Isomers and oblate collectivity at high spin in neutron-rich Pt isotopes

Isomers and high-spin structures with rotation-aligned oblate configurations have been studied in several Pt isotopes. The 12 states in the even Pt isotopes from 192−198Pt are found to be metastable, and have (i13/2) neutron character. The progression of E2 transition probabilities from the 12 to 10 states across the Pt isotopic chain implies reduction in collectivity, followed by an abrupt decrease at N=120 (198Pt). This behavior is quite distinct from the gradual decrease of B(E2) values near the respective ground states. A large contribution from aligned angular momentum, to the rotational sequences built on the 12 states, is visible. This is due to the relatively small crossing frequencies for nucleons in low-Ω orbitals at oblate deformation in comparison to higher values for prolate shapes. As a result, oblate rotation is found to be increasingly favored for higher neutron numbers.


Introduction
The large majority of nuclei across the periodic chart are deformed, with prolate shapes being the most common.The moment of inertia of a rigid prolate rotor is higher in comparison to that of an oblate one for similar magnitudes of quadrupole deformation [1].Consequently, the excitation energies for prolate rotational states, particularly at high spin, are expected to be lower than the corresponding oblate ones.While this is generally found to be the case for most nuclei, in a limited region around A=190, collective oblate rotation is the favored excitation mode at high spin.This rather unusual phenomenon is realized since the proton and neutron Fermi levels are located near low-Ω, high-j intruder orbitals for oblate deformation, while for prolate deformation, they are in the vicinity of high-Ω orbitals from the same subshells.Since low-Ω orbitals typically exhibit a higher degree of alignment compared to high-Ω ones over a similar range of rotational frequency, oblate states are found to be lower in energy than the corresponding prolate ones.While this phenomenon was first predicted quite some time ago [2], as yet, there are a relatively small number of nuclei where collective oblate rotation is experimentally observed to the favored excitation mode [3-5].Oblate shapes are expected to be more favored in neutron-rich nuclei however these are experimentally difficult to explore.
While isotopes of Hf (Z = 72) and W (Z = 74) are established to be well-deformed, rigid rotors [6, 7], with increase in both proton and neutron numbers approaching the doubly magic 208 Pb, the ground state deformation is found to decrease gradually.The behavior at high spin is however not as well documented.Proton-rich Pt isotopes have been studied rather extensively e.g.[4, 8, 9], a e-mail: sujit.tandel@cbs.ac.in and found to exhibit well-developed rotational bands both near the ground states and at high spin.With increase in neutron number from the lightest stable isotope 190 Pt (N=112) to the heaviest 198 Pt (N = 120), the decrease in ground state deformation and collectivity is evidenced by the increase in 2 + 1 excitation energy in even-A nuclei accompanied by a corresponding reduction in B(E2; 2 + →0 + ) values.Previously, there was little information on the evolution of collectivity at high spin in the Pt isotopic chain.
This work is focused on oblate, rotation-aligned configurations in 192,194,196,198 Pt, for which the lowest (12 + ) states are metastable in nature.Most of the new information presented here pertains to isomers in the heaviest stable isotopes 196,198 Pt, and rotational sequences in 192,194,196 Pt.Oblate rotation is found to be particularly favored in energy for higher neutron numbers.In addition, an abrupt reduction in collectivity at high spin is observed for 198 Pt (N = 120) compared to lighter isotopes, quite unlike the steady decrease near the respective ground states.

Experiment and results
Excited states in Pt isotopes were populated through multinucleon transfer using a 1450-MeV 209 Bi beam incident on a thick (≈50 mg/cm 2 ) 197 Au target.The beam was delivered by the ATLAS accelerator at Argonne National Laboratory and γ rays emitted in the deexcitation of the reaction products were detected by the Gammasphere array consisting of 100 high-purity, Compton-suppressed Ge detectors [10].The data were sorted into both symmetric and asymmetric histograms ranging from two-to four-fold, depending on the energy and time parameters involved; details may be found in [11].Lifetimes of isomeric states were determined, and both prompt and delayed (from isomeric decays) transitions were established from the data  In 192,194 Pt as well, states up to I π =(26 + ) were identified.The 12 + states in even-Pt isotopes from 188−198 Pt are isomeric in nature; in 196 Pt, this state is newly identified.The half-lives for these states (except for the one in 198 Pt) have been determined using the centroid shift method.This is illustrated in Fig. 1, wherein the centroid of the time distribution of a delayed transition is shifted with respect to that of a prompt one by an amount equal to the mean life of the state.For 198 Pt, the half-life has been determined by observing the time variation in cumulative intensity of delayed transitions [11].Isomer half-lives and B(E2) values are listed in Table 1.

Discussion
The lightest stable Pt isotopes have considerable deformation which is manifested in enhancement of B(E2; 2 + →0 + ) values.For 192 Pt, the enhancement is 57 times greater than the single-particle (Weisskopf) estimate (Table 1).With increase in neutron number, the shell closure at N = 126 is approached, leading to reduction in deformation and collectivity.This is reflected in the trend of gradually decreasing B(E2; 2 + →0 + ) values from 192 Pt to 198 Pt (Table 1).However, a considerable amount of collectivity is evident even in 198 Pt, where the 2 + → 0 + transition is enhanced by a factor of 31 over the Weisskopf value.
The trend in the variation of B(E2; 12 + → 10 + ) values is rather different: these are similar in 192 Pt and 194 Pt (Table 1).A significant drop is evident in 196 Pt, though the transition is enhanced 23 times over the Weisskopf estimate.A much more abrupt decrease in visible in 198 Pt, with B(E2; 12 + → 10 + ) being at most 2.4 times the singleparticle estimate (Table 1), providing strong evidence for quenching of collectivity at high spin around N=120.This aspect is in marked contrast to the smooth decrease in collectivity near the respective ground states.
In addition to other observables, the collective character of the 12 + isomers is suggestive of a rotation-aligned interpretation for these states.In the A ≈190 region, spin of 12 for a two-quasiparticle state can only be a realized from the full alignment of a pair of i 13/2 neutrons.Measured values of g factors for the 12 + states viz.-0.18(9), -0.17 (7) in 192,194 Pt [12] substantiate this assignment.
Results of cranking calculations performed using standard Nilsson parameters in the Ultimate Cranker (UC) code [13] and the universal parameterization of the Woods-Saxon potential [14] aid in a detailed understanding of the observed phenomena.Pairing energies were adapted from five-point odd-even mass differences [7, 15,  16].Total Energy Surface plots for 192,194 Pt indicate oblate energy minima near and beyond the 12 + states as illustrated in Fig. 2. The rotation-aligned configurations therefore have oblate character.The energies for oblate configurations deduced from UC calculations are in good   192,194,196 Pt.The reference rotor has J 0 = 8 2 MeV −1 and J 1 = 35 4 MeV −3 .Two nucleon alignments are clearly visible in all three isotopes.The first alignment occurs at ω≈0.2 MeV in all isotopes.The second alignment in 192 Pt ( ω≈0.3 MeV) is delayed in comparison to the corresponding ones in 194,196 Pt ( ω≈0.2 MeV).
agreement with the ones inferred from experiment; prolate minima are predicted to become progressively more non-yrast with increasing neutron number [11].The magnitude of quadrupole deformation is predicted to decrease for higher neutron numbers consistent with the reduction in B(E2; 2 + → 0 + ) values described earlier.Shape evolution for lighter isotopes (up to 192 Pt) follows a similar pat-tern with triaxial shapes being favored at intermediate spin (I ≤ 10 ), and oblate ones lowest in energy at high spin.In 194,196 Pt though, an oblate shape is realized at lower spin and persists to high spin [11].The excitation energy of the 12 + states gradually decreases with increase in neutron number up to 194 Pt, and is associated with the lowering of the oblate energy minimum evident from calculations [11].
Beyond 194 Pt, the 12 + energy increases since the complete filling of the i 13/2 subshell at N=120 ( 198 Pt) approaches, as a result of which more energy is required to excite a pair of neutrons from this state.The excitation energy for the 12 + state is highest in 198 Pt.
Successive rotation alignments are evident in the yrast positive parity bands of 192,194,196 Pt (Fig. 3).The alignment gain at the first band crossing (≈11 ), and the crossing frequency ( ω ≈ 0.2 MeV), are quite similar for all three isotopes.The second alignments in 194,196 Pt are evident at the same frequency (0.2 MeV), with aligned angular momentum ≈ 7 .In 192 Pt, the second alignment is visible at a somewhat higher frequency (≈ 0.3 MeV) (Fig. 3).The first crossing is associated with the (νi 13/2 ) 2 alignment based on the quasineutron levels for oblate deformation obtained from Woods-Saxon cranking calculations (Fig. 4).The (νi 13/2 ) 2 alignment is expected at ω ≈ 0.2 MeV for oblate deformation consistent with the experimental value, while that for prolate deformation is expected at a significantly higher frequency ( ω = 0.38 MeV).The second alignment may be attributed to h 11/2 protons or a second pair of i 13/2 neutrons (Fig. 4).The latter interpretation is considered more likely due to the observation of different alignment frequency in 192 Pt compared with 194,196 Pt.With h 11/2 proton character for the second crossing, the frequencies would have been similar in all three cases.The higher frequency for the second crossing in 192 Pt may be understood in terms of the aligning i 13/2 neutrons occupying relatively higher-Ω orbitals for oblate deformation, as the neutron Fermi level is at lower energy in 192 Pt compared to 194,196 Pt.

Summary
Rotation-aligned states in an oblate deformed potential well have been studied across the Pt isotopic chain.The 12 + states in the aligned configurations are isomeric with half-lives in the nanosecond range.Reduced E2 transition probabilities for deexcitation of the isomeric states point to a sudden drop in collectivity at high spins near N = 120 unlike the more gradual decrease near the ground state.Considerable contribution from aligned angular momentum to the rotational sequences at high spin is indicated both from experiment and results of cranking calculations.

DOI: 10 7KLVFigure 1 .
Figure 1.(Color online) Centroid-shift analysis for determination of half-lives of 12 + states in: (a) 192 Pt (b) 194 Pt (c) 196 Pt.The dotted (blue) and solid (red) lines indicate the time distributions for prompt and delayed transitions, respectively.

Figure 3 .
Figure 3. (Color online) Aligned angular momentum as a function of rotational frequency in192,194,196  Pt.The reference rotor has J 0 = 8 2 MeV −1 and J 1 = 35 4 MeV −3 .Two nucleon alignments are clearly visible in all three isotopes.The first alignment occurs at ω≈0.2 MeV in all isotopes.The second alignment in 192 Pt ( ω≈0.3 MeV) is delayed in comparison to the corresponding ones in194,196  Pt ( ω≈0.2 MeV).

Figure 4 .
Figure 4. (Color online) Neutron quasiparticle levels for 194 Pt calculated using the universal parameterization of the Woods-Saxon potential [14] for prolate deformation (a) and oblate deformation (b).