Identification of high spin states in Zr100

PHYSICAL REVIEW C 74, 017303 (2006) Identification of high spin states in 100 Zr J. K. Hwang,1 A. V. Ramayya,1 J. H. Hamilton,1 J. O. Rasmussen,2 Y. X. Luo,1,2 D. Fong,1 K. Li,1 C. Goodin,1 S. J. Zhu,1,3 S. C. Wu,2 M. A. Stoyer,4 R. Donangelo,5 X.-R. Zhu,6,7 and H. Sagawa6 1 Physics Department, Vanderbilt University, Nashville, Tennessee 37235, USA 2 Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 3 Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China 4 Lawrence Livermore National Laboratory, Livermore, California 94550, USA 5 Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, Brazil 6 Center for Mathematical Sciences, University of Aizu, Aizu-Wakamatsu, Fukushima 965-8560, Japan 7 Department of Physics, Xiamen University, Xiamen 361005, People’s Republic of China (Received 20 April 2006; published 18 July 2006) Eight new high spin states and 23 new γ transitions have been identified in 100 Zr from studies of 252 Cf spontaneous fission with Gammasphere. A near-spherical excited band in 100 Zr based on the 331.1 keV 0+ state is extended from 4+ up to 12+ . A I = 1 band with band-head energy of 2316.1 keV is extended. DOI: 10.1103/PhysRevC.74.017303 PACS number(s): 23.20.Lv, 21.60.Cs, 25.85.Ca, 27.60.+j It has recently been shown that nuclei around A = 100 (36
Z
45 and 54
N
65) have interesting features such as coexistence of nearly spherical and well deformed shapes [1–3] and degenerate doublet bands claimed to be evidence of chirality [4]. The isotopes in this region change very rapidly from a spherical shape for nuclei with N
56 to well deformed shape for nuclei with N ∼ 60–62 because of deformation-driving orbitals such as ν9/2[404] and the reinforcement of proton and neutron shell gaps at the same deformation in the Kr, Sr, and Zr nuclei [1,5,6]. Gammaunstable or triaxial shapes could be built between these coexisting two deformations [4,7]. A triaxial shape, where broken chiral symmetry may occur, gives rise to a pair of nearly degenerate bands as reported in 104 Rh [4,7]. 100 Zr with N = 60 exhibits clear coexistence of a nearspherical band built on the 331.1 keV state and a ground band with well deformed prolate shape [β2 =0.32(2)] [8]. The deformed ground band has been well established up to 20+ from the fission work of 248 Cm [6] and a near-spherical band upto 4+ from our earlier fission work of 252 Cf [1]. Therefore, it is interesting to identify the high spin members of the near-spherical band and also the other states that may show complexities associated with prolate, oblate, and possibly triaxial shapes. The measurements were carried out at the Lawrence Berkeley National Laboratory with a covered 252 Cf source of about 60 µCi inside the reaction chamber of Gammasphere with 102 Ge detectors. The source was sandwiched between two Fe foils of thickness 10 mg/cm2 . The coincidence data (5.7×1011 triple and higher fold) were analyzed with the RADWARE software package [9]. The very high statistics enabled us to identify new states and transitions. The known γ transitions in 100 Zr and the Ce partner isotopes were used to identify the new transitions. In the present work, a near-spherical excited band in 100 Zr is extended from 4+ up to 12+ . This is the highest spin to which a coexisting near-spherical band has been observed in this region. Our new level scheme is shown in Fig. 1. In Figs. 2(a) and 2(b), parts of coincidence spectra with double gates on 275.6 0556-2813/2006/74(1)/017303(4) 017303-1 and 267.3 keV transitions and 899.8 and 497.3 keV transitions, respectively, are shown. Two new transitions of energies 301.3 and 336.5 keV as seen in Fig. 2(a) are assigned to 100 Zr. From this coincidence spectrum and several other coincidence spectra, these two transitions are placed in band -(3) as shown in Fig. 1. Three new transitions of 440.1, 564.4, and 617.5 keV are observed as shown in Fig. 2(b). Also, a new 615.3 keV transition is observed clearly in the coincidence spectrum with the double gate on the 1331.9 and 625.5 keV transitions. Band -(2) was reported from the fission work of 248 Cm [6]. Only the 2754.4 and 3022.2 keV levels were known in band -(3) from our earlier fission work [1,10]. Four new states with energies of 2316.1, 2526.1, 3323.5, and 3660.2 keV in band -(3) and three new states with energies of 2579.2, 3019.3, and 3634.6 keV in band -(4) and one state with energy of 2859.7 keV in the side band are added in the present work. 23 new transitions with energies of 301.3, 336.7, 392.2, 438.8, 440.1, 496.5, 547.0, 564.4, 568.6, 615.3,617.5, 638.0, 891.8, 1172.3, 1208.1, 1254.2, 1331.9, 1397.1, 1405.6, 1434.7, 1464.2, 1698.6, and 1751.5 keV are identified. Relative intensities (Iγ ) of γ transitions (keV) in 100 Zr are shown in Table I. The uncertainties in the intensities range from about 5% for the strong transitions to 30% for the weak transitions. Also, the Iγ (I → I -2) values relative to the Iγ (I → I -1) values in the bands -(2) and -(3) are shown in Table II. Thicknesses of the arrows indicate the relative intensities of the γ transitions. The band-head of band -(2) at 2259.8 keV in 100 Zr was tentatively assigned the spin and parity of 6+ in Refs. [6,11] and 5− in Refs. [1,12] because of transitions to the known 4+ and 6+ but not to 2+ levels. The 2259.8 keV state was assigned a configuration of ν9/2[404]×ν3/2[411] [11] based on the fact that the experimental (|gK − gR )/Q0 | value (0.12 (eb)−1 ) [6] is consistent with the calculated one [0.13 (eb)−1 ] [6]. However, the 6+ assignment to band -(2) raises two objections. First, a K = 6 transition to the ground band would result in a very long half life as observed for the 17/2+ state with 8.6(8) µs half-life in 99 Y [13]. However, the half-life of the band-head of band -(2) is not more than several ns. Secondly, the energy ©2006 The American Physical Society PHYSICAL REVIEW C 74, 017303 (2006) BRIEF REPORTS FIG. 1. Level scheme of 100 Zr observed from the spontaneous fission of 252 Cf. The transition patterns do not exclude the spin and parity of 5 for band-head of bands -(2). Eight new states and 23 new transitions are added in the present work. − splitting (695.8 keV) of the Gallagher-Moskowski interaction observed for a similar band in 98 Sr [14] is too large compared with the average value of 400 keV in this region [14]. A spin TABLE I. Relative intensities (Iγ ) of γ transitions (keV) in 100 Zr. Intensity errors range between about 5% for the strong transitions and 30% for the weak transitions. and parity of 5− for the band head of band -(2) was proposed based on the proton configuration of π 5/2[303]×5/2[422] [1, 12]. The short half-life of the 2259.8 keV state does not exclude K = 5 K-forbidden E1 transitions with K = 5 as a good quantum number. The spins and parities to the levels of band -(3) have never been assigned before. γ transition Iγ γ transition Iγ γ transition Iγ γ transition Iγ TABLE II. Relative intensities (Iγ ) of γ transitions (Eγ keV) in bands -(2) and -(3). 212.6 219.5 250.4 267.3 275.6 283.9 301.3 314.7 336.7 344.0 352.0 392.2 404.0 438.8 440.1 100 5.5 2.4 1.0 2.6 2.1 0.8 1.0 0.3 0.5 84 0.3 0.5 0.1 0.4 441.1 469.9 496.5 497.3 534.3 536.0 547.0 556.3 564.4 568.6 598.6 615.3 617.5 625.5 658.7 0.9 0.1 0.9 65 0.5 6.8 3.0 0.5 0.3 0.1 0.2 0.1 0.6 26 0.2 638.0 666.1 739.1 841.4 845.1 850.1 891.8 899.8 939.8 1172.3 1197.9 1202.1 1208.1 1254.2 1291.2 0.1 7.0 5.2 2.1 8.8 9.5 1.0 2.3 0.5 0.8 1.8 1.9 0.5 2.0 0.2 1331.9 1346.6 1397.1 1405.6 1434.7 1464.2 1695.2 1698.6 1751.5 1.1 2.9 0.7 1.1 0.1 1.8 4.9 0.1 1.7 Level energy (keV) 2729.7 3013.6 3323.5 3328.3 3660.2 3672.3 017303-2 γ transition (keV) Iγ 469.6 250.4 534.3 283.9 568.6 301.3 598.6 314.7 638.0 336.7 658.7 344.0 4 100 24 100 13 100 20 100 33 100 40 100 PHYSICAL REVIEW C 74, 017303 (2006) BRIEF REPORTS (a) (b) FIG. 2. (a) Coincidence spectrum with double gates on 275.6 and 267.3 keV transitions and (b) coincidence spectrum with double gates on 899.8 and 497.3 keV transitions in 100 Zr. The new 615.3 keV transition can be seen clearly in the coincidence spectrum with the double gate on 1331.9 and 625.5 keV transitions. In other words, around the excitation energy of bands -(2) and -(3), two quasi-particle bands of π 5/2[303]× 5/2[422](K = 5− ) and ν9/2[404]×3/2[411] (K = 6+ ) are possible in 100 Zr [15]. Therefore, bands -(2) and -(3) may come from two kinds of quasi-particle excitations. However, the absence of K forbiddenness and inconsistency of the Gallagher-Moskowski interaction value may suggest that these two bands are not from an axially symmetric shape, but from a possible triaxial shape where K is not a good quantum number. Let us examine a single particle level diagram for axial shapes, such as Fig. 1 of Skalski et al. [17]. We can identify regions of quadrupole deformation and particle number with levels near Fermi energy that will be mixed by Y22 shape matrix elements. For 100 40 Zr60 those candidate two quasipaticle configurations for bands -(2) or -(3) which have ν1/2[411]or ν3/2[411] will be subject to triaxial shape driving, as the system can minimize energy through Y22 mixing between the above two orbitals. The nearby 5/2[413] orbital can also mix and help drive toward Y22 deformation. Also, another two-quasiparticle excitation with the configuration of ν1/2[411]×9/2[404] could produce a rotational band with K π = 5+ . Therefore, the spins and parities of bands -(2) and -(3) are consistent with several internal configurations which need further study. The spins and parities of band -(2) in 100 Zr in Fig. 1 were tentatively assigned by Durell et al. [11] up to 11+ based on the cascade to crossover ratios. In band -(3), only band-head spin and parity were assigned tentatively as (5− ,6+ ) in the present work. The cascade transitions in bands -(2) and -(3) dominate over the E2 crossover transitions except for the first two states in band -(3). The dominance of M1/E2 cascade transitions over E2 crossover transitions in 100 Zr can be explained by smaller quadrupole moments of the bands -(2) and -(3) that reduce the E2 crossover transition rate and the E2 admixture in the M1/E2 cascade transition. This means that the nuclear shape of bands -(2) and -(3) is much less deformed than β2 = 0.32(2) [8] of the ground band. We carried out the deformed HF+BCS calculations for 100 Zr with a Skyrme interaction SIII [16]. These predict a coexistence of the prolate shape (β2 = 0.365) at the ground state and an oblate shape (β2 = −0.195) at 560 keV as shown in Fig. 3. A similar result was reported by Skalski et al. [17] suggesting the coexistence of the prolate shape (β2 = 0.34) at the ground state and an oblate shape (β2 = −0.21) at 0.85 MeV using the Nilsson-Strutinsky-BCS method [17]. The calculated values of |β2 | ≈ 0.37 for the ground state and |β2 | ≈ 0.12 for the excited 0+ state at 331.1 keV were obtained by using a band mixing theory [2]. These ground state deformations are reasonably close to the experimental value of β2 = 0.32(2) [8]. However, whether the band -(4) starting at 331.1 keV has an oblate shape remains in question. The larger rotational spacing in the excited 0+ band is consistent with the ground band being prolate and the excited 0+ band being oblate. There is evidently considerable band mixing between them, giving rise to strong cross band transitions. The likely coexistence of the prolate and oblate shapes of the 0+ bands in 100 Zr could lead to a possible coexistence of the prolate and oblate as well as triaxial shapes at the highly excited 2 quasiparticle bands such as bands -(2) and -(3). In summary, eight new high spin states and 23 new γ transitions are identified in 100 Zr. A near-spherical excited band -(4) in 100 Zr is extended from 4+ up to 12+ . A I = 1 band -(3) is proposed. The work at Vanderbilt University, Lawrence Berkeley and Livermore National Laboratories are supported, respectively, FIG. 3. The deformed HF+BCS calculations with a Skyrme interactions SIII. 017303-3 PHYSICAL REVIEW C 74, 017303 (2006) BRIEF REPORTS by U.S. DOE under grant No. DE-FG05-88ER40407, Contract Nos. W-7405-ENG48, and DE-AC03-76SF00098 and at Tsinghua University by the Major State Basic Research Development Program under Grant No. G2000077405. 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