Br (ref. 1171)and at J = 11 in 76Br (ref. [181), for which nuclei of both the unpaired proton and the neutron are considered to occupy a g9,2 orbital and hence j, + j, = 9. For the yrast states in 82Y a typical rotational band is constructed above J = 8, which is close to j, +>, = 9. Since band 1 and 2 are connected by A J = 1 inter-band transitions, these bands are probably signature partners. In this case, the odd-spin (a = 1) sequence is
215
J. Mukai et al. / High spin states
-3
0
0.5
1.0
1.5
tiw( MeV) Fig. 5. Kinematic (top) and dynamic ~middIe~ moments of inertia and experimental routhian (bottoms of the yrast band. Reference parameters in the routhian plot are taken as J, = 20.0 h2 MeV-’ and J, = 0.
expected to be energetically favored because the favored signature of a g9,* nucleon should be + 3 in the cranking model, and in fact, the positive signatures of g9,2 band behave as favored sequences in both odd-2 and odd-N nuclei in this mass region [2-111. Indeed, band 1 composed from odd-spin states is lowered relative to band 2 above the 8+ state. Signature inversion is seen at the 7+ state, which is a lower spin value than those of the inverting points in the odd-odd neighbors [17-201. Fig. 5 shows f O), kinematical moments of inertia, J(*), d~amical moments of inertia, and e’, experimental routhians, for band 1 and 2. To calculate these values the K quantum number is assumed to be the same as the band-head spin, that is, 6. The selection of K does not give any serious effect in high-spin region, especially to relative values such as signature splitting. Reference parameters of J, = 20.0 h* MeV-* and J, = 0 are chosen only to emphasize the splitting, and do
216
J. Mukai et al. / High spin states
not represent a reasonable vacuum configuration. The Jo) in band 2 has a sharp rise starting at hw = 0.6 MeV, in contrast to the gradual increase in band 1 at the same frequency. These rises correspond to the sharp and broad peaks around hw = 0.65 MeV in the J(‘) plots for band 2 and 1, respectively. After this rise, Jo) of band 2 closely approaches to that of the band 1 and almost degenerates. On the other hand, the splitting of the routhian increases as the rotational frequency increases in the region below 0.6 MeV, and above this point shows a nearly constant value of = 500 keV. In the 2 = 37 nucleus 79Rb, moments of inertia and routhians for both signatures of the yrast rg9,2 band have very similar behavior to those of band 1 and 2, as shown in Figs. 8 and 10 of ref. [14]. The signature splitting between band 1 and 2 is hence suggested to be caused by the unpaired proton in the same orbital as in the 79Rb case. The configurations of band 1 and 2 are considered to be rg9,*, CY= + + CSyg9,z, (Y= + i and rrg9,2, (Y= - ; @ ugg,*, (Y= + i, respectively. The
0.5
1.0
J 1.5
Aw( MeV) Fig. 6. Same as Fig. 5 but for the yrare band.
J. Mukui et al. / High spin states
217
property of the yrast band in 79Rb has been theoretically investigated in ref. 1341. In this ref. the irregular point observed in moments of inertia and routhians in both signatures is interpreted to correspond to the first crossing caused by an alignment of g9,2 neutron pair. Total routhian surface (TRS) calculations [34] have shown a stable prolate shape of p = 0.33 in 79Rb at low spin. In the calculations this shape is conserved at higher spin in the favored band, while a clear change to a nearly oblate shape has been shown at the band crossing in the unfavored band. The crossing at fro = 0.65 MeV observed in the yrast bands in 82Y is probably caused by an alignment of g9,2 neutrons, as in 79Rb, although the nuclear shape has not been determined for 82Y. The unpaired neutron in a g,,,, orbital is expected to block the first alignment of g,,, neutrons. It is not clearly understood why the alignment occurs in “Y at nearly the same frequency as in a non-blocked system 79Rb. This may be explained as a shift of the crossing frequency by different shape in the two nuclei. Another possibility is that the aligning neutrons of both nuclei are not in a g,,, orbital but in ds,z, which has been proposed as the lowest neutron state in a N = 42 system at p2 = 0.35, y = - 7” as given in Fig. 18 of ref. 111. As the unpaired neutron in a g,,,, orbital does not block d,,,, neutron alignments, the first crossing in ‘*Y may occur at the same frequency as in N = 42 79Rb. However, calculations of theoretical routhians are necessary to pursue these explanations. The signature splitting between the band 1 and 2, which is considered to arise from the unpaired g 9,2 proton, can be compared to that of rg9,* bands in 2 = 39 isotopes. In 83Y the splitting in energy has been observed to be about 500 keV up to hw = 0.8 MeV (ref. [35]), which is very close to that of 82Y. In “Y the unfavored band has been established only at lower spin region (ho = 0.4 MeV), and the splitting is about 250 keV (ref. [lo]). 4.3. Biznd 3 and 4 Band 3 and 4 are considered to be the signature partners of a yrare band. Fig. 6 shows J(l), JC2)and e’ for them. The signature splitting is much smaller than that of the yrast band, about 100 keV. Such a small energy splitting can not be considered resulting from g9,2 nucleon, because g,,,* bands show large signature splitting of several hundreds keV for both odd-proton and odd-neutron systems in this mass region [5-101. It is very probable that one unpaired nucleon occupies a negative-parity orbital with small j (therefore small signature splitting), and its anguiar momentum couples to that of another odd nucleon in a g,,, orbital to compose the K” = 4- band head. In .7(i) for both signatures there is an abrupt increase which gives a sharp peak in 3”’ around ho = 0.65 MeV, nearly the same as the crossing frequency in the yrast band. Such a rapid increase of Jo’ in both signatures has not been reported in neighboring nuclei. However, a number of levels could be identified in “Y tarp
218
J. Mukai et al. / High spin states
channel) in the present data [36], and it was found that the first alignment occurs at hw = 0.67 MeV in the favored signature of the yrast band, giving a rapid increase in Jo) similarly to the 82Y case. The alignment in band 3 and 4 of 82Y may be due to g,,, neutrons as same as in "Y . It may be considered that the unpaired neutron occupies a negative-parity orbital and hence does not block the g,,, neutron alignment. In ‘lSr (ref. [9]> and 83Zr (ref. [7,8]) the yrare band is built on a J” = $- state coming from the f5,2 shell. In these K" = $- bands the LY= - i sequence is slightly favored, and the magnitude of the signature splitting is about 60 keV in ‘lSr (ref. [9]) and 150 keV in s3Zr (ref. [7]). Combined to the favored signature of + i for a g,,, proton, the f5,2 neutron will make the LY= 0 sequence as a favored band in 82Y. Indeed, band 4 of the even-spin sequence was observed to be favored relative to band 3. The most probable configurations for band 3 and 4 are rgg,2, (Y= ++f cr = + $ and rrg9,2, (Y=+i@)Vf 5/27 a = - $, respectively. S/2) These assignments of the negative-parity states indicate only the main components as they are not pure states due to the level mixing.
5. Summary Excited states in 82Y were investigated through two types of experiments. Delayed coincidence measurements of particle-y and yy were effective to construct the low-lying level structure including the band heads of the high-spin bands. On the other hand, high-spin structures were established by a prompt coincidence measurement with higher incident energy. Four rotational bands were observed up to the highest spin among odd-odd nuclei in this mass region. Two of the bands were identified as signature partners and they are the yrast states. The magnitudes of moments of of m,/, Q %9/2, inertia are similar to those of neighboring nuclei. Large signature splitting was observed likewise in g,,, bands of the odd-A neighbor. Signature inversion at low spin, which is a rather common feature in odd-odd nuclei [17-20,371, was observed only for the lowest state of the yrast band. A band crossing of very similar behavior with 79Rb was observed at nearly the same rotational frequency in the 79Rb case for both signatures. It is not clear yet whether this is the non-blocked first crossing or the second crossing shifted to a lower frequency. Two other bands were considered to be signature partners, probably with negative parity. There is a small signature splitting between them, which is similar to the negative-parity bands in odd-A neighbors. An onset of band crossing was seen at the highest spin observed for both signatures. For the comparison with theoretical predictions it is important to determine the nuclear shape experimentally, because the properties of a quasi-particle diagram such as crossing frequencies predicted by calculations strongly depend on the
J. Mukai et al. / High spin states
deformation parameters. necessary.
Further experiments including lifetime measurements
219
are
We would Iike to thank Dr. W. Nazarewicz for helpful discussions and the Niels Bohr Institute for its hospitali~. We gratefully ac~owledge Prof. S.L. Tabor (FSU) for access to his unpublished data on “Y (ref. [2.5]) and the Nuclear Physics referees for pointing out their existence. This work was partly supported by the Japanese government (grant numbers: 01044037 and 024520271, the Danish Natural Science Research Council and the Swedish Natural Science Research Council. One of us (S.M.) was also supported by the Yamada Science Foundation.
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