New isomers in 125 Pd 79 and 127 Pd 81 : Competing proton and neutron excitations in neutron-rich palladium nuclides towards the N = 82 shell closure

The neutron-rich isotopes of palladium have attracted considerable interest in terms of the evolution of the N = 82 neutron shell closure and its inﬂuence on the r -process nucleosynthesis. In this Letter, we present the ﬁrst spectroscopic information on the excited states in 125 Pd 79 and 127 Pd 81 studied using the EURICA γ -ray spectrometer, following production via in-ﬂight ﬁssion of a high-intensity 238 U beam at the RIBF facility. New isomeric states with half-lives of 144(4) ns and 39(6) μs have been assigned spins and parities of (23 / 2 + ) and (19 / 2 + ) in 125 Pd and 127 Pd, respectively. The observed level properties are compared to a shell-model calculation, suggesting the competition between proton excitations and neutron excitations in the proton-hole and neutron-hole systems in the vicinity of the doubly magic nucleus 132 Sn. © 2019 The Author(s). an the CC BY license by SCOAP 3 .


a r t i c l e i n f o a b s t r a c t
The neutron-rich isotopes of palladium have attracted considerable interest in terms of the evolution of the N = 82 neutron shell closure and its influence on the r-process nucleosynthesis. In this Letter, we present the first spectroscopic information on the excited states in 125 Pd 79 and 127 Pd 81 studied using the EURICA γ -ray spectrometer, following production via in-flight fission of a high-intensity 238 U beam at the RIBF facility. New isomeric states with half-lives of 144(4) ns and 39 (6) μs have been assigned spins and parities of (23/2 + ) and (19/2 + ) in 125 Pd and 127 Pd, respectively. The observed level properties are compared to a shell-model calculation, suggesting the competition between proton excitations and neutron excitations in the proton-hole and neutron-hole systems in the vicinity of the doubly magic nucleus 132 Sn. Atomic nuclei are self-bound, quantum many-body systems consisting of two types of constituents (nucleons), protons and neutrons, which interact strongly with each other in a finite volume. The protons and neutrons respectively occupy their singleparticle orbits in a mean-field potential, giving rise to a distinct pattern of the energy spacing between the orbits, so-called shell structure. In a shell-model approach, individual energy/spin eigenstates are described as the combination of proton and neutron configurations formed within the available model space assuming a doubly closed-shell nucleus as an inert core; therefore, a main difficulty is ascribed to an increasing number of configurations that have to be dealt with in the calculation, when increasing the proton/neutron valency moving away from the closed shells. Nowadays, the shell structures are known to be changed with the variation of the proton or neutron number, as well as with specific particle-hole excitations within the same nucleus, due predominantly to the monopole part of the proton-neutron interaction that includes the central and tensor forces [1,2]. 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 (see, for instance, Ref. [3] and references therein). As such, spectroscopic studies of short-lived rare isotopes (exotic nuclides) around proton/neutron shell closures are of crucial significance in corroborating the shell evolution far off stability. The available spectroscopic data of excitation spectra can serve as a good testing ground for developing nuclear shell models.
The advent of the 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]. Concerning 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 β-and isomericdecay measurements [9][10][11] and in-beam γ -ray spectroscopy [12] in the last decade. Especially emphasized is that the 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 waitingpoint nucleus that contributes significantly to the formation of the second peak in the r-process solar abundance distribution [13,14], a seniority isomer with a spin and parity of (8 + ) had been identified, serving as an 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 even-even 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 Letter presents previously unreported isomeric states and their decay properties in 125 Pd 79 and 127 Pd 81 , which have three and one neutron holes relative to the N = 82 shell closure, respectively. The obtained results are compared to a shell-model calculation, which predicts the competition between proton and neutron excitations in the protonhole and neutron-hole systems in the south-west quadrant of the doubly magic nucleus 132 Sn.
The neutron-rich odd-A palladium isotopes, 125 Pd and 127 Pd, were separated through the BigRIPS in-flight separator [15], following production via in-flight fission of a 238 U 86+ beam at 345 MeV/u incident on a beryllium target with a thickness of 3 mm. The primary beam intensity ranged from 7 to 12 pnA during the experiments. About 3.1 × 10 5 ( 125 Pd 46+ ) and 8.7 × 10 3 ( 127 Pd 46+ ) ions 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 [16]. 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 EURICA γ -ray spectrometer [16,17], consisting of 12 Cluster-type detectors, each of which contained seven HPGe crystals packed closely. The methodology of how to analyze the experimental data taken with the EURICA setup is described in detail in a recent review article [18].
Since 125 Pd and 127 Pd were discovered as new isotopes at RIBF [6,7], their spectroscopic information has so far been limited only to the ground-state β-decay half-lives [9]. In the present work, γ rays emitted from the excited states in these neutron-rich odd-A nuclei have been observed for the first time. Detailed experimental results of each isotope are described as follows: 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. 1(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. 1(b), as well as by their consistent time behavior as summarized in the last column of Table 1. An example of the time spectrum obtained with a gate on the 757-keV γ ray is shown in Fig. 2(a). A weighted average of the respective fits to the decay curves results in an isomeric half-life of 144(4) ns.
According to the β-decay studies of 125 Pd [21] carried out in parallel with the present analysis, there are two β-decaying states with similar half-lives, as systematically found in neutronrich odd-A isotopes of 50 Sn and 48 Cd with N 82 [23,24]. 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 γ rays assigned previously in the decay scheme from an isomeric state at 1501 keV towards the (9/2 + ) state in 125 Ag [19,20] are labeled with their energy values, while transitions reported as feeding the (1/2 − ) state [21] are marked with diamonds. The coincidence spectrum shown in the panel (d) is obtained with a sum of additional gates on the 108-, 115-, 757-, and 825-keV γ rays, which are observed within a 900-ns time window opened 100 ns after the ion implantation. (e) and (f): Within a time range of 0.25 − 100 μs after implantation of 127 Pd ions. An additional gate is set on the 422-keV γ ray to make the coincidence spectrum shown in the panel (f).

Table 1
Summary of transitions from the isomeric states in 125 Pd and 127 Pd. Each column shows the initial level energy E i , spin and parity of the initial (final) state J π i ( J π f ), γ -ray energy E γ , electromagnetic transition multipolarity σ λ, total conversion coefficient α cal T calculated by the BrIcc code [22], relative γ -ray intensity I γ , total transition intensity I tot = (1 + α cal T )I γ , and half-life T 1/2 derived from a fit to the γ -ray time distribution.    [19,20], are unambiguously observed, supporting the presence of the (11/2 − ) state in 125 Pd that undergoes β decay to 125 Ag. In addition to these known transitions, it was found that several new γ rays emerge, being assigned as feeding the low-spin states in 125 Ag. Further details of the β-γ analysis will be presented elsewhere [21].
In order to clarify on which β-decaying state ( J π = 3/2 + or 11/2 − ) the aforementioned 144-ns isomer is built in 125 Pd, the correlation between the β-delayed γ rays and the preceding isomeric-decay transitions has been confirmed. Fig. 1(d) shows a γ -ray energy spectrum created under the same gate condition for the implant-β-γ correlation as that used for Fig. 1(c), and additionally, with a sum of energy gates on the 108-, 115-, 757-, and 825-keV γ rays observed within a 0.1 − 1.0 μs time interval after implantation of the 125 Pd ions. With this constraint on the "isomer implantation" events, it is expected that delayed γ rays following the β decay from the state to which the 144-ns isomer finally decays can be enhanced, compared to the transitions populated from the other β-decaying state. It can be seen in Fig. 1(d) that γ -ray peaks at 670 and 714 keV, which were previously assigned as the 125 Ag, respectively [19,20], are clearly visible, while the other γ rays reduce their peak counts as low as the background fluctuations. Therefore, the 144-ns isomer turned out to be built on the β-decaying state with J π = (11/2 − ) in 125 Pd, though it is still unclear whether this level is the ground state or the long-lived isomer from the present experimental result. Note that whichever the (11/2 − ) level is, the ground state or the long-lived isomer, the discussions and conclusions regarding higher-lying levels presented below are not changed. The excitation energy of the 144-ns isomer was determined to be 1805 keV relative to the (11/2 − ) state.
The level scheme of 125 Pd established in the present work is exhibited in Fig. 3 (left). The order of the 757-and 825-keV cascade transitions was determined in comparison with the 693-keV [(2 + ) → 0 + ] and 788-keV [(4 + ) → (2 + )] transitions in the neighboring N = 80 isotope 126 Pd [11]. However, the possibility of inversion of these transitions can not be entirely ruled out due to the closeness of their energies. The levels at 757 (or 825) and 1582 keV relative to the (11/2 − ) state were tentatively assigned spins and parities of 15/2 − and 19/2 − , respectively, which are interpreted as a neutron (hole) in the h 11/2 orbital coupled to the (2 + ) and (4 + ) states in 126 Pd. Meanwhile, the 15/2 + assignment for the 1582-keV state, the analog of the one observed in the N = 79 isotone 129 Sn [25], can be ruled out because of the absence of a competing E1 branch towards a (presumed) 13/2 − state, which arises predominantly from the νh −1 11/2 ⊗ 2 + multiplet, and therefore, is expected to appear in the proximity of the (15/2 − ) state.
The transitions of 108 and 115 keV are placed in cascade above the 1582-keV level. For the 108-keV transition, a total internal conversion coefficient α T of 1.1(3) can be deduced from its γ -ray intensity being compared to the total intensity of the 757-keV, E2 transition, see Table 1. This α T value is in good agreement with the   Table 1. theoretical value of 1.05 for an E2 multipolarity [22]. Similarly, the value obtained from the intensity balance analysis for the 115-keV transition, α T = 0.0(1), is consistent only with an E1 multipolarity within the margin of error. The ordering of these transitions was determined based on the arguments on transition strengths. If the 108-keV (E2) transition were placed below the 115-keV (E1) transition, an intermediate state presumed at 1690 keV should have a half-life of the order of a few or several hundreds of nanoseconds [e.g. T 1/2 ≈ 500 ns given the reduced transition probability B(E2) = 1 W.u. for the 108-keV transition]. This is at variance with what was observed from time difference spectra having al-most symmetric distributions, as shown in Figs. 2(b), 2(c), and 2(d). Therefore, we conclude that the 108-keV transition deexcites the 144-ns isomer at 1805 keV relative to the (11/2 − ) state, followed by the 115-keV transition that feeds the 1582-keV level. It is to be noted that the measurement of the prompt relative-time distributions shown in Figs. 2(b), 2(c), and 2(d) also indicates that neither the (intermediate) 1697-keV state nor the 1582-keV state is isomeric, supporting the 19/2 − assignment for the latter level, and accordingly, excluding the possibility of 19/2 + analogous to the one identified as the 17.5-μs isomer in the N = 79 isotone 127 Cd [26].
Based on the above arguments on intensity balances and transition strengths, either a spin-parity assignment of 23/2 + → 19/2 + → 19/2 − or 25/2 + → 21/2 + → 19/2 − can be proposed for the 108 − 115-keV cascade between the 144-ns isomer and the 1582-keV state in 125 Pd. In the following discussion, the former sequence is adopted with the help of shell-model calculations. The reduced transition probability, B(E2) = 129(4) e 2 fm 4 = 3.47 (9) W.u., can be obtained for the 108-keV transition from the measured half-life of the 1805-keV isomeric state, taking into account the internal conversion process with the calculated α T value [22].
This B(E2) value is comparable to the corresponding 23/2 + → 19/2 + transition observed in the N = 79 isotone 129 Sn [25]. The level scheme of 127 Pd is proposed as exhibited in Fig. 3  (right). The 39-μs isomeric state has been identified at an excitation energy of 1718 keV with respect to the (11/2 − ) level, which is assumed to be the lowest-lying state in the isomeric-decay cascade in analogy with 125 Pd. The 1296-keV transition was assigned as feeding the (11/2 − ) state from the (15/2 − ) level owing to a close resemblance of the energy to the (2 + ) → 0 + transition (1311 keV) in the neighboring N = 82 nucleus 128 Pd [10]. Concerning the 422-keV transition that de-excites the isomeric state, E3 and higher-multipole possibilities can be virtually ruled out because their strengths would be unlikely enhanced compared to the transitions known in this region (see Table 2 in Ref. [18]). Meanwhile, a single de-excitation of 422 keV with an E1, M1, or E2 multipolarity would not result in such a long-lived isomeric state. Consequently, the 422-keV transition is expected to have M2 character with a reduced transition probability of 9.6(15) × 10 −2 μ 2 N fm 2 = 2.3(4) × 10 −3 W.u., which is emitted from the (19/2 + ) isomeric state to the (15/2 − ) state.
Here, it is to be noted that the possible existence of a lowenergy (unobserved) transition above the 1718-keV level as deexciting the 39-μs isomeric state can be excluded for the following reasons: In this scenario, the presumed non-isomeric state at 1718 keV is expected to have 19/2 − , which decays to the (15/2 − ) state at 1296 keV via an E2 transition, similar to the decay sequence observed for 125 Pd. Assuming an observation limit of 20 counts for an expected γ -ray peak in the ion-γ correlated spectrum shown in Fig. 1(e), depending on conversion, limits on the transition energy can be determined for different multipolarities λ. Regardless of the transition energy, the 39-μs isomeric-decay transition is unlikely to proceed with λ ≥ 3 and λ = 1 on account of the same reason as the one concerning the transition strengths discussed in the previous paragraph. Provided that the unobserved transition has M2 multipolarity, the transition energy would have to be lower than 90 keV with the reduced transition probability of the order of 1 W.u. or larger. Such an unhindered M2 transition, which exceeds a recommended upper limit of the transition strength [27], hardly occurs in the region of interest. If the isomeric decay is of E2 character from a 23/2 − state, an upper limit of the transition energy would be 75 keV for it not to have been observed. For such a lowenergy transition, the B(E2) value from the 39-μs isomeric state is estimated to be in the order of 0.01 − 0.1 W.u., which could be possible as observed for the (8 + ) → (6 + ) isomeric transition in 128 Pd [10]. However, if a 23/2 − state were isomeric, it would prefer to decay via a fast E1 transition to a lower-lying 21/2 + level, which is predicted by a shell-model calculation as will be discussed later, rather than the nearby 19/2 − state. Thus, the possibility of a low-energy isomeric-decay transition can be ruled out for any multipolarities, supporting the (19/2 + ) assignment for the 39-μs isomeric state at 1718 keV relative to the (11/2 − ) level. In order to understand systematically the level properties of the neutron-rich Pd isotopes towards N = 82, shell-model calculations based on the extended pairing plus quadrupole-quadrupole forces combined with monopole corrections (EPQQM) [28] have been performed for 125,126,127 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 proton/neutron single-particle energies, effective charges and g-factors, and the parameters of the EPQQM Hamiltonian employed in the present calculations are consistent with those adopted in the previous works [29][30][31][32]. The observed and calculated level energies are compared in Fig. 4, where the columns marked with SM exhibit the results of a large-scale 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 2.
As mentioned earlier, experimentally there remains a possible spin-parity assignment of 23/2 + → 19/2 + or 25/2 + → 21/2 + for the 108-keV transition deexciting the isomeric state in 125 Pd. However, the yrast 25/2 + level is unlikely to be isomeric in comparison with the shell-model calculation, which predicts that the energy difference between the 25/2 + and 21/2 + states is much larger than the observed transition energy, as shown in Fig. 4. Consequently, the excited states at 1697 and 1805 keV in 125 Pd are assigned spins and parities of (19/2 + ) and (23/2 + ), respectively. For the higher-lying levels in 125 Pd, the shell-model calculation predicts that there are two 19/2 + states below an excitation energy of 2 MeV, as indicated with different colors in Fig. 4. The first 19/2 + (hereinafter denoted by 19/2 + 1 ) state is predicted to involve predominantly a two-proton-hole excitation π(g −1 9/2 p −1

1/2 )
together with an inactive proton-hole pair π(g −2 can not proceed between their main configurations. Within the Z = 28 − 50 major shell, an M2 decay can take place through the π f 5/2 → π g 9/2 transition. It is therefore expected that the large hindrance of the order of 10 −3 W.u. (see Table 2) is ascribed to the small admixture of the π(g −3 9/2 f −1 5/2 ) ⊗ ν(h −1 11/2 ) component in the 19/2 + isomeric state. It is worth mentioning finally about the evolution of singleparticle levels in this neutron-rich region and its impact on the N = 82 shell closure, which is also crucial for a better understanding of the r-process nucleosynthesis [13,14]. In Ref. [31], largescale shell-model calculations, which have been done in the same framework as that adopted in the present work, suggested that the size of the N = 82 shell gap decreases gradually with decreasing proton number from 48 ( 130 Cd) to 36 ( 118 Kr) on account of the dynamic effect of the monopole interaction between the π g 9/2 and νh 11/2 orbitals. Since the 125,127 Pd states discussed above consist of these high-j orbits, the experimental results obtained in this work can serve as a stringent benchmark for testing shell models to foresee a possible N = 82 shell quenching in exotic nuclei, which are still inaccessible for spectroscopic study.
To conclude, spectroscopic studies of 125 Pd and 127 Pd have been performed at RIBF, and accordingly, we have provided for the first time experimental information on the excited level structure of these neutron-rich nuclei, which have triple-and single-neutron vacancies relative to the N = 82 closed-shell nucleus 128 Pd. In 125 Pd, a previously unreported isomeric state with a half-life of 144(4) ns was assigned tentatively a spin and parity of 23/2 + based on the results of the γ -ray intensity balance analysis and the measured transition strengths with the aid of a shell-model calculation. This isomer and the lower-lying (19/2 + ) states were interpreted as being ascribed predominantly to three-neutron-hole excitations within the N = 50 − 82 major shell. Meanwhile, the (19/2 + ) isomer identified with T 1/2 = 39(6) μs in 127 Pd was expected to involve the proton-hole excitation π(g −3 9/2 p −1 1/2 ) coupled to a neutron hole in the h 11/2 orbit. Thus, it turned out that the (19/2 + ) states observed at almost the same excitation energy in 125 Pd and 127 Pd are quite different in nature. A future experimental challenge is to corroborate the argument on the different isomerism of these states by measuring nuclear magnetic moments using more intense radioactive-isotope beams.