Erratum to “Collective and intrinsic structures in 183W” [Nucl. Phys. A 660 (1999) 171–196]

Nuclear Physics A 669 Ž2000. 381–406 www.elsevier.nlrlocaternpe

Erratum to ‘‘Collective and intrinsic structures in 183 W’’ wNucl. Phys. A 660 Ž1999. 171–196x q T.R. Saitoh a,2 , N. Saitoh-Hashimoto a,b, G. Sletten a , R.A. Bark a,3, M. Bergstrom ¨ a, P. Regan c , S. Tormanen ¨ ¨ a, P.G. Varmette a,4, c P.M. Walker , C. Wheldon c a

b

The Niels Bohr Institute, UniÕersity of Copenhagen, Copenhagen, Denmark Department of Physics and Tandem Accelerator Center, UniÕersity of Tsukuba, Ibaraki, Japan c Department of Physics, UniÕersity of Surrey, Guildford, UK Received 20 July 1999; accepted 2 September 1999

Abstract The structure of 183 W has been studied by employing the 176 YbŽ 14 C, a 3n. reaction at 68 MeV. Five previously known rotational structure with one-quasiparticle configurations have been extended to higher spin states, and five new rotational bands with three- and five-quasiparticle configurations and a g-vibration of a one-quasiparticle structure have been newly identified. In the n 7r2yw503x and n 11r2qw615x rotational structures, a signal of an admixture of an octupolevibrational structure has been observed in their in-band B ŽM1.rB ŽE2. ratios and g K factors. In the K p s 19y rotational band, a Coriolis effect on the n 1r2y w510x neutron has been identified. In all, 17 K-forbidden transitions have been observed. Energies of intrinsic states below 4 MeV have been calculated based on the Blocked BCS theory, and they are used in support of the configuration assignments. q 2000 Elsevier Science B.V. All rights reserved. PACS: 21.10.Re; 21.10.Tg; 23.20.En; 23.20.Lv; 27.70.qq

Keywords: NUCLEAR REACTION 176 YbŽ 14 C, a 3n.183 W E s 68 MeV, slow beam pulsing; measured g-g coincidences, DCO ratios, a-g coincidences; 183 W deduced levels, K, I, p , T1r2 , configurations, rotational bands; deduced B ŽM1.rB ŽE2. ratios and g K factors; BCS calculations with blocking

q

PII of original article: S0375-9474Ž99.00381-4 Present address: Department of Physics, Brookhaven National Laboratory, Upton, NY, USA, and Department of Physics, VA TECH, Blacksburg, VA, USA. 3 Present address: Department of the Nuclear Physics, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, Australia. 4 Present address: The Physics and Astronomy Department, Mississippi State University, Mississippi State, USA. 2

0375-9474r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 Ž 0 0 . 0 0 1 3 9 - 1

382

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

1. Introduction In the A ; 180 region, high-V orbitals of both protons and neutrons lie near the Fermi surface, thus the presence of high-K isomers near the yrast line is expected. Stable or neutron-rich nuclei in this mass region have been of special interest because these nuclei are placed near a transitional region, where the nuclear shapes change from prolate to g-soft or triaxial shapes by the addition of only a few protons or neutrons. Therefore, a breakdown of the K-selection rules is expected and significant new information on K-forbidden transitions might be obtained. However, experimental information for these nuclei has been rather restricted because of difficulties in populating high-spin states by heavy-ion fusion-evaporation reactions. In the present work, the structure of the stable nucleus, 183 W, has been studied. This nucleus was previously studied by Coulomb excitation w1x and particle transfer experiments w2x. However, the structure with high-spin or high-seniority has remained unknown. In the present work, high-spin states of 183 W have been populated by a radioactive 14 C induced reaction on a 176 Yb target, and g-g coincidence measurements with charged-particle detection have been conducted. In all, 11 rotational structures have been identified, and these will be discussed in the following sections.

2. Experiments The nucleus 183 W was populated via the 176 YbŽ 14 C, a 3n.183 W reaction, with DC and pulsed beams from the Niels Bohr Institute Tandem Van de Graaff accelerator. In this reaction, enhancement of the population of this nucleus due to incomplete fusion has been observed. Properties of incomplete fusion reactions have been reported by Dracoulis et al. w3x. 2.1. The g – g coincidence measurements with a DC-beam Coincident g-ray measurement with a DC-beam have been conducted by using the NORDBALL array w4x. In this measurement, the 14 C beam bombarded a 5 mgrcm2 enriched 176 Yb target at 68 MeV, and the nucleus 183 W was populated via an a 3n channel. Gamma-rays were detected by the NORDBALL Ge-detector array in coincidence with charged particles detected by a Si-ball w5x, which consists of 30 170 m m silicon detectors. Six rings consisting of five Si-detectors were placed at 15.98, 47.68, 61.58, 70.08, 97.98 and 132.48 relative to the beam direction. Events were characterized by at least two Ge-detectors firing during a period of 552 ns after at least one Si-detector had fired. Low energy g-rays were detected by two planar, low energy photon ŽLEP. detectors. A total of 9.5 = 10 6 g-g coincidence events in coincidence with one a-particle were sorted off-line into two-dimensional g-g matrices. 2.2. Search for a long liÕed isomer by using a pulsed

14

C beam

Since the coincidence timing window of the g-g coincidence measurement using the DC-beam was 552 ns, g-rays which depopulate long-lived isomers with a half-life

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

383

longer than a few microseconds could not been observed in these experiments. Therefore, a pulsed beam experiment was made. In this experiment, beam bursts of 5 m s duration were separated by 1 ms, and coincident g-rays were detected, within a time window of 552 ns, only in the beam-off period. In total, 1 = 10 5 g-ray events were collected. All g-rays observed in these experiments were already known, and no new long lived isomers in 183 W were observed. 2.3. DCO ratio analysis Measurements of DCO ratios ŽDirectional angular Correlation from Oriented states. w6x, in the NORDBALL array, have been used for the assignment of spins. The NORDBALL array had detectors placed at u values of 378, 798, 1018 and 1438 with respect to the beam direction. Since axially symmetric oriented states around a beam axis are considered, the angles of 1018and 1438 are equivalent to 798 and 378, respectively. The intensity ratio, R DC O , of transitions from axially symmetric oriented states are generated by selective gating on pairs of g-rays, and the ratio is defined by either R DC O s

1 2 Iugs378 Gatedugs798 1 2 Iugs798 Gatedugs378

or R DC O s

2 1 Iugs798 Gatedugs378 2 1 Iugs378 Gatedugs798

,

where the g 2 is the g-ray following g 1. The experimental DCO ratio was compared with theoretical calculations in which a spin orientation parameter, srJ s 0.3, is assumed.

3. Experimental results In this section, the level scheme of 183 W will be discussed with reference to Figs. 1 and 2 and Table 1. In Figs. 1 and 2, the band structures are labelled numerically or by proposed configurations. Gamma-ray energies, intensities and assignments are listed in Table 1. In the present work, transitions are generally assigned as either E1, M1 or E2 character Žexcept for transitions depopulating isomeric states.. Since we populated 183 W by fusion-evaporation or incomplete-fusion reactions, states close to yrast are mainly populated. Therefore, bands populated with high intensity are assumed to be closer to the yrast line than weakly populated structures. A rotational band is labelled by a K quantum number taken as the spin of the lowest state identified in the band. 3.1. One-quasiparticle negatiÕe parity bands: n 1 r 2 y[ 510], n 7 r 2 y[ 503] and n 3 r 2 y[ 512] The stable ground state of 183 W is characterized by the n 1r2y w510x neutron orbital w1x. In earlier works, a rotational band built on this ground state has been observed up to the 17r2y state in a Coulomb excitation experiment w1x, and a level at 1332 keV was

384

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

Fig. 1. Partial level scheme of

183

W, Part 1.

tentatively assigned as the Ž19r2y. member of this band w1x. This level was confirmed by a strong 478 keV E2 transition that defines the 19r2y level at 1328 keV. Eight other stretched cross-over E2 transitions have been observed in this band, thus extending the n 1r2yw 510x rotational band to the 35r2y state at 4043 keV. Figs. 3a, b show g-ray spectra in coincidence with the 573 and 533 keV transitions, respectively, in the n 1r2yw 510x rotational band. The n 7r2yw 503x bandhead at 453 keV and a 9r2y rotational member at 595 keV were firstly established in a b-decay study w7x. These states were also observed in Žd,p. and Žd,t. reactions w8x and were more recently studied by Žn,nXg . and Žn,g . reactions w2x. An 11r2y rotational level was observed at 770 keV by Prokofjevs et al. w2x, and they observed a 324 keV g-ray depopulating this state to the 7r2y bandhead. In the present work, the n 7r2yw 503x bandhead has been identified with five transitions depopulating it

Fig. 2. Partial level scheme of

183

W, Part 2.

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

385

to the n 1r2yw 510x and the n 3r2yw 512x bands, and a rotational band based on this state has been strongly populated, see Fig. 1. Nine cascading D I s 1 transitions and nine cross-over E2 transitions define the n 7r2yw 503x rotational levels up to the 27r2y state at 3010 keV. The energy of the 11r2y rotational state at 766 keV is slightly different from that reported in w2x. The half-life of the 7r2y bandhead was previously reported to be 18.5 ns w9x. In the present work, a half-life of 21.5Ž20. ns has been deduced by fitting the decay curve of the 245 keV g-ray when gated on the 142, 171, 199, 225, 370 keV transitions. A corresponding timing spectrum is shown in Fig. 4a. A n 3r2yw 512x rotational band up to the 13r2y level based on the state at 209 keV was previously populated by Coulomb excitation w1x, and a number of inter-band transitions from the n 3r2yw 512x band to the n 1r2yw 510x band were observed w1x. In the present work, this structure has been weakly populated and is observed only to the 7r2y level. The 3r2y bandhead at 209 keV is depopulated by three transitions, 110, 162, and 210 keV, to the n 1r2yw 510x structure. Only two inter-band g-rays with energies of 84 and 203 keV were observed in the present work. 3.2. The n 11 r 2 q[ 615] and n 9 r 2 q[ 624] bands Since the neutron Fermi surface in 183 W lies approximately half-way between the n 9r2qw 624x and n 11r2qw 615x orbitals, it is expected that both these i 13r2 neutrons play an important role in this nucleus. The n 11r2qw 615x single-particle state with a half-life of 5.2 s was first assigned at 310 keV from a b-decay study w7x. This state decays only via a 102 keV M2 transition to the 7r2y level of the n 1r2y w510x rotational band. A 13r2q rotational member at 486 keV was observed in a Žd,p. study w2x, and a 176 keV g-ray which depopulates the 13r2q state to the 11r2q bandhead was observed in an Žn,n’g . experiment w2x. In the present work, the band has been extended to the 37r2q level. Fig. 3-Žc. shows a g-spectrum gating on the 604 keV transition in this band, and g-rays of this band are clearly seen. All observed structures, except for the n 1r2yw 510x , n 7r2yw 503x and n 3r2yw 512x bands, finally decay to this rotational band. The n 9r2qw 624x configuration has been assigned to the 9r2q bandhead at 623 keV identified in a Žd,t. study w8x. A second excited rotational level, the 13r2q state at 960 keV, was observed in the same experiment. In the b-decay experiment described in ref w7x, a 313 keV transition was observed to depopulate the 9r2q bandhead to the n 11r2qw 615x bandhead, therefore the energy of the 9r2q bandhead was determined to be 622.7 keV. In the present work, a weak 315 keV transition and two transitions in coincidence with it have been observed. Although the energy of the 315 keV g-ray is slightly different from that in Ref. w7x, we propose that the level at 624 keV depopulated by the 315 keV is the n 9r2qw 624x bandhead. Therefore, we regard two further levels above the 624 keV state as members of this band. As will be discussed in the following sections, these n i 13r2 orbitals are involved in other high-K structures and characterize their features. 3.3. BAND 1 based on the isomer at 1746 keV Five delayed transitions which populate levels of the n 7r2yw 503x and n 11r2qw 615x rotational bands define an isomeric state at 1746 keV Žsee Fig. 2.. Fig. 5 shows a prompt

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

386

Table 1 List of the g-rays in 183 W detected by the NORDBALL array. Relative intensities and energies are determined by the g – g coincidence measurements with an a-particle detection in prompt coincidence Eg wkeVx

Ig

Ei wkeVx

E f wkeVx

Ž Jp , K .i

Ž Jp , K .f

83.0Ž2. 84.1Ž6. 99.1Ž1. 107.8Ž1. 109.8Ž4. 112.1Ž1. 142.0Ž1. 143.8Ž1. 153.6Ž1. 154.1Ž2. 161.0Ž1. 161.0Ž1. 162.0Ž1. 166.1Ž1. 167.5Ž2. 167.7Ž1. 171.0Ž1. 175.7Ž1. 192.6Ž1. 198.6Ž1. 202.2Ž1. 203.1Ž1. 209.7Ž1. 209.8Ž1. 218.7Ž1. 219.1Ž1. 224.9Ž1. 227.1Ž1. 243.0Ž1. 245.1Ž1. 249.7Ž1. 253.6Ž1. 253.8Ž2. 263.4Ž1. 265.7Ž1. 268.1Ž1. 271.0Ž1. 273.6Ž1. 275.6Ž1. 282.8Ž1. 289.7Ž1. 293.3Ž3. 293.5Ž2. 294.4Ž1. 296.9Ž1. 301.5Ž1. 304.3Ž1. 306.1Ž1. 306.5Ž1. 307.0Ž1.

4.24Ž87. 2.36Ž56. 4.27Ž39. 5.65Ž120. 1.36Ž121. 12.19Ž46. 14.34Ž66. 1.33Ž10. 1.20Ž16. 1.49Ž20. 3.37Ž74. 4.94Ž36. 6.01Ž554. 6.88Ž33. 1.04Ž13. 11.45Ž39. 18.02Ž68. 47.23Ž160. 4.94Ž18. 16.14Ž58. 80.26Ž264. 6.62Ž73. 19.88Ž160. 4.43Ž410. 3.59Ž19. 25.90Ž82. 15.74Ž54. 57.48Ž183. 24.79Ž83. 8.66Ž62. 7.92Ž30. 27.67Ž91. 0.55Ž22. 8.64Ž33. 2.28Ž13. 11.59Ž60. 11.90Ž43. 2.79Ž17. 0.83Ž12. 6.81Ž26. 13.08Ž46. 0.80Ž11. 0.51Ž10. 2.15Ž16. 3.35Ž19. 3.92Ž19. 54.89Ž173. 6.94Ž27. 11.41Ž39. 5.80Ž26.

291.9Ž4. 291.9Ž4. 99.3Ž1. 207.4Ž2. 208.6Ž3. 2101.1Ž4. 594.9Ž3. 452.9Ž2. 1900.3Ž7. 778.2Ž13. 207.4Ž2. 452.9Ž2. 208.6Ž3. 475.3Ž2. 2874.0Ž13. 2268.9Ž4. 766.0Ž3. 485.2Ž4. 3348.5Ž4. 964.8Ž3. 687.6Ž4. 411.7Ž8. 309.1Ž2. 208.6Ž3. 850.3Ž3. 2268.9Ž4. 1189.9Ž3. 914.8Ž4. 1988.9Ž4. 452.9Ž2. 1439.5Ž3. 1168.6Ž4. 2154.2Ž13. 2252.4Ž4. 1327.9Ž3. 475.3Ž2. 1439.7Ž4. 1713.2Ž4. 2429.8Ž16. 2535.2Ž4. 2339.7Ž4. 2706.5Ž5. 2723.4Ž18. 2007.5Ž5. 2043.3Ž4. 2836.8Ž5. 2049.9Ž4. 1746.2Ž4. 1745.7Ž3. 1745.7Ž3.

208.6 207.4 0.0 99.3 99.3 1988.9 452.9 309.1 1745.7 624.2 45.8 291.9 45.8 309.1 2706.5 2101.1 594.9 309.5 3155.9 766.0 485.2 208.6 99.3 0.0 631.3 2049.9 964.8 687.6 1745.7 207.4 1189.9 914.8 1900.3 1988.9 1062.2 207.4 1168.6 1439.5 2154.2 2252.4 2049.9 2413.1 2429.8 1713.2 1746.2 2535.2 1745.7 1439.7 1439.5 1439.7

5r2y,3r2 5r2y,3r2 5r2y,1r2 7r2y,1r2 3r2y,3r2 23r2 Žq.,23r2 9r2y,7r2 7r2y,7r2 Ž19r2q,19r2. 11r2q,9r2 7r2y,1r2 7r2y,7r2 3r2y,3r2 11r2y,1r2

3r2y,3r2 7r2y,1r2 1r2y,1r2 5r2y,1r2 5r2y,1r2 21r2y,19r2 7r2y,7r2 9r2y,1r2 19r2y,19r2 9r2q,9r2 3r2y,1r2 5r2y,3r2 3r2y,1r2 9r2y,1r2 29r2q,11r2 23r2 Žq .,23r2 9r2y,7r2 11r2q,11r2 29r2y,19r2 11r2y,7r2 13r2q,11r2 3r2y,3r2 5r2y,1r2 1r2y,1r2 13r2y,1r2 23r2y,23r2 13r2y,7r2 15r2q,11r2 19r2y,19r2 7r2y,1r2 15r2y,7r2 17r2q,11r2 Ž19r2q,19r2. 21r2y,19r2 17r2y,1r2 7r2y,1r2 19r2q,11r2 17r2y,7r2 Ž21r2q,19r2. 23r2y,19r2 23r2y,23r2 27r2q,11r2 Ž23r2q,19r2. 19r2y,7r2 23r2q,11r2 25r2y,19r2 19r2y,19r2 21r2q,11r2 17r2y,7r2 21r2q,11r2

25r2 Žy.,25r2 11r2y,7r2 13r2q,11r2 31r2 Žy.,31r2 13r2y,7r2 15r2q,11r2 7r2y,3r2 9r2y,1r2 3r2y,3r2 15r2y,1r2 25r2 Žy.,25r2 15r2y,7r2 17r2q,11r2 21r2y,19r2 7r2y,7r2 17r2y,7r2 19r2q,11r2 Ž21r2q,19r2. 23r2y,19r2 19r2y,1r2 11r2y,1r2 21r2q,11r2 19r2y,7r2 Ž23r2q,19r2. 25r2y,19r2 25r2y,23r2 29r2q,11r2 Ž25r2q,19r2. 21r2y,7r2 25r2q,11r2 27r2y,19r2 23r2y,23r2 23r2q,11r2 19r2y,19r2 19r2y,19r2

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

387

Table 1 Ž continued . Eg wkeVx

Ig

Ei wkeVx

E f wkeVx

Ž Jp , K .i

Ž Jp , K .f

308.8Ž1. 313.0Ž1. 314.7Ž1. 315.1Ž1. 317.2Ž2. 318.9Ž1. 321.5Ž1. 322.1Ž1. 328.1Ž1. 329.7Ž6. 333.4Ž1. 333.7Ž1. 341.3Ž1. 353.8Ž1. 355.4Ž10. 359.9Ž1. 369.8Ž1. 370.0Ž1. 371.6Ž4. 375.0Ž1. 378.1Ž1. 392.4Ž1. 408.8Ž1. 416.8Ž1. 424.0Ž1. 429.5Ž1. 430.9Ž1. 443.3Ž1. 454.7Ž3. 475.0Ž1. 477.7Ž1. 481.1Ž1. 507.2Ž1. 523.4Ž1. 525.1Ž1. 533.3Ž1. 541.6Ž1. 546.5Ž1. 555.6Ž1. 568.0Ž1. 569.3Ž3. 573.2Ž1. 577.1Ž1. 577.6Ž1. 584.3Ž1. 598.9Ž1. 603.7Ž1. 610.6Ž17. 610.9Ž1. 620.8Ž1. 626.5Ž1. 637.7Ž1.

8.08Ž32. 5.51Ž28. 7.03Ž48. 15.38Ž51. 1.35Ž15. 5.88Ž24. 30.80Ž98. 33.54Ž117. 3.46Ž17. 0.28Ž11. 7.69Ž29. 7.99Ž52. 21.88Ž70. 2.67Ž22. 0.05Ž12. 1.66Ž13. 1.76Ž16. 9.60Ž39. 0.38Ž9. 21.79Ž79. 29.44Ž114. 4.45Ž18. 1.22Ž12. 15.01Ž49. 16.28Ž57. 48.16Ž161. 28.53Ž96. 4.72Ž19. 0.53Ž10. 8.79Ž34. 17.54Ž62. 36.73Ž123. 2.38Ž17. 3.95Ž23. 23.54Ž82. 17.69Ž60. 1.65Ž11. 4.20Ž20. 14.71Ž50. 2.98Ž20. 0.78Ž14. 13.43Ž48. 13.97Ž51. 18.83Ž73. 3.19Ž18. 2.85Ž20. 14.77Ž54. 0.21Ž15. 2.94Ž19. 6.32Ž26. 10.99Ž40. 1.44Ž15.

2648.5Ž5. 766.0Ž3. 624.2Ž6. 3663.6Ž5. 2324.2Ž6. 3155.9Ž4. 2590.4Ž4. 631.3Ž2. 2976.7Ž6. 2655.0Ž10. 3996.9Ž5. 957.9Ž8. 2931.7Ž4. 452.9Ž2. 2101.1Ž4. 3291.6Ž8. 2413.1Ž5. 964.8Ž3. 3663.6Ž5. 850.3Ž3. 687.6Ž4. 4389.4Ž6. 452.9Ž2. 3348.5Ž4. 1189.9Ž3. 914.8Ž4. 1062.2Ž3. 4440.2Ž6. 3161.1Ž7. 1439.5Ž3. 1327.9Ž3. 1168.6Ž4. 2252.4Ž4. 1713.2Ž4. 1439.7Ž4. 1595.5Ž3. 4538.5Ž8. 2535.2Ž4. 1745.7Ž3. 2007.5Ž5. 2723.4Ž18. 1901.2Ž4. 1745.7Ž3. 1746.2Ž4. 2836.8Ž5. 2648.5Ž5. 2043.3Ž4. 2049.9Ž4. 2324.2Ž6. 3155.9Ž4. 2222.1Ž4. 2976.7Ž6.

2339.7 452.9 309.5 3348.5 2007.5 2836.8 2268.9 309.1 2648.5 2324.2 3663.6 624.2 2590.4 99.3 1745.7 2931.7 2043.3 594.9 3291.6 475.3 309.5 3996.9 45.8 2931.7 766.0 485.2 631.3 3996.9 2706.5 964.8 850.3 687.6 1745.7 1189.9 914.8 1062.2 3996.9 1988.9 1189.9 1439.5 2154.2 1327.9 1168.6 1168.6 2252.4 2049.9 1439.7 1439.7 1713.2 2535.2 1595.5 2339.7

27r2y,23r2 11r2y,7r2 9r2q,9r2 33r2 Žy.,31r2 23r2y,7r2 29r2y,19r2 27r2 Žy.,25r2 13r2y,1r2 29r2y,23r2 25r2y,7r2 35r2 Žy.,31r2 13r2q,9r2 29r2 Žy.,25r2 7r2y,7r2 23r2 Žq.,23r2 31r2 Žy.,25r2 27r2q,11r2 13r2y,7r2 33r2 Žy.,31r2 15r2y,1r2 15r2q,11r2

25r2y,23r2 7r2y,7r2 11r2q,11r2 31r2 Žy .,31r2 21r2y,7r2 27r2y,19r2 25r2 Žy .,25r2 9r2y,1r2 27r2y,23r2 23r2y,7r2 33r2 Žy .,31r2 9r2q,9r2 27r2 Žy .,25r2 5r2y,1r2 19r2y,19r2 29r2 Žy .,25r2 25r2q,11r2 9r2y,7r2 29r2 Žy .,25r2 11r2y,1r2 11r2q,11r2 35r2 Žy.,31r2 3r2y,1r2 29r2 Žy .,25r2 11r2y,7r2 13r2q,11r2 13r2y,1r2 35r2 Žy.,31r2 29r2q,11r2 13r2y,7r2 15r2y,1r2 15r2q,11r2 19r2y,19r2 15r2y,7r2 17r2q,11r2 17r2y,1r2 35r2 Žy.,31r2 21r2y,19r2 15r2y,7r2 17r2y,7r2 Ž21r2q,19r2. 19r2y,1r2 19r2q,11r2 19r2q,11r2 23r2y,19r2 23r2y,23r2 21r2q,11r2 21r2q,11r2 19r2y,7r2 25r2y,19r2 21r2y,1r2 25r2y,23r2

7r2y,7r2 31r2 Žy.,31r2 15r2y,7r2 17r2q,11r2 17r2y,1r2 31r2q,11r2 17r2y,7r2 19r2y,1r2 19r2q,11r2 23r2y,19r2 19r2y,7r2 21r2q,11r2 21r2y,1r2 25r2y,19r2 19r2y,19r2 21r2y,7r2 Ž25r2q,19r2. 23r2y,1r2 19r2y,19r2 23r2q,11r2 27r2y,19r2 27r2y,23r2 25r2q,11r2 23r2y,23r2 23r2y,7r2 29r2y,19r2 25r2y,1r2 29r2y,23r2

(continued on next page)

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

388 Table 1 Ž continued . Eg wkeVx

Ig

Ei wkeVx

E f wkeVx

Ž Jp , K .i

Ž Jp , K .f

647.6Ž1. 659.3Ž1. 662.8Ž2. 663.2Ž1. 666.9Ž1. 686.2Ž4. 700.2Ž2. 708.1Ž1. 717.2Ž1. 730.5Ž1. 731.7Ž17. 748.0Ž1. 751.8Ž2. 758.1Ž1. 773.0Ž2. 776.5Ž1. 778.9Ž8. 819.6Ž3. 830.9Ž1. 965.8Ž4. 976.0Ž3. 981.4Ž5. 986.3Ž1.

1.50Ž15. 9.52Ž36. 1.29Ž15. 6.84Ž31. 8.70Ž37. 0.45Ž12. 0.88Ž10. 5.64Ž23. 3.09Ž18. 4.62Ž20. 0.45Ž11. 2.81Ž19. 0.64Ž9. 2.56Ž15. 0.76Ž10. 1.41Ž11. 0.59Ž30. 0.68Ž12. 20.66Ž70. 1.22Ž27. 1.64Ž32. 1.89Ž46. 3.51Ž32.

2655.0Ž10. 2560.5Ž4. 2931.7Ž4. 2706.5Ž5. 2413.1Ž5. 3010.4Ž26. 3348.5Ž4. 2930.1Ž5. 3423.7Ž7. 3291.0Ž6. 3663.6Ž5. 3161.1Ž7. 4042.8Ž14. 3348.5Ž4. 4196.7Ž15. 3706.6Ž8. 1466.6Ž23. 3980.8Ž18. 1745.7Ž3. 1880.5Ž22. 1663.6Ž21. 1466.6Ž23. 1900.3Ž7.

2007.5 1901.2 2268.9 2043.3 1746.2 2324.2 2648.5 2222.1 2706.5 2560.5 2931.7 2413.1 3291.0 2590.4 3423.7 2930.1 687.6 3161.1 914.8 914.8 687.6 485.2 914.8

25r2y,7r2 27r2y,1r2 29r2 Žy.,25r2 29r2q,11r2 27r2q,11r2 27r2y,7r2 31r2 Žy.,31r2 29r2y,1r2 33r2q,11r2 31r2y,1r2 33r2 Žy.,31r2 31r2q,11r2 35r2y,1r2 31r2 Žy.,31r2 37r2q,11r2 33r2y,1r2

21r2y,7r2 23r2y,1r2 25r2 Žy .,25r2 25r2q,11r2 23r2q,11r2 23r2y,7r2 27r2y,23r2 25r2y,1r2 29r2q,11r2 27r2y,1r2 29r2 Žy .,25r2 27r2q,11r2 31r2y,1r2 27r2 Žy .,25r2 33r2q,11r2 29r2y,1r2 15r2q,11r2 31r2q,11r2 17r2q,11r2 17r2q,11r2 15r2q,11r2 13r2q,11r2 17r2q,11r2

35r2q,11r2 19r2y,19r2

Ž19r2q,19r2.

g-ray spectrum Ž"15 ns. created by a delayed gate Ž3 to 487 ns after the detection of a prompt g-ray. on the 831 keV transition below the isomer. This figure indicates structures above the isomer. In the analyses of prompt g-rays, coincidence relations of these g-rays reveal level structures, and these structures are arranged in five rotational bands, labelled as BAND 1 to BAND 5 in Fig. 2, and four intrinsic states. The half-life of this isomer has been deduced by fitting the summed decay curve of the 831, 556, 307 and 577 keV transitions when gated on the 243 keV, 263 keV and 283 keV g-rays above the isomer, and a half-life of 12.7Ž20. ns has been obtained, see Fig. 4-Žb.. The spin of this isomeric state was determined by DCO analyses, briefly described in Section 2.3. The DCO ratio of the 831 keV transition depopulating the isomer when gated on the 430 keV 17r2q™ 13r2q E2 g-ray in the n 11r2q w615x band has been deduced to be 0.60Ž9., indicating that the possible spin of the isomer is either 19r2 or 15r2 if the 831 keV transition is of pure multipolarity. A DCO ratio of 0.94Ž11. for the 424 keV 15r2y™ 11r2y E2 g-ray in the n 7r2y w503x rotational band, when gated on the 556 keV transition feeding from the isomer, also indicates that the possible spin of the isomer is either 19r2, 15r2 or 11r2 assuming that the 556 keV transition has a pure multipolarity. The I s 19r2 assignment is preferred because this isomer is strongly populated, which indicates that this state lies near the yrast line. For the I s 19r2 assignment, the 556 keV transition would be a pure electric quadrupole transition, because an M2 transition would be expected to introduce a longer g-ray partial half-life. Therefore, we propose I p s 19r2y for this isomer, and the 831 keV transition is

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

389

Fig. 3. Gamma-ray spectra gating on the Ža. 573 keV, Žb. 533 keV, and Žc. 604 keV transitions. The ) symbols indicate known contaminations.

therefore assigned as a pure E1 transition. No M2 transition feeding from the 19r2y isomer to the 15r2q level in the n 11r2q w615x band has been observed. While the isomer is mainly populated by a 304 keV transition which depopulates the level at 2050 keV, five cascading and four cross-over transitions are observed in delayed coincidence with the g-rays depopulating the isomer Žsee Fig. 5., and these transitions define a rotational band with six levels. This K p s 19r2y rotational band based on the 1746 keV isomer is labelled BAND 1 in Fig. 2.

390

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

Fig. 4. Ža. Decay curve of the 245 keV transition gated on the 142, 171, 199, 225, 370 and 424 keV transitions, and Žb. summed decay curve of the 831, 556, 307 and 577 keV transitions when gated on the 243 keV, 263 keV and 283 keV transitions.

3.4. BAND 2 based on the 2050 keV leÕel and BAND 3 based on the 2269 keV leÕel The 2050 keV state is populated by three transitions with energies of 290, 599 and 219 keV. The 290 keV g-ray is observed in coincidence with further 309 and 328 keV transitions, and these cascading transitions together with two cross-over transitions

Fig. 5. Prompt g-spectrum gated on the delayed 831 keV transition.

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

391

define the three levels of the band above the 2050 keV state. Since the energies of those levels obey the rotational formula E ) ; AI Ž I q 1. assuming that the cascading transitions are D I s 1, we suggest that these levels are members of the rotational band built on this 2050 keV state. This band is labelled BAND 2 in Fig. 2. The 2050 keV level is also depopulated by a 611 keV g-ray to the 21r2q state of the n 11r2q w615x band. Since the 2050 keV level is the head of BAND 2, we propose that the 219 keV transition depopulates the head of another rotational band, labelled BAND 3, which contains three excited rotational levels. This bandhead also decays by a 168 keV transition to an isolated level at 2101 keV, which is itself depopulated by 112 and 355 keV transitions to members of BAND 1. The DCO ratio of the 831 keV pure E1 transition depopulating the 1746 keV isomer when gated by the 304 keV transition has been deduced to be 1.83Ž29.. A DCO ratio of 1.04Ž9. for the 556 keV pure E2 transition depopulating the isomer when gated on the 304 keV transition has also been obtained. These DCO ratios indicate the possible spin as either 23r2, 19r2 or 15r2 if the 304 keV transition has a pure multipolarity. Taking the large intensity of the 304 keV transition into account, it indicates that the head of BAND 2 lies closer to the yrast line than the 21r2y state in BAND 1. We assign I p s 23r2y to the head of BAND 2 since no half-life of this bandhead has been measured. The DCO ratio of the 322 keV transition populating the head of BAND 3 has been deduced to be 1.12Ž6. when gated on the 219 keV g-ray depopulating this bandhead. This value indicates that the spin of this bandhead is 25r2 and that the 219 keV g-ray is a D I s 1 transition with a pure multipolarity of either E1, M1, E2 or M2, assuming that the 322 keV is a pure M1 transition. A DCO ratio of 1.54Ž11. for the 168 keV transition from this bandhead has been deduced when gated by the 322 keV M1 transition. Theoretical calculations for the I s 23r2 assignment of the 2101 keV level reproduce the experimental value when the 168 keV transition is either pure dipole, quadrupolerdipole mixed with arctan d s y1.2 or quadrupolerdipole mixed with arctan d s y0.3. The intensity balance of g-rays at the bandhead of BAND 3 indicates that the 219 keV transition is either a pure E1 or a pure E2. If the 219 keV is pure E1, the 168 keV transitions has three options of mixed E2rM1 with arctan d s y1.2, mixed E2rM1 with arctan d s y0.3 and mixed M2rE1 with arctan d s y0.3. Assuming that the 219 keV g-ray is pure E2, the 168 keV transition can be either mixed E2rM1 with arctan d s y1.2 or mixed M2rE1 with arctan d s y0.3. Tentatively, we assigned the 219 keV transition to pure E2 and the 168 keV transition to mixed M2rE1 with arctan d s y0.3, but other options can not be ruled out completely from the experimental data. Therefore, we tentatively give a negative parity to the bandhead of BAND 3 and a positive parity to the 2101 keV I s 23r2 state. 3.5. BAND 4 based on the leÕel at 3348 keV and three intrinsic states aboÕe 4 MeV Four transitions are observed to depopulate a level at 3348 keV to the 27r2 Žy. and the 29r2 Žy. states of BAND 3, to the 27r2y state of BAND 2 and to the 29r2y state in BAND 1, via transitions with energies of 758, 417, 700 and 193 keV, respectively. Two cascading transitions with energies of 315 and 333 keV are observed in coincidence with those four transitions. We propose that these two cascading transitions are

392

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

in-band D I s 1 transitions in a rotational band based on the 3348 keV level. The spin assignment of the 3348 keV bandhead has been made by using a DCO ratio of 1.00Ž7. for the 417 keV transition, when gated on the 341 keV D I s 1 M1 transition in BAND 3. This implies the spin of the bandhead is either 31r2 or 27r2 if the 417 keV g-ray is a pure stretched transition. However, once again taking the population intensity of the bandhead into account, the I s 31r2 assignment is most likely. Since two D I s 2 g-rays depopulating the bandhead are observed and since no half-life has been measured, we regard these as E2 transitions which gives further support to the K p s 31r2 Žy. assignment to the 3348 keV level. The decay from the 33r2 band member is discussed in Section 4.3.5. Three levels decay to the 35r2 Žy. state of BAND 4 via the 392 keV, 443 keV and 542 keV transitions. No band structure built on these states has been identified. Since these states are weakly populated, DCO ratio analyses of the transitions could not been made. Possible spins and their intrinsic structures will be discussed with reference to BCS calculations with blocking, briefly described in Section 4.3.1. 3.6. BAND 5 based on the leÕel at 1900 keV A rotational sequence based on a level at 1900 keV has been newly observed in the present work, and this structure is referred to as BAND 5 in Fig. 2. The bandhead decays to the 19r2y isomer by a 154 keV g-ray and to the 17r2q level of the K p s 11r2q band by a 986 keV g-ray. Since this structure has been weakly populated in the present work, the spin of these states could not been determined by a DCO ratio analysis. We propose tentatively a K p s Ž19r2q. assignment for this structure, and the configuration will be discussed by comparison with BCS calculations with blocking, in Section 4.3.6. 3.7. LeÕels at 1467, 1664, 1881 and 2874 keV Four high-energy transitions with energies ; 1 MeV populate low-spin members of the n 11r2qw 615x rotational band and define three levels at 1467, 1664 and 1881 keV, see Fig. 1. The level spacings between the 1664 keV and the 1467 keV level and between the 1881 keV and the 1664 keV levels are 197 and 217 keV, respectively, which are close to the energies of in-band cascading g-rays in the n 11r2qw 615x rotational band. Therefore we regard these 1467, 1664, 1881 keV levels as vibrational excitations of the 13r2q, 15r2q and 17r2q levels of the n 11r2q w615x band, respectively, and this structure is referred to as BAND 6. The nature of this structure will be discussed later in Section 4.3.7. A level at 2874 keV has been observed to decay to the 29r2q state of the n 11r2qw 615x band by a 168 keV g-ray, see Fig. 1. The weak intensity of this transition prevents the spin assignment by a DCO ratio analysis. Therefore, the spin and parity have not been experimentally determined. 4. Discussion In this section, the structures in 183 W will be discussed by means of in-band B ŽM1.rB ŽE2. ratios and g K factors. Possible admixture of octupole-vibrational components in the n 7r2yw 503x and n 11r2qw 615x configurations will be also discussed.

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

393

4.1. The g K factors and B( M1 ) r B( E2 ) ratios The intensity ratio of E2 cross-over to M1 q E2 cascade transitions within a band can be used to deduce g K factors, and hence this value can be compared to theoretical predictions for the proposed Nilsson configurations of the band. The branching ratio of magnetic dipole and electric quadrupole transitions at a given level can be related to the transition energies, mixing ratio and the K quantum numbers by the well-known rotational model expression

d2 1qd 2

sl

Eg5 Ž I ™ I y 1 . ² IK 20 < I y 1 K :2 Eg5 Ž I ™ I y 2 . ² IK 20 < I y 2 K :2

,

Ž 1.

where the branching ratio l is defined by l s Tg Ž I ™ I y 2.rTg Ž I ™ I y 1.. The ratio of the reduced transition probabilities, B ŽM1, I ™ I y 1.rB ŽE2, I ™ I y 2., is given by B Ž M1, I ™ I y 1 . B Ž E2, I ™ I y 2 .

s 0.6967

Eg5 Ž I ™ I y 2 .

m2N

1

Eg3 Ž I ™ I y 1 . l Ž 1 q d 2 .

e2 b2

.

Ž 2.

In the strong coupling limit, a theoretical B ŽM1. value can be calculated by the following equation: B Ž M1, I ™ I y 1 . s

2

3 8p I 2

'I 2 y K 2 Ý Ž g j y g R . V j

½

j

5

m2N .

Ž 3.

However, the Coriolis effect on particles in high-j intruder orbitals, for example n 11r2qw 615x and n 9r2qw 624x , makes these particles align to the rotational axis, thus a significant aligned angular momentum is observed. In order to take into account this Coriolis effect, a generalization of the semi-classical formula w10x for the B ŽM1, I ™ I y 1. value has been used: B Ž M1, I ™ I y 1 . s

3 8p I 2

½ ž

'I 2 y K 2 Ý

1 " d jk

j

D eX "v

/Ž

g j y gR . V j

5

2

yK

½ÝŽ j

g j y gR . i j

5

m2N ,

Ž 4.

where Ks Ý Vj j

and i j is the aligned angular momentum of the jth nucleon of the configuration which has a g K value of g j . The D eX is a signature splitting, due to the k th single-particle orbital, at the corresponding rotational frequency " v of the spin I state. The sign before d jk corresponds to the sign of a I y a Iy1 where a I is the signature quantum number at the spin I state. Theoretical values of g j are calculated from the wave-functions in w11x, at d s 0.2, and are listed in Table 2. The aligned angular momenta i j were taken from the neighbouring nuclei, also listed in Table 2. An alternative to experimental B ŽM1, I

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394

Table 2 The g j factors and aligned angular momenta of single-particle orbitals considered for

183

W

Neutron

gj

ij

Proton

gj

ij

9r2w624x 7r2w514x 5r2w512x 7r2w503x 11r2w615x 7r2w633x 1r2w510x 1r2w521x 3r2w512x

y0.24 0.27 y0.37 y0.35 y0.22 y0.26 y1.71 0.88 0.57

1.0 0.0 0.0 0.0 0.5 2.0 0.5 0.5 0.0

7r2w404x 9r2w514x 5r2w402x 1r2w411x 1r2w541x

0.63 1.29 1.57 y0.98 0.76

0.0 0.5 0.0 0.0 3.0

™ I y 1.rB ŽE2, I ™ I y 2. ratios uses experimental g K values from the rotational model formula: gK y gR

s "0.933

Q0

Eg Ž I ™ I y 1 .

d'I 2 y 1

.

Ž 5.

The experimental g K factors derived from this formula can be compared with theoretical effective g K factors of the proposed configurations, which are obtained from Ref. w12x,

Ý Ž g j y gR . V j g Keff s

j

Ý Ž g j y gR . i j y

K

j

'I 2 y K 2

q gR .

Ž 6.

In the present work we have employed constant values of g R s 0.25 and Q 0 s 7.0 eb. For calculations for B ŽM1. values, aligned angular momenta of 1.0, 0.5 and 0.5 for n 9r2w624x, n 11r2w615x and n 1r2w510x, respectively, are considered. 4.2. One-quasiparticle bands 4.2.1. The K p s 1 r 2 y ground state band The K p s 1r2y ground state band was studied by Coulomb excitation, and g-factors of the 7r2y, 9r2y, 11r2y, 13r2y and 17r2y states were measured by using the transient-field technique w1x. In the present work, g K factors and B ŽM1.rB ŽE2. ratios extracted from intensity ratios of in-band E2 cross-over to cascading transitions are compared to the theoretical values of the proposed n 1r2yw 510x configuration. In order to extract experimental values and to calculate theoretical values, constant values of Q0 s 7.0 eb, g R s 0.25 and i x s 0.5 " are assumed. The signature splitting of this band extracted from the experimental data is also considered. Figs. 6a.1 and Figs. 6b.1 show experimental B ŽM1.rB ŽE2. ratios and g K factors Žfilled circles. in comparison with theoretical calculations for the n 1r2yw 510x structure. A satisfactory agreement between experimental and theoretical values confirms the n 1r2yw 510x assignment to this band. The aligned angular momentum of this band is shown in Fig. 7. Its magnitude and small signature splitting due to K s 1r2 are consistent with the proposed configuration.

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

395

Fig. 6. Experimental B ŽM1.r B ŽE2. ratios in units of m2N re 2 b 2 and g K factors of the n 1r2y w510x , the n 7r2y w503x and the n 11r2q w615x rotational bands Žfilled circles., compared with the theoretical calculations Žsolid and dotted lines.. See text for details.

4.2.2. The K p s 7 r 2 y and 11 r 2 q rotational bands: Signals of octupole-Õibrational components. Experimental B ŽM1.rB ŽE2. ratios and g K factors of the K p s 7r2y rotational band are plotted in Figs. 6a.2 and -Žb-2., respectively. Theoretical calculations for the proposed n 7r2yw 503x configuration, shown by solid lines, are compared with the experimental values. The calculations do not reproduce the experimental values. An admixture of the n 7r2yw 514x configuration with n 7r2yw 503x was calculated in earlier work w2x. However, this mixing cannot reproduce experimental values because the g K y g R of the n 7r2yw 514x configuration is approximately zero. The increasing alignment of this band shown in Fig. 7 would suggest an s-band component in the band, but the experimental values cannot be explained by an s-band component, either.

396

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Fig. 7. Experimental aligned angular momenta of the rotational bands in I 0 s 30.3 " 2 MeVy1 and I 1 s 35.3 " 3 MeVy4 are used.

183

W. The Harris parameters

Fig. 8 shows experimental g K factors of the n 7r2yw 503x band with g R s 0.2, 0.25 and 0.3 and with Q 0 s 6.0, 6.5 and 7.0 eb, and these values are compared to a theoretical value of g K s y0.35 for the proposed n 7r2yw 503x configuration, which is independent to the assumed g R and Q0 values because the n 7r2yw 503x orbital is not Coriolis mixed. None of experimental values is in good agreement with the theoretical values except for at I s 25r2. Calculations based on Quasiparticle-Phonon Model ŽQPM. predict an octupole-vibrational n 11r2qw 615x y Q 32 and a b-vibrational n 7r2yw 503x q Q20 components, and Quasiparticle-Rotation-Vibration Model ŽQRVM. predicts a b-vibrational n 7r2yw 503x q Q20 component, in the n 7r2yw 503x wave function w2x. The main two-quasiparticle components calculated in Ref. w2x are listed in Table 3. Since the Q20 component gives no contribution to g K factors and B ŽM1.rB ŽE2. ratios, we consider only the n 11r2qw 615x y Q32 component in the n 7r2yw 503x configuration. A 3% admixture of n 11r2qw 615x y Q32 was calculated by QPM w2x, and calculated B ŽM1.rB ŽE2. ratios and g K factors are shown in Fig. 9a.1 and Fig. 9b.1 by dotted lines. It is shown in these figures that this 3% component improves slightly the comparison between the theoretical calculations and the experimental values. However, in order to reproduce the experimental values, 30% Ždashed line in Fig. 9-Ža-1. and -Žb-1.. and 60 % Ždashed-dotted lines in Fig. 9-Ža-1. and -Žb-1.. of n 11r2qw 615x y Q32 components are needed near the bandhead and at high-spin states, respectively, assuming g R s 0.25 and Q0 s 7.0 eb. Such large components were not predicted in the earlier theoretical work w2x, however, it would be a further theoretical challenge to understand the electro-magnetic structure of this band.

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397

Fig. 8. Experimental g K factors of the n 7r2y w503x rotational band with Q0 s6.5, 7.0 and 7.5 eb, and with g R s 0.2, 0.25 and 0.3.

Experimental B ŽM1.rB ŽE2. ratios and g K factors of the n 11r2qw 615x rotational band are shown in Figs. 6-Ža-3. and -Žb-3. by filled circles. Theoretical calculations for the n 11r2qw 615x configuration with a constant aligned angular momenta of 1.0 " are shown in these figures by solid lines, and in the calculation a signature splitting extracted from experimental data is considered. At high spin, the experimental g K -factors deviate from the theoretical values. The experimental aligned angular momentum of this band is shown in Fig. 7, and it shows a Coriolis effect on this band and a large signature splitting at high frequency. Therefore, we took advantage of the experimental aligned angular momentum in Eq. Ž4.. The results of the calculation are shown in Figs. 6-Ža-3. and -Žb-3. by dotted lines. The calculations give a satisfactory agreement with the experimental values in the whole observed spin range expect for the 27r2q and 31r2q states. In Figs. 9-Ža-2. and -Žb-2., theoretical calculations with 30 and 60%

Table 3 Main two-quasiparticle components in Q20 and Q32 The main two-particle component Q20

Q32

n 2 7r2w503x y 7r2w503x n 2 9r2w624x y 9r2w624x n 2 1r2w510x y 1r2w510x p 2 9r2w514x y 5r2w402x n 2 11r2w615x y 7r2w503x n 2 1r2w521x q 3r2w642x

13% 12% 8% 83% 5% 2%

398

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

Fig. 9. Experimental B ŽM1.r B ŽE2. ratios in units of m2N re 2 b 2 and g K factors of the n 7r2y w503x and the n 11r2q w615x rotational bands Žfilled circles., compared with the theoretical calculations with and without the octupole-vibrational component Žsolid, dotted, dashed and dotted-dashed lines.. See text for details.

admixture of the n 11r2qw 615x y Q32 components are shown by dashed and dasheddotted lines, respectively. The staggering observed both for the B ŽM1.rB ŽE2. ratios and g K factors at high-spin is not understood. 4.3. Three- and fiÕe-quasiparticle bands In this section, three- and five-quasiparticle structures will be discussed. The predictive power of the BCS calculations with blocking ŽBBCS. was used to find possible configurations for these bands. A brief description of the BBCS calculation will be given in Subsection 4.3.1. 4.3.1. BCS calculations with blocking Calculations of level energies for three, five and higher seniority quasiparticle states in 183 W have been carried out following the prescription outlined by Jain et al. w13x. In this approach, which is referred to as a BBCS calculation ŽBCS calculation with blocking., the unpaired nucleons are allowed to influence the superfluid properties of the system since their levels are no longer available for pair correlations. Single-particle energies were calculated by using a Nilsson potential with deformation parameters e 2 s 0.225 and e 4 s 0.093 and were adjusted to reproduce one-quasiparticle levels in 183 W and single-particle levels in neighbouring nuclei. The single-particle energies used in the BBCS calculations are shown in Fig. 10. The calculated excitation energies, with a monopole paring strength of 23.8rA for protons and 21.5rA for neutrons, were corrected by orbital dependent residual nucleon–nucleon interactions which were obtained from experimental level energies of A ; 180 nuclei w13x and two-quasiparticle

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

Fig. 10. Single-particle energies relative to Fermi surfaces used in BBCS calculations for

399

183

W.

level energies in 180 Ta w14x. The strengths of the residual interactions used in the calculations are listed in Table 4. Details of these results will be discussed in the following sections. Table 5 summarizes the configurations of three- and five-quasiparticle rotational bands. 4.3.2. The K p s 19 r 2 y rotational band, BAND 1. Coriolis mixing of the n 1 r 2 y [510] configuration The BBCS calculations show that a K p s 19r2y coupling with the 3 n 9r2w624x11r2w615x1r2w510x configuration is lower in energy than any other intrinsic states with K 0 15r2. Therefore, this state is expected to be an isomer. Since the bandhead of BAND 1 has a T1r2 s 12.7Ž2. ns half-life, and since the experimental bandhead energy is 1745 keV which is close to the calculated value of 1624 keV, we assign the n 3 9r2w624x11r2w615x1r2w510x configuration to BAND 1. The experimental B ŽM1.rB ŽE2. ratios and g K factors shown by filled circles in Fig. 11a.1 and Fig. 11b.1 are compared to the theoretical calculations of the proposed configuration Žsolid line.. The theoretical calculations cannot reproduce the experimental values. However, the Coriolis force acting on the 1r2yw 510x neutron in the configuration induces a K s 21r2 component, with an opposite angular momentum direction of n 1r2yw 510x in the K s 19r2 coupling. Therefore, calculations considering this Coriolis mixing have been done. Theoretical values with 50% Coriolis mixing can reproduce the experimental values, except at I s 23r2, see dotted line in Fig. 11-Ža-1. and Žb-1.. We therefore propose a n 3 9r2w624x11r2w615x y 1r2w510x structure with a 50% K s 21r2 component. The aligned angular momentum of this band is shown in Fig. 7. The large values observed are consistent with the two i 13r2 neutrons assigned to the configuration. 4.3.3. BAND 2, the K p s 23 r 2 y rotational band Experimental B ŽM1.rB ŽE2. ratios and g K factors of BAND 2, extracted from the in-band intensity ratios of E2 cross-over to cascading transitions, are plotted in

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

400

Table 4 The strength of orbital dependent residual interactions in keV. From top to bottom, for proton–proton, neutron–neutron, and proton–neutron pairs

p yp

7 2

7 2 9 2 5 2 1 2 1 2

y 239 424 300 300

239 y 399 300 300

424 399 y 300 300

300 300 300 y 300

300 300 300 300 y

n yn

9 2

7 2

1 2

3 2

1 2

9 2 7 2 1 2 3 2 1 2 5 2 7 2 7 2 11 2

y 136 256 300 255 343 400 300 300

136 y 300 300 295 118 136 300 300

256 300 y 300 300 300 256 300 300

300 300 300 y 300 300 300 300 300

255 295 300 300 y 306 255 300 300

343 118 300 300 306 y 330 300 300

400 136 256 300 255 330 y 300 300

300 300 300 300 300 300 300 y 300

300 300 300 300 300 300 300 300 y

p yn

9 2

7 2

1 2

3 2

1 2

5 2

7 2

7 2

11 2

7 2 9 2 5 2 1 2 1 2

y176 y33 y208 y110 y232

w404x w514x w402x w411x w541x

w624x w514x w510x w512x w512x w512x w633x w503x w615x

w404x w514x w402x w411x w541x

9 2

w404x

w624x

w624x

5 2

w514x

w514x

w514x

y120 y67 y110 y152 y150

w402x

w510x

w510x

y125 y150 y93 y150 y150

1 2

w411x

w512x

w512x

y150 y150 y215 y150 y150

1 2

w541x

w521x

w521x

y74 y171 y94 y193 y149

5 2

w512x

w512x

y161 y146 y122 y228 y186

7 2

w633x

w633x

y84 y129 y124 y110 y232

7 2

w503x

w503x

y150 y150 y92 y150 y150

11 2

w615x

w615x

y150 y150 y225 y150 y150

Fig. 11-Ža-2. and -Žb-2. by filled circles. The theoretical calculations for the n 3 3r2w512x9r2w624x11r2w615x configuration are also shown in this figure by solid lines. A satisfactory agreement between experimental and theoretical values is shown, therefore we assign this configuration to BAND 2. The aligned angular momentum of the band is plotted in Fig. 7, and similar values to BAND 1 are consistent with the proposed configuration involving two i 13r2 neutrons. The single-particle energy of the n 3 3r2w512x9r2w624x11r2w615x configuration was predicted to be 1888 keV by the BBCS calculations, which is close to the experimental observation at 2050 keV.

Table 5 head Proposed configurations for BANDs 1 through 5 with three- and five-quasiparticle structures. Eexp and Ecal denote experimental energies of bandheads and the calculated energies by the BBCS theory, respectively Kp BAND 1 BAND 2 BAND 3 BAND 4 BAND 5

head w Eexp keVx y

y

19r2 and 21r2 23r2y 25r2 Žy. 31r2 Žy. Ž19r2q .

1746 2050 2269 3348 1900

Proposed conf. 3

n 9r2w624x11r2w615x1r2w510x n 3 9r2w624x11r2w615x3r2w512x p 2 9r2w514x5r2w402xn 11r2w615x p 2 7r2w404x5r2w402xm19r2y n 3 1r2w510x11r2w615x7r2w514x

Ecal wkeVx 1624 1888 2642 3182 2060

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

401

Fig. 11. The experimental B ŽM1.r B ŽE2. ratios and g K factors of BAND 1 and 2 Žfilled circles., compared with the theoretical calculations Žsee text..

4.3.4. BAND 3, the K p s 25 r 2 (y ) rotational band The K p s 25r2 Žy. rotational band based on the level at 2269 keV is characterized by much stronger in-band cascading transitions than E2 cross-over g-rays. The BBCS calculations show that the lowest three-quasiparticle K p s 25r2y state at 2642 keV has the p 2 9r2w514x5r2w402xn 11r2qw 615x configuration. This configuration gives large B ŽM1.rB ŽE2. ratios because the g K values of these proton orbitals are large. The experimental B ŽM1.rB ŽE2. ratio and g K factor are extracted only at the 29r2 level. They are 36.4Ž44. and 0.95Ž4., respectively, while the theoretical values are 11.9 and 0.64. However, there are no other configurations that give larger B ŽM1.rB ŽE2. ratios than this proposed configuration. Therefore, we assign this configuration to BAND 3. The aligned angular momentum of this band is shown in Fig. 7. The values are slightly smaller than those of BAND 1 and 2. As discussed in the previous sections, the configurations of BAND 1 and 2 include two i 13r2 neutrons, while the configuration of BAND 3 includes a p 9r2yw 514x proton instead of a n 9r2qw 624x neutron, so that a smaller alignment is expected. 4.3.5. BAND 4, the K p s 31 r 2 (y ) rotational band We propose the five-quasiparticle configuration p 2 7r2w404x5r2w402x m19r2y for the K p s 31r2 Žy. rotational band, BAND 4. Since no E2 cross-over transition is observed in this band, only limits of the B ŽM1.rB ŽE2. ratio and g K factor at the 35r2 Žy. level have been obtained, and they are ) 9.3 and ) 0.51, respectively. The theoretical values for this proposed configuration are calculated to be 10.5 and 0.52, respectively, which both are in good agreement with the experimental limits. As discussed in Section 4.3.2, the Coriolis force acting on the n 1r2yw 510x neutron induces D K s 1 components. Therefore, we also calculated the theoretical values with a 50%

402

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

K s 29r2 component. The theoretical B ŽM1.rB ŽE2. ratio and g K factor of 6.0 and 0.46, respectively, are not within the experimental limits, which might indicate a lack of the D K s 1 component in this structure. The single-particle energy of the proposed configuration was also calculated by BBCS, and a calculated energy of 3182 keV is in quite good agreement with the experimental observation at 3348 keV. The aligned angular momentum of this band is the largest of all observed bands in 183 W , see Fig. 7. From the 33r2 Žy. state of this band, two inter-band transitions with energies of 372 and 732 keV to BAND 3 have been observed. This may reveal mixing of the wave-functions of the 33r2 Žy. levels of these bands. A two-band mixing calculation has been made assuming that an unobserved I s 33r2 state of BAND 3 would depopulate by a 379 keV g-ray to the 31r2 Žy. member at 3292 keV. The two 33r2 levels would then be only 7 keV apart. A mixing matrix element of 0.46 keV can explain the intensity ratio of the 372 keV inter-band transition to that of the 315 keV in-band transition in BAND 4. 4.3.6. BAND 5, the K p s (19 r 2 q) rotational band We proposed that the regular level sequence, BAND 5, as a rotational structure with K p s Ž19r2q. . The experimental B ŽM1.rB ŽE2. ratio and g K factor have been deduced at the Ž25r2q. state at 2723 keV to be 0.88Ž23. and 0.04Ž3., respectively. We propose the n 3 1r2w510x 11r2w615x 7r2w514x configuration for this band. At I p s 25r2q, the theoretical B ŽM1.rB ŽE2. ratios and g K factors are calculated to be 0.95 and 0.07, respectively, which are very close to the observed values. Fig. 7 shows the aligned angular momentum of this band by star symbols. The experimental values smaller than bands which contain two i 13r2 neutrons and larger than all one-quasiparticle bands are consistent with the proposed configuration. The BBCS calculations predict this proposed structure at 2060 keV, which is in good agreement with the experimental observation at 1900 keV. 4.3.7. BAND 6 We propose that levels of BAND 6 are vibrational states built on the n 11r2qw 615x structure since no in-band transitions is observed and since the level spacings between the 1664 keV and 1467 keV levels and between the 1881 keV and 1664 keV levels are close to those between 15r2q and 13r2q states and between 17r2q and 15r2q states, respectively, of the n 11r2qw 615x band. Since the head of the n 11r2qw 615x band at 310 keV is a long-lived isomer with T1r2 s 5.2 s, and no in-band transition in BAND 6 is observed, one cannot determine the lowest state of this vibrational structure. However, one can expect a lowest state at approximately 970 keV relative to the n 11r2qw 615x bandhead. Fig. 12 shows the energies of the lowest vibrational levels observed in A ; 180 nuclei. In 182 W, the lowest states of a b-band, a g-band and an octupole band are observed at 1136, 1221 and 1289 keV, respectively w9x. In 184 W, an octupole- and a g-band are observed at 903 and 1130 keV, respectively, but no b-band is observed w9x. The proposed energy of the lowest state of BAND 6 is approximately between the energies of the bandheads of the g-bands in the neighbouring nuclei, and we therefore suggest that this structure is a g-vibration built on the n 11r2qw 615x structure. 4.3.8. LeÕels at 2101, 4389, 4440 and 4539 keV The head of BAND 3 is depopulated by a 168 keV transition to the 2101 keV level, and this 2101 keV state is depopulated by two transitions with energies of 112 and 355

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

403

Fig. 12. The energy of observed b-, g- and octupole vibrational bands in Hf, W and Os isotopes. Data are taken from Refs. w9,15x.

keV to BAND 1, see Fig. 2. We suggested in Section 3.4 that this state has K p s 23r2 Žq.. BBCS calculations show a 23r2q state with the p 2 5r2w402x7r2w404x n 11r2w615x configuration at 1880 keV, which is close to the observed energy of this state. Therefore, we tentatively assign this configuration to this state. Three g-rays populate the 35r2 Žy. state of BAND 4 and define three levels at 4389, 4440 and 4539 keV. The spins of these levels have not been assigned in the present work. Taking the population intensities into account, we propose that these states lie near the yrast line. Therefore, we suggest the spins of these states to be either 37r2 or 39r2. Only negative parity is considered if I s 39r2. The BBCS calculations show six possible K s 37r2 and three 39r2y structures with two protons and three neutrons around the observed energy region. These are summarized in Table 6.

Table 6 Possible configurations for the 4389, 4440 and 4539 keV levels. Listed energies are calculated by the BBCS theory Žsee text. Kp

Energy wkeVx

Configuration q

37r2 37r2q 37r2q 37r2y 37r2q 37r2y 39r2y 39r2y 39r2y

2

3

p 5r2w402x9r2w514xn 3r2w512x11r2w615x9r2w624x p 2 5r2w402x7r2w404xn 3 11r2w615x7r2w503x7r2w514x p 2 7r2w404x9r2w514xn 3 1r2w510x11r2w615x9r2w624x p 2 7r2w404x9r2w514xn 3 3r2w512x11r2w615x7r2w514x p 2 7r2w404x11r2w505xn 3 y1r2w510x11r2w615x9r2w624x p 2 5r2w402x9r2w514xn 3 11r2w615x7r2w503x5r2w512x p 2 5r2w402x7r2w404xn 3 11r2w615x7r2w503x9r2w624x p 2 5r2w402x9r2w514xn 3 11r2w615x7r2w503x7r2w514x p 2 5r2w402x7r2w404xn 3 11r2w615x9r2w624x7r2w514x

3960 4255 4560 4640 4770 4925 4377 4620 4735

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

404

4.4. Half-liÕes and hindrance In the present work, half-lives of two bandheads have been measured by fitting the decay curve of g-rays depopulating these bandheads, and those of four bandheads have been restricted by analysis of the centroid shift of Ge-time spectra gated by feeding and depopulating transitions. These are summarized in Table 7. The Weisskopf hindrance factor F for the transition depopulating these states is obtained by comparing to the single-particle estimate Fs

g T1r2 W T1r2

,

Ž 7.

g W where the T1r2 is the measured partial g-ray half-life and the T1r2 is the Weisskopf estimate. The hindrance factors of g-rays depopulating the bandheads listed in Table 7 are shown in Table 8. A multipolarity with parentheses indicates that the multipolarity is assumed. The hindrance is often related to the change of the K-quantum number, and a reduced hindrance factor for K-forbidden transitions is defined by

fn s F 1r n ,

Ž 8.

where n s D K y l, and l is the multipolarity of transitions. Reduced hindrance factors of fn s 10 ; 100 have been observed systematically for both electric and magnetic transitions w16x. However, for one-time K-forbidden Ž n s 1. E2 transitions,two-times K-forbidden M1 transitions and one-time K-forbidden M1 transitions, fn s 10 ; 10 4 , 100 ; 1000 and 1 ; 10 4 , respectively, are found in the same work. Since E1 transitions are hindered in themselves by large factors w16,17x, the Weisskopf estimates were multiplied by a factor of 10 4 when calculating the reduced hindrance factor. Most of reduced hindrance factors of K-forbidden transitions are approximately within the systematic values, except for the 19r2y™ 15r2y four-times K-forbidden E2 transitions and the 31r2 Žy. ™ 29r2y five-times K-forbidden ŽM1. transition. The reduced hindrance factors of these two transitions are deduced to be 4.3Ž2. and - 3.9, respectively, which indicate that these transitions are less forbidden than other transitions. It should be noted that the configurations of the 19r2y and 31r2 Žy. states involve both the n 11r2qw 615x and n 9r2qw 624x i 13r2 neutrons. In 182 W w18x and 183 Re w19x, small reduced hindrance factors of fn ; 5 have been observed for E2 transitions which depopulate high-K bandheads whose configurations also involve these two i 13r2

Table 7 Half-lives measured or restricted in the present work Ip

Kp y

7r2 19r2y 23r2y 25r2 Žy. 31r2 Žy. Ž19r2q .

E x wkeVx y

7r2 19r2y 23r2y 25r2 Žy . 31r2 Žy . Ž19r2q .

453 1746 2050 2269 3348 1900

T1r2 wnsx 7r2w503x BAND 1 BAND 2 BAND 3 BAND 4 BAND 5

21.5Ž20. 12.7Ž20. -1.5 - 3.0 - 0.5 - 3.0

T.R. Saitoh et al.r Nuclear Physics A 669 (2000) 381–406

405

Table 8 Hindrance and reduced hindrance factors of transitions depopulating the bandheads listed in Table 7. Iip , K i

Ei I pf , K f wkeVx

Eg Mult. wkeVx

n DK y l F

7r2y,7r2

453 9r2y,1r2 7r2y,1r2 5r2y,1r2 3r2y,1r2 5r2y,3r2 1746 17r2q,11r2 19r2q,11r2 21r2q,11r2 15r2y,7r2 17r2y,7r2 2050 19r2y,19r2 21r2q,11r2 2269 23r2 Žq .,23r2

144 245 354 409 161 831 557 307 556 307 304 557 168

2 2 2 1 1 3 3 3 4 5 allowed 5 allowed

19r2y,19r2

23r2y,23r2 25r2 Žy.,25r2

23r2y,23r2 3348 29r2 Žy .,25r2 27r2 Žy.,25r2 27r2y,23r2 29r2y,19r2 Ž19r2q .,Ž19r2. 1900 19r2y,19r2 17r2q,11r2 31r2 Žy.,31r2

219 417 758 700 193 154 986

ŽM1. ŽM1. ŽM1. E2 ŽM1. E1 ŽE1. ŽE1. E2 ŽM1. E2 ŽE1. E1rM2 d sy0.3 E1 M2 E2 ŽM1. E2 E2 ŽM1. ŽE1. ŽM1.

allowed 2 1 2 5 allowed 3

6.8Ž9.=10 ^4 5.2Ž6.=10 ^4 5.0Ž7.=10 ^5 6.8Ž10.=10 ^2 2.6Ž3.=10 ^4 1.2Ž2.=10 ^8 5.8Ž9.=10 ^7 2.1Ž3.=10 ^7 3.5Ž6.=10 ^2 1.1Ž2.=10 ^5 - 0.5 - 4.6=10 ^8

- 3.2=10 ^5 - 2.2=10 ^y1 - 3.2=10 ^y2 - 3.1=10 ^3 -1.5=10 ^2 - 3.0=10 ^2 -9.4=10 ^2 - 2.1=10 ^5 -1.8=10 ^5

fn 260.8Ž173. 228.0Ž132. 707.1Ž495. 680.0Ž1000. 2.6Ž3.=10 ^4 22.9Ž13. 18.0Ž9. 12.8Ž6. 4.3Ž2. 10.2Ž4. -8.6

- 55.7 -1.5=10 ^2 -17.3 - 3.9 - 56.5

neutrons. These small reduced hindrance factors are also consistent with the systematics reported in Refs. w20,21x.

5. Conclusion High-spin states in 183 W have been populated by fusion-evaporation reactions of 68 MeV 14 C with 176 Yb. In the present work, five one-quasiparticle rotational bands have been extended to much higher spin than previously known. Six rotational bands with three- and five-quasiparticle configurations above a 19r2y T1r2 s 12.7 ns isomer, and the g-vibrational band built on the n 11r2w615x structure, have been newly identified. In the one-quasiparticle rotational bands with the n 7r2w503x and n 11r2w615x configurations, an admixture of the octupole-vibrational component, n 11r2w615x y Q 32 and n 7r2w503x q Q32 , respectively, has been proposed based on the analyses of in-band B ŽM1.rB ŽE2. ratios and g K factors. In the K p s 19r2y rotational band with n 311r2w615x9r2w624x y 1r2w510x based on the isomer, a K p s 21r2y component due to the Coriolis force acting on the 1r2w510x neutron has been identified. The experimental energies of the bandheads of three- and five-quasiparticle rotational bands are in good agreement with BBCS calculations. A total of 17 K-forbidden transitions has been observed, and their hindrance factors compare well with the systematic values.

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