Beta decay of the axially asymmetric ground state of 192 Re

The β decay of 19275 Re 117 , which lies near the boundary between the regions of predicted prolate and oblate deformations, has been investigated using the KEK Isotope Separation System (KISS) in RIKEN Nishina Center. This is the ﬁrst case in which a low-energy beam of rhenium isotope has been successfully extracted from an argon gas-stopping cell using a laser-ionization technique, following production via multi-nucleon transfer between heavy ions. The ground state of 192 Re has been assigned J π = ( 0 − ) based on the observed β feedings and deduced log ft values towards the 0 + and 2 + states in Os, which is known as a typical γ -soft nucleus. The shape transition from axial symmetry to axial asymmetry in the Re isotopes is discussed from the viewpoint of single-particle structure using the nuclear Skyrme-Hartree-Fock model.  2021 The Authors. under

Given axially symmetric deformations like prolate (elongated) and oblate (flattened) ellipsoidal shapes, the systems are invariant under a rotation around the symmetry axis. The rotational invariance is broken in nuclei having three different radii in the intrinsic coordinates. The degree of triaxial distortion, represented by the angular variable γ , tends to be developed in regions where shape transitions and/or coexistence between prolate and oblate deformations can take place [2][3][4][5][6]. Since, however, the occurrence of well-established asymmetric shapes is rather rare compared to the large abundance of axially symmetric (in particular, prolately deformed) cases, the exploration of some nuclei that are triaxial in their ground states is a long-standing challenge in nuclear structure physics. Concerning axial asymmetry in medium-heavy and heavy nuclei, 192 76 Os 116 and its vicinity have attracted considerable interest both experimentally and theoretically. The second 2 + state at 489 keV in 192 Os is the lowest in energy of the 2 + 2 levels ever identified as the bandhead of the (quasi) γ band for even-even nuclei throughout the chart of nuclides, indicating that this nucleus is an especially promising candidate for enhanced ground-state axial asymmetry [7]. However, neither the rigid triaxial rotor nor the large-amplitude fluctuation in the γ direction, two extreme pictures of axially asymmetric nuclei, are adequate to reproduce E2 matrix elements extracted from Coulomb excitation of 192 Os [8].
The γ -soft properties of even-even nuclei in this shape transitional region can be explained well as being almost exactly intermediate between the two geometrical limits, using the interacting boson model Hamiltonian determined with energy density functionals [9,10]. Such γ softness causes the mixing of configurations with different K values, the angular momentum projection on the symmetry axis of an axial shape, and thereby results in a serious violation of K -forbidden transitions involved in radioactive decays, as observed for the J π = K π = (10 − ) isomer in 192 Os [7]. In this Letter, we report on the β decay from 192 75 Re 117 to 192 Os. Although the same decay channel was studied before [11,12], the β-decay intensities and log ft values have never been evaluated.
The present work focuses in particular on the previously unreported spin-parity assignment for the ground state of the parent nucleus 192 Re. From theoretical point of view, there are two local minima being almost equal in depth at prolate and oblate deformations on the potential energy curve calculated for 192 Re [13]. However, the shape of each state in such a "critical-point" nucleus depends sensitively on the deformed single-particle structure. Total Routhian Surface calculations for 192 Re predict the prolate ground state with a high-K configuration, which coexists with an oblate shape that is stabilized by the rotation alignment of the unpaired proton and neutron in the highj orbitals [14].
Experimentally, it is still difficult to produce 192 Re even at modern radioactive-isotope-beam (RIB) facilities [15,16]. A currently utilized method to synthesize heavy neutron-rich nuclei in this mass region is cold fragmentation of 208 Pb beams at 1 GeV per nucleon at GSI [17]. Following this, isomeric states were discovered in 192 Re [18,19]. Another choice to get access to this hard-to-reach area approaching the N = 126 shell closure is to employ heavyion-induced multi-nucleon transfer (MNT) reactions with neutronrich (stable) isotopes [20,21]. In conjunction with a gas-cell arrangement in which the reaction products are stopped/ionized and with subsequent mass separation, one can obtain low-energy RIBs even for refractory elements that are hard to be vaporized. This article presents the first successful extraction of Re ions using a new RIB-production scheme based on the MNT method, the KEK Isotope Separation System (KISS) [22][23][24].
A RIB of 192 Re was produced via MNT between a 50-pnA projectile of 136 Xe and a natural Pt target with a thickness of 10.7 mg/cm 2 . The 10.75-MeV/u primary beam from the RIKEN Ring Cyclotron was decelerated to 8.8 MeV/u after passing through Ti degraders placed in front of the Pt target to optimize the production of the target-like fragments. The reaction products were thermalized and neutralized in a doughnut-shaped gas cell filled with high-pressure (80 kPa) gaseous argon, and then transported by a gas flow to the cell outlet, where a two-color, two-step resonant laser ionization technique is applied for an unambiguous selection of a single element. The singly charged 192 Re + ions were extracted through the RF ion guides and reaccelerated to 20 keV, followed by mass separation using the KISS spectrometer. The reader is referred to [25,26]  12-µm-thick aluminized mylar tape of a tape-transport system installed at the end of the KISS beamline. The decay measurements were carried out with three different beam-on/off conditions of 90/180, 24/48, and 45/15 s in order to accommodate decays both from the ground state (T 1/2 = 16(1) s [ 11]) and from a previously reported long-lived isomer (T 1/2 = 61 +40 −20 s [ 19]) in 192 Re. The implantation position was surrounded by a multi-segmented proportional gas counter (MSPGC) that covered 80% of the 4π solid angle with two layers of 16 counters [27]. This layered arrangement of the counters served to distinguish between high-energy β rays and low-energy internal-conversion electrons. Each element of MSPGC has a capability of position correlation in the vertical direction using the pulse-height information taken from both ends of the counter. The MSPGC was surrounded by four large-volume Clover-type HPGe detectors in a close geometry, having a γ -ray add-backed full-energy peak efficiency of 7.8% at 1 MeV. The implementation of a highly efficient detection system enabled β-γ -γ coincidence analyses.
It is to be remarked that no events relevant to the decay from a long-lived isomer in 192 Re, which was identified at E x = 267(10) keV with T 1/2 = 61 +40 −20 s for highly charged ions in the GSI Experimental Storage Ring (ESR) [19], have been observed in the present work, despite a careful inspection with the sufficient statistics. A possible reason for its non-observation is that the isomeric halflife in 192 Re is much shorter than the mean extraction time from the KISS system (∼ 500 ms [24]). Such a change in lifetime can be caused by suppression of internal conversion in highly charged ions [28]. Thus, the decay scheme from this isomer remains unclear, and we report only on the results of β-decay spectroscopy of the 192 Re ground state below.  Table 1. Observed were the 2 + 1,2 and 0 + 2 states, being consistent with the previous β-decay study [11]. The γbranching ratios deduced for the 2 + 2 and 0 + 2 levels are also consistent with the reference values [11]. In addition, β feedings towards other known excited states at 1206, 1879, and 2128 keV have been identified by the observation of γ rays that were reported to deexcite these levels [11]. Based on these observations, the decay scheme of 192 Re was constructed as displayed in Fig. 2, where the spins and parities of the 192 Os levels are presented if they  are firmly assigned in [11]. The 1879-keV state was previously assigned (2 + ) with a branch towards the 4 + 3 state at 1070 keV [11]. However, the spin-parity assignment for this state is not given in Fig. 2 since neither the transition feeding nor deexciting the 4 + 3 state could be observed in the present β-decay measurement. Another γ -decay branch of 1390 keV from the 1879-keV level to the 2 + 2 state [11] has been confirmed by a γ -γ coincidence analysis, as demonstrated in Fig. 1(b).
The β-branching ratio I β to each excited state was derived from an imbalance of the total intensities (1 + α T )I γ , where α T denotes the total conversion coefficient [30], between the incoming and outgoing transitions. Similarly, the β-branching ratio to the ground state was determined to be 89(2)% from the difference between the total number of β particles associated with the 192 Re decay by a fit to the growth-decay curves and the sum of the 206-and 489-keV total transition intensities. In this analysis, possible contributions from (unobserved) E0 transitions between the 0 + states were omitted. However, the argument on spin-parity assignment given below should be unaltered with the lack of allowance for E0 transitions since their relative intensities are most likely negligible, as observed for 188 Os and 196 Pt [31]. It should be noted that the values of I β given in Fig. 2 are considered as upper limits, in the present work with better precision than in the previous work [11], as shown in Fig. 3.
The evaluated log ft values put constraints on the spin-parity assignment for the parent β-decaying state. A strong β-decay branch towards the 0 + ground state of 192 Os should favor an assignment of 0 + or 0 − for the ground state of 192 Re. ( J π = 1 ± assignment is unlikely due to I β ≈ 0f o r feeding the 2 + 1,2 states.) However, the possibility of 0 + can be ruled out since the β-decay branches to the 0 + 1 states in 192 Os have much smaller log ft values than all known "isospin forbidden" 0 + → 0 + β transitions in heavy nuclei (see Table 4 in [32]). The value of log ft obtained for feeding the 192 Os ground state is comparable to log ft = 5.75 and 5.18 measured before for the 0 − → 0 + first-forbidden non-unique transitions involved in the β decays of 196 Ir [33] and 206 Tl [32], respectively. Based on these observations, the ground state of 192 Re is assigned tentatively J π = (0 − ).
In the neutron-rich A ≈ 190 region, the ground-state properties of even-even nuclei have been theoretically investigated within the mean-field framework using a variety of interactions and forces [6,35,36]. There are slight differences in the position and depth of deformed minima on the potential energy surfaces constrained by the quadrupole deformation variables β and γ , depending on the interactions/functionals used in the calculations. However, the overall trend of prolate-to-oblate shape transitions passing through γ -soft nuclei with increasing the number of neutrons is predicted in common for the even-even 74 W, 76 Os, and 78 Pt nuclei. The odd and odd-odd systems are also of significance in understanding the shape-polarization effects by the unpaired nucleons, yet they have been scarcely studied in the self-consistent meanfield approach in this mass region. To interpret the low-lying level structure in the 75 Re isotopes approaching N = 116, which is supposed to be the critical neutron number for the occurrence of ground-state prolate-to-oblate shape transition and enhanced γ softness, we have performed Skyrme-Hartree-Fock (SHF) calculations using the symmetry-unrestricted HFODD code [37].
At first, the low-energy excitation spectra are calculated for odd-A Re isotopes and compared to the experimental observables, as a benchmark for testing various Skyrme functionals available in HFODD ver. 2.73y [38]. The observed excitation energies of lowlying J π = 1/2 + , 9/2 − , and 5/2 + states are plotted as a function of the mass number from 185 to 191 in Fig. 4(a). These levels are interpreted as being of proton one-quasiparticle nature associated with the Nilsson orbitals, [411]1/2 + , [514]9/2 − , and [402]5/2 + , respectively [34]. A remarkable feature in this plot is that the 1/2 + level falls rapidly in energy relative to the 5/2 + and 9/2 − states with increasing mass number and it becomes the ground state in 191 Re. The observed systematic trends can be reproduced fairly well by the SHF calculations with the use of the SVI functional [39], as demonstrated in Fig. 4(b). We have confirmed that the general tendency of the odd Re isotopes considered here can be reproduced to a certain extent by the calculations with other Skyrme interactions, such as SkM* [40], SLy4 [41], and SkP [42], but the calculation with SVI is a much better description than the others. It should be noted that Fig. 4(b) displays the calculated relative energies of the HF states, each of which has the largest overlap with the asymptotic state [411]1/2 + , [514]9/2 − , or [402]5/2 + . Since the pairing correlations are not taken into account, the calculated energies are about twice as large as the corresponding experimental excitation energies. However, the fair agreement in qualitative behavior between the experimental and theoretical single-particle spectra validates to employ the HF+SVI calculations for discussing the properties of low-lying levels in this transitional region.
In the previous work [34], the rapid decrease in energy of the  [411]1/2 + deformation. The present SHF calculations, in which the hexadecapole component is also taken into account, reveal that the γ deformation plays a pivotal role in the level evolution in terms of the single-particle orbitals near the Fermi surface. In Fig. 5, the single-particle energies (SPEs) are described as functions of the positive (prolate) and negative (oblate) axial quadrupole moments  Table 2 are not necessarily a halfinteger unless the nucleus has an axially symmetric (γ = 0 • or 60 • ) shape on account of the K -mixing.
The HF+SVI calculations predict that the γ deformations of the lowest-lying states increase from 0 • in 185 Re to 35 • in 191 Re (see Table 2). For the [514]9/2 − levels, which are associated with the 18th negative-parity orbital, the values of γ are estimated to be 10 • in 187 Re, 19 • in 189 Re, and 31 • in 191 Re, consistent with those derived from the signature splitting of the corresponding rotational bands in comparison with a particle-plus-triaxial-rotor model [43]. As such, all these arguments point to the occurrence of shape transition from axial symmetry to axial asymmetry as the neutron number increases towards N = 116 in the Re isotopic chain. In a similar way, the low-lying levels of an N = 117 isotone 193 Os have been calculated to confirm the validity of the SVI interaction for neutron orbitals. The 31st negative-parity orbital (see the upper panel of Fig. 5) occupied by the last unpaired neutron is involved in the ground-state configuration for 193 Os. At the predicted deformation Q 2 = 11.5b and γ = 24 • , this neutron orbital is characterized with the asymptotic quantum numbers [512]3/2 − of the largest component in the wave function, in agreement with the experimentally observed 3/2 − ground state of 193 Os [44]. The HF+SVI calculation also predicts that a 13/2 + state emerges at low excitation energy from the occupation of the 29th positiveparity orbital with Q 2 = 11.8b and γ = 35 • . Such a level has not been observed for 193 Os so far [44], but the analogous state has been identified recently as a long-lived (T 1/2 = 47 ± 3s ) isomer in 195 Os [26].
It is noteworthy that there are sizable gaps at N = 116 and Z = 76 around γ = 30 • in the SPE diagram shown in Fig. 5   ground state, which has been experimentally assigned a spin and parity of (0 − ) in the present work. The results of the HF+SVI calculations for low-energy excitations in 192 Re are summarized in Table 3, where the configurations are expressed as a set of the orbital numbers for both neutrons and protons in four parity-signature blocks. The configuration listed in the sixth row in Table 3 gives rise to nearly null spin with negative parity, and therefore, this state is the most probable candidate for the observed (0 − ) ground state of 192 Re. (For the HF states calculated with the absence of the pairing correlations, uncertainties in energy of the order of several hundreds of keV are tolerable.) The predicted γ deformation for the 0 − state follows the increasing trend in the Re isotopes (see Table 2) beyond the maximum axial asymmetry at γ = 30 • .
This observation implies that the nuclear deformation is driven towards an oblate shape in the heavier Re isotopes, which have a significant impact on the formation of the 3rd-abundance peak around A = 195 in the rapid-neutron capture process [45], when approaching the N = 126 shell closure.
In Table 3, there are high-spin ( J ≈ 7, 10) states predicted to emerge at low excitation energy, which are likely to be long-lived due to the large difference in spin from the J π = (0 − ) ground state. The previously identified isomers in 192 Re [18,19]m i g h t arise from these configurations, though their decay properties remain a challenge for future experiments.
To summarize, 192 Re is located close to the predicted critical point of a prolate-to-oblate shape transition via enhanced axial asymmetry in the neutron-rich A ≈ 190 region. We have performed decay spectroscopy of this rare, refractory isotope using the newly developed KISS setup at RIKEN. Apparent β feedings to the known levels in 192 Os and the corresponding log ft values have been evaluated for the first time, whereby a spin and parity of 0 − are assigned tentatively for the 192 Re ground state. The lowenergy level systematics for the neighboring odd-A nuclei can be explained as being ascribed to the variation of single-particle energies with triaxial deformation γ , indicative of the shape transition from prolate-axial symmetry to axial asymmetry approaching N = 116. The (0 − ) ground state in 192 Re is predicted to have a shape exceeding the maximum axial asymmetry at γ = 30 • , suggesting that the nuclear deformation evolves to an oblate shape in heavier Re isotopes. A future experimental challenge is to measure nuclear moments of the Re isotopes to pin down the structural evolution discussed in this Letter.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.