Shell evolution and isomers below 132 Sn: Spectroscopy of neutron-rich 46 Pd and 47 Ag isotopes

. Neutron-rich isotopes of Pd ( Z = 46) and Ag ( Z = 47) have attracted considerable interest in terms of the evolution of the N = 82 shell closure and its inﬂuence on the r -process nucleosynthesis. Such previously unreachable exotic nuclides have become accessible by means of in-ﬂight ﬁssion of a high-intensity 238 U beam available at a new-generation radioactive isotope (RI) beam facility, the RI Beam Factory (RIBF) in RIKEN Nishina Center. In this report, recent spectroscopic results of Pd and Ag isotopes obtained as part of the EURICA (EUROBALL-RIKEN Cluster Array) project at RIBF are presented.


Introduction
The shell structures of atomic nuclei are nowadays known to change with the variation of the proton or neutron number, due predominantly to the monopole part of the protonneutron interaction that includes the central and tensor forces [1]. Such a shell evolutionary behavior is expected to become pronounced when the proton-neutron imbalance is very large, leading to lost or new magic numbers [2]: For example, the conventional magic numbers N = 8, 20, and 28 disappear and new magicity emerges at N = 16, 32, and 34, depending on the location of the nucleus in the N − Z plane. However, it is not known yet whether similar changes of the shell structure can take place at the heavier conventional magic numbers N = 50, 82, and 126, which also play an important role in determining the solar abundance distribution, particularly around the three prominent peaks at A ≈ 80, 130, and 195, respectively, that would result from the rapid neutroncapture (r) process [3].
The advent of a new generation in-flight-separator facility, the RI-Beam Factory (RIBF) in RIKEN Nishina Center [4], has enabled us to explore previously inaccessible nuclear regions with a highly unbalanced ratio of neutrons to protons [5]. Neutron-rich palladium ( 46 Pd) isotopes, those with A = 125 − 131 (N = 79 − 85), have been identified as new isotopes at RIBF [6][7][8], followed by spectroscopic studies by means of βand isomeric-decay measurements [9][10][11] and in-beam γ-ray spectroscopy [12] in the last decade. Especially emphasized is that delayed γ-ray measurements following isomeric decays can provide a powerful tool for investigating the excited level structure, in particular, when the nucleus of interest lies at the boundaries of availability for spectroscopic studies. For 128 Pd 82 , which is a presumed waiting- * e-mail: hiroshi@ribf.riken.jp point nucleus that contributes significantly to the formation of the second peak in the r-process solar abundance distribution [3,13], a seniority isomer with a spin and parity of (8 + ) had been identified, serving as indirect evidence for the robustness of the N = 82 shell closure [10]. In the two-neutron-hole neighbor 126 Pd 80 , it turned out that the proton-neutron monopole properties of the central and tensor forces play an important role in the emergence of the long-lived (10 + ) isomer [11]. Compared to such eveneven systems, neighboring odd-mass nuclei exhibit more complicated excitation spectra, which provide crucial information on the effect of unpaired nucleons on the level structure. This proceedings reports on isomeric states and their decay properties in 125,127 Pd 79,81 [14] and low-lying β-emitting isomers in 123,125 Ag 76,78 [15].

Experimental details
Neutron-rich Pd and Ag isotopes were separated through the BigRIPS in-flight separator [16], following production via in-flight fission of a 238 U 86+ beam at 345 MeV/u incident on a Be target with a thickness of 3 mm. The primary beam intensity ranged from 7 to 12 pnA during the experiments. The beamline included two wedgeshaped aluminum degraders with thicknesses of 2.9 and 2.5 mm at the first and second dispersive foci, respectively, and focal plane detectors such as position-sensitive parallel plate avalanche counters (PPACs), plastic scintillation counters, and ionization chambers. More detailed information on the detector configuration and the particleidentification analysis with the BigRIPS separator can be found in Ref. [17]. The ions of interest were transported through the BigRIPS-ZeroDegree spectrometer and finally implanted into the WAS3ABi active stopper, which consisted of eight layers of double-sided silicon-strip detectors (DSSSDs) stacked compactly [18]. Each DSSSD had a thickness of 1 mm with an active area segmented into sixty and forty strips (1-mm pitch) on each side in the horizontal and vertical dimensions, respectively. Gamma rays emitted following the heavy-ion implantation and their subsequent radioactive decay were detected by the EU-RICA γ-ray spectrometer [18], consisting of 12 Clustertype detectors, each of which contained seven HPGe crystals packed closely. The excited states of 123 Ag and 125 Ag have been investigated following the β decays from the respective parent nuclei 123 Pd and 125 Pd. The decay schemes constructed in Ref. [15] are exhibited in Fig. 2. In addition to the previously reported transitions that are involved in the decay sequences from the J π = (17/2 − ) isomeric states [19], a number of new γ rays have been observed in prompt coincidence with β rays. Note that the (17/2 − ) isomers were not clearly populated in the present work on account of the large spin difference from the parent levels. It turned out that there are two β-decaying states with similar half-lives in the parent Pd isotopes. Either a spin-parity of 11/2 − or 3/2 + is assigned for the β-decaying isomer, and the counterpart for the ground state. The β decay from the 11/2 − state is likely to feed J = 9/2, 11/2, and 13/2 levels in the daughter nucleus, while comparatively low-spin states can be populated in the β decay from the 3/2 + state. New results shown in Fig. 2 Figure 2. Systematics of experimental energy differences between the lowest-lying 1/2 − and 9/2 + states in odd-A Ag isotopic chain [15]. Copyright (2019), with permission from the American Physical Society.
dence pattern suggests that the 611-keV transition feeds a level, which decays via two parallel transition paths. Similarly, for 125 Ag, the 625-keV transition has a clear coincidence with the 1119-keV transition, as well as with the 415-and 606-keV transitions. Based on the γ-γ coincidences, intensity balance, and systematics of the odd-A Ag isotopes, for 125 Ag, the transition sequence of 415-and 606-keV is suggested to decay to the (1/2 − ) long-thought isomeric state, and the 1119-keV transition decays to the (9/2 + ) ground state. The remarkable similarity in γ-γ coincidence pattern in 123 Ag and 125 Ag suggests that, for 123 Ag, the transition sequence of 383-and 594-keV feeds the (1/2 − ) isomeric state, and the 1009-keV transition decays to the (9/2 + ) state. Figure 2 exhibits the systematics of the measured energy difference between the lowest-lying 1/2 − and 9/2 + states in odd-A Ag isotopes as a function of the neutron number. These levels are interpreted as being ascribed to active proton holes in the 2p 1/2 and 1g 9/2 orbitals, respectively, which define a spherical sub-shell gap at Z = 40. The sizable (positive) energy difference around N = 50 indicates the stability of the Z = 40 gap. With increasing neutron number, this energy difference drops quickly. At N = 58, the ordering of these two levels swaps and the 1/2 − state becomes the lowest state. Following nearly flat evolution between N = 58 and 70, the order of these levels is inverted again at N = 76. However, the slope on the neutron-rich side is less steep than that on the neutron-deficient side, suggesting that the Z = 40 subshell gap is eroded when the neutron number increases towards N = 82.

125 Pd 78 and 127 Pd 80
For 125 Pd, four γ rays at energies of 108, 115, 757, and 825 keV are clearly visible within a time interval of 250−1250 ns after the ion implantation, as exhibited in Fig. 3(a). They are unambiguously assigned as the transitions forming a single cascade from an isomeric state, which can be  confirmed by their mutual coincidence as demonstrated in Fig. 3 [14]. Each level is labeled with the spin-parity (J π ) and energy (relative to the 11/2 − state) values. The measured (isomeric) half-lives are indicated in bold.
ion implantation, and their coincidence relationship confirmed by γ-γ coincidence analyses, see Figs. 3(c) and 3(d). The isomeric half-life was determined to be 39(6) µs from a weighted average of the respective fits to the time distributions of the 422-and 1296-keV γ rays. The level schemes of 125 Pd and 127 Pd are shown in Fig. 4. More detailed arguments on the spin-parity assignments are given in Ref. [14].
To interpret systematically the level properties of the neutron-rich Pd isotopes towards N = 82, shell-model calculations based on the extended pairing plus quadrupolequadrupole forces combined with monopole corrections (EPQQM) [20] have been performed for 125,126,127,128 Pd. With the doubly magic nucleus 78 Ni as the closed core, the model space considered includes four orbits in the Z = 28 − 50 major shell and the g 7/2 , d 5/2 orbits above the Z = 50 shell gap for protons, and five orbits in the N = 50 − 82 major shell and the f 7/2 , p 3/2 orbits above the N = 82 shell gap for neutrons. The observed and calculated level energies are compared in Fig. 5, where the columns marked with SM exhibit the results of a largescale shell model that allows the excitation of a neutron across the shell gap of N = 82. The measured and calculated values of the reduced transition probabilities for the selected transitions are summarized in Table 1.
According to the present shell-model calculation for 125 Pd, the major components of the 23/2 + wave function differ significantly from those of the 19/2 + 1 state, resulting in a strongly hindered E2 transition (see Table 1). On the other hand, very similar wave functions are predicted for the 23/2 + and 19/2 + 2 states of 125 Pd. The fact that the measured B(E2) value for the isomeric deexcitation is fairly consistent with the calculated B(E2; 23/2 + → 19/2 + 2 ) value indicates that both the experimental (23/2 + ) and (19/2 + ) levels are dominated by the neutron excitations. A candidate for the 19/2 + 1 shell-model state, which is dominated by the proton excitations, has not been identified in the current experiment.
Finally, it is noteworthy that for the N = 82 closedshell nucleus 128 Pd an excited state with a spin and parity of 5 − is predicted to be lower in energy than both the experimental and theoretical 4 + levels, as shown in Fig. 5. The main component of the 5 − state is π(g −3 9/2 p −1 1/2 ), the same as that involved in the 19/2 + state of 127 Pd, which is well reproduced by the present shell-model calculations, as discussed in the last paragraph. With the calculated energies and B(E3; 5 − → 2 + ), as well as the theoretical α T value [21], the half-life of the 5 − state is estimated to be 5 ms. Such a long-lived isomer has not been identified in Refs. [10,11] due presumably to insufficient statistics,