Isomers and shell evolution in neutron-rich nuclei below the doubly magic nucleus 132 Sn

The level structures of the very neutron-rich nuclei Pd82 and Pd80 have been investigated for the first time. A new isomer with a half-life of 5.8(8) μs in Pd is proposed to have a spin and parity of 8 and is associated with a maximally aligned configuration arising from the g9/2 proton subshell with seniority υ = 2. The level sequence below the 8 isomer is similar to that in the N = 82 isotone Cd, but the electric quadrupole transition that depopulates the 8 isomer is more hindered in Pd than in Cd, as expected in the seniority scheme for a semi-magic, spherical nucleus. For Pd, three new isomers with J = (5), (7), and (10) have been identified with half-lives of 0.33(4) μs, 0.44(3) μs, and 23.0(8) ms, respectively. The smaller energy difference between the 10 and 7 isomers in Pd than in the heavier N = 80 isotones can be interpreted as being ascribed to the monopole shift of the h11/2 neutron orbit. The nature of the N = 82 shell closure scrutinized with these characteristic isomers is discussed.


Introduction
The concept of magicity is of supreme importance for many-body fermionic systems in a confined space.The stability of atomic nuclei, which consist of a number of sub-atomic particles called protons and neutrons (nucleons), is much influenced by a shell structure and its resulting magic numbers; nuclei with specific numbers of nucleons (2,8,20,28,50, 82 both for protons and for neutrons, and also 126 for neutrons) near the β-stability line necessitate relatively high energies to remove one or two nucleons compared to the neighboring isotopes.For the last few decades, however, the study of exotic nuclei using radioactive isotope (RI) beams revealed that the aforementioned magic numbers are not necessarily universal and are subjected to a change in some regions of light-mass nuclei with highly unbalanced ratios of protons and neutrons [1,2].Such a paradigm shift is one of the frontier issues in nuclear physics, and whether it will also take place at the heavier traditional magic numbers is an open question worth investigating.
The present work focuses on neutron-rich nuclei below the doubly magic nucleus 132 Sn.It is still under debate that the N = 82 spherical shell gap is quenched as approaching the neutron drip line.From an astrophysical point of view, it has been argued that the property of the N = 82 shell closure far from the valley of β-stability affects the Solar System abundance pattern particularly around the prominent A ≈ 130 peak in the r-process nucleosynthesis [3], and hence, a proper understanding of the underlying nuclear structure of the r-process isotopes is highly required.The characteristic isomers that involve highj orbits, such * e-mail: hiroshi@ribf.riken.jpas πg 9/2 and νh 11/2 , in their configurations can serve as a sensitive probe for the evolution of shell structures in this exotic region.We have performed decay spectroscopy experiments at the RI Beam Factory (RIBF) facility [4], which has the capability of providing the world's strongest RI beams, as part of the EURICA campaign using highintensity 238 U beams.New results obtained include the seniority isomer with J π = (8 + ) in 128 Pd [5], the longlived (10 + ) isomeric state in 126 Pd [6], and a high-spin βdecaying isomer in 127 Ag [7].In this report, the nature of the N = 82 shell closure will be discussed in terms of the seniority isomerism in the N = 82 isotones, as well as the effect of the monopole interaction between the g 9/2 proton and h 11/2 neutron subshells.

Experimental procedures
Neutron-rich isotopes below the doubly magic nucleus 132 Sn have been produced using in-flight fission of a 238 U 86+ beam accelerated up to 345 MeV/u by a series of accelerators at RIBF facility [4], cooperated by RIKEN Nishina Center and CNS, University of Tokyo.The primary beam with the intensity ranging from 7 to 12 pnA impinged on a 3-mm thick beryllium target.The nuclei of interest were separated and transported through the Bi-gRIPS separator and the following ZeroDegree spectrometer [9], operated with wedge-shaped aluminum degraders with thicknesses of 2.9 and 2.5 mm at the first and second dispersive focal planes, respectively, for purification of the secondary beams.Identification of particles with the atomic number (Z) and the mass-to-charge ratio (A/Q) was achieved on the basis of the ∆E-TOF-Bρ method, in which the energy loss (∆E), time of flight (TOF), and mag- netic rigidity (Bρ) were measured using the focal-plane detectors on the beam line [10].A particle-identification spectrum obtained in the present experiment is displayed in Fig. 1.
The identified fragments were implanted into a highly segmented active stopper, named WAS3ABi [11], which consisted of eight double-sided silicon-strip detectors (DSSSD) stacked compactly.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.The DSSSDs also served as detectors for electrons following β-decay and internal conversion (IC) processes.Gamma rays were detected by the EURICA array [12] that consisted of twelve Cluster-type detectors, each of which contained seven HPGe crystals packed closely.The γ-ray measurements were carried out with a time condition up to 100 µs relative to the trigger signal generated either from a plastic scintillation counter placed at the end of the beam line or from WAS3ABi.
The beam, electron, and γ-ray events were timestamped and recorded by independent data-acquisition systems.For the analysis of beam-γ (delayed) coincidence, the γ-ray data sets were combined with those of the beam particles on an event-by-event basis using information on the time stamp.Isomeric states with (sub)microsecond lifetimes were identified with appropriate time gates.All data sets containing beam, electron, and γ-ray events were used for β-γ and IC-γ coincidence analyses, in which the implantation of an identified particle was associated with the subsequent electron events that were detected in the same DSSSD pixel.Decay halflives (T 1/2 ) in the millisecond range were extracted from the time distributions of γ-ray gated electron events with respect to the fragment implantation.

Results and discussion
3.1 128 Pd 82 Figure 2(a) shows a γ-ray energy spectrum measured in delayed coincidence with 128 Pd ions.Four γ rays at energies of 75, 260, 504, and 1311 keV have been unambiguously observed.These γ rays are found to be in mutual coincidence and exhibit consistent time behavior.Therefore, we conclude that they proceed through a single cascade originating from one isomeric state.A least-squares fit of the summed gated time spectra of the isomeric-decay transitions yields T 1/2 = 5.8(8) µs.The total internal conversion coefficient (α T ) for the 75-keV transition derived from a comparison with the 1311-keV γ-ray intensity is 2.6 (17), which is consistent with the theoretical value of α T = 3.88 for an E2 multipolarity.Based on these arguments, the level scheme of 128 Pd is proposed as displayed in Fig. 3, where the spin and parity of the 5.8-µs isomeric state at 2151 keV is assigned as J π = 8 + .A transition strength of B(E2; 8 + → 6 + ) = 0.22(3) W.u. can be obtained from the measured half-life of the 2151-keV isomeric state.
Assuming that the excited states in 128 Pd are the same multiplet members (with seniority υ = 2, as will be discussed later), the half-life of the J π = 6 + state is estimated to be 22(3) ns from that of the 8 + isomer.Since this value is significantly shorter than the flight time of fragments from the production target to the implantation position (∼ 650 ns), there would be little 128 Pd ions remaining at this state during the flight.Hence, the observed intensities of the four cascade γ rays should depend only on the population of the 8 + isomeric state.
The excitation energies of the J π = 2 + − 8 + states in 128 Pd are comparable to those in 130 Cd [13].The constancy of level energies is characteristic of the seniority scheme, where seniority υ counts the number of nucleons that are not in pairs coupled to spin zero.In case of a nparticle (or n-hole) system in a single-j shell, the level energies with identical J π and υ are independent of n.Thus, the excited states in 128 Pd can be interpreted in terms of the υ = 2 configuration of the πg 9/2 subshell, which locates just below the Z = 50 shell gap.
A direct implication of the N = 82 shell closure can be corroborated from the behavior of the E2 transition strength for the 8 + → 6 + isomer decay in 128 Pd.The E2 matrix elements between υ = 2 states are close to zero near the middle of the valence shell in semi-magic nuclei, giving rise to seniority isomerism.For the N = 82 isotones, it turns out that the B(E2; 8 + → 6 + ) value is much smaller in 128 Pd than in 130 Cd, as expected in the exact seniority classification, namely, B(E2; υ = 2, n = 4) = 1 9 B(E2; υ = 2, n = 2).This observation indicates that both the J π = 8 + and 6 + states in the N = 82 isotones have good seniority υ = 2 in the well isolated πg 9/2 subshell, in consequence of the robust shell closure.

126 Pd 80
The level scheme of 126 Pd constructed in the current work is also shown in Fig. 3  .0≤ ∆t eγ ≤ 0.5 µs, and additionally, with a gate on the electron peak marked with "I" in the inset, where the spectrum depicted with the red line (multiplied by a factor of ten) is obtained with a sum of gates on the γ rays below the (5 − ) isomer in 126 Pd, while the blue line represents an electron spectrum without γ-ray gates.
the most intense peak of those observed in delayed coincidence with 126 Pd ions [Fig.2(b)], is assigned as the 2 + → 0 + transition.The coincidence spectrum with a gate on the 542-keV γ ray clearly exhibited γ rays at energies of 693, 788, and 86 keV, but not at 1330 keV, indicating that two parallel cascades stem from a common level at 2023 keV.The 86-keV transition is placed just above the 2023-keV level, because this γ ray was observed to precede all the four transitions.
The γ rays below these isomers, except for the 86-keV line, have been also observed in coincidence with electrons that were associated with the prior implantation of 126 Pd, as demonstrated in Fig. 2(c).This observation implies the existence of a long-lived, higher-spin isomer which decays via the cascades that include electromagnetic transitions with relatively large total conversion coefficients.With gates on these γ rays, a prominent peak can be found  established in the present work [5,6].
in an electron spectrum [marked with "I" in the inset of Fig. 2(c)]; this corresponds to the conversion electrons for the 86-keV, E2 transition (α T = 2.374).In Fig. 2(d), a γray at 297 keV is clearly visible in addition to the γ rays below the (5 − ) isomer by gating on the 86-keV IC peak.
The appearance of the 297-keV peak is emphasized by taking a γ-ray time condition earlier than electron events, as is evident from the inset of Fig. 2(c), suggesting that this new γ ray precedes the highly converted 86-keV transition.Thus, the long-lived isomer can be identified at an excitation energy of 2406 keV.A peak marked with "II" in the inset of Fig. 2(d) is expected to arise from the conversion electrons for the 297-keV transition, being most likely of an E3 character (α T = 0.1197).In addition to the internaldecay branch, β decay from the long-lived isomer was observed to populate excited states at high spins in 126 Ag.The isomeric half-life was determined to be 23.0(8)ms by taking a weighted average of those derived from the time distributions of the internal-and external-decay branches.
The main surprise in the present work is the small energy difference between the (10 + ) and (7 − ) isomers, ∆E 10 + 7 − , in 126 Pd, compared to the analogous levels in the heavier N = 80 isotones, as demonstrated in Fig. 4. Since these two levels consist predominantly of maximally aligned two neutron-hole configurations, (ν1h −2 11/2 ) 10 + and (ν1h −1 11/2 2d −1 3/2 ) 7 − , their level energies depend on the singleparticle energies (SPEs) of the ν1h 11/2 and ν2d 3/2 neutron orbits, as well as the strength of interactions between them.It can be seen in Fig. 4 that the energy of the 11/2 − level relative to the 3/2 + ground state in the neighboring N = 81 isotones decreases when approaching Z = 50.Note that these states are of one neutron-hole nature, and that the smooth reduction in energy can be essentially interpreted in terms of a short-range proton-neutron interaction as follows: The π1g 7/2 proton orbit lies just above the Z = 50 shell closure.The monopole interaction between π1g 7/2 and ν1h 11/2 , a spin-flip pair with ∆ℓ = 1 and ∆n = 0, is stronger than the π1g 7/2 -ν2d 3/2 pair, due to the larger overlap between the radial wave functions of the two orbits.Therefore, when emptying the π1g 7/2 subshell, the 7 − , in N = 80 (filled circles) and between the 11/2 − and 3/2 + states in N = 81 (filled squares).For Z ≤ 50, the differences in energy between the 1h 11/2 and 2d 3/2 neutron orbits calculated by V MU interaction [15] and ∆E 10 + 7 − by shell-model (SM) calculations with monopole corrections (MC) are also depicted.ν1h 11/2 orbit is relatively less bound than the ν2d 3/2 one.The moderation in the slope at higher Z may be ascribed to the partial occupation of the π2d 5/2 orbit, which exerts a weaker (stronger) monopole interaction on the ν1h 11/2 (ν2d 3/2 ) neutrons than π1g 7/2 .As is evident from the comparison in Fig. 4, a similar trend is observed for ∆E 10 + 7 − .This finding supports that these isomers can serve as sensitive probes for the evolution of the constituent neutron shell orbits.
Below Z = 50, protons in the π1g 9/2 subshell play a major role in changing the neutron SPEs, because this orbit is near the Fermi surface.The neutron SPEs are estimated by the monopole-based universal interaction, V MU , which consists of the Gaussian central force and the tensor force based on the π+ρ meson exchanges, using the parameters fixed in Ref. [15].The V MU interaction has been applied to other regions of exotic nuclei and successfully reproduced various types of the shell evolution [15].Figure 4 shows the evolutions of the relative 11/2 − energy starting from the experimental value in 131 Sn, predicted by the V MU calculation with A = 130.In the calculation, the π1g 9/2 subshell is considered to be well isolated between Z = 50 and 40.In Fig. 4, only with the central force the 11/2 − energy rapidly decreases to negative values as the proton number decreases, indicating that the ν1h 11/2 orbit moves away from the ν2d 3/2 one towards the N = 82 gap.If there is the tensor force effect, however, the slope becomes less steep.The observed reduction in ∆E 10 + 7 − from 130 Sn to 126 Pd is consistent with the expectation of V MU including both the central and tensor forces, given the same trend as the 11/2 − relative energies.Based on these findings, it can be concluded that the tensor force slows down the upward drift of the ν1h 11/2 SPE when protons are removed from the π1g 9/2 orbit below 132 Sn.

Figure 1 .
Figure 1.Particle-identification spectrum obtained in the present work. 127Ag 47+ and 126,128 Pd 46+ ions are indicated with circles.The figure is taken from Ref. [8].

Figure 2 .
Figure2.Gamma-ray spectra measured (a) in coincidence with128 Pd ions within a time range of 0.15−25 µs, (b) in coincidence with126 Pd ions within 0.15−5 µs, and (c) within 50 ms after the 126 Pd implantation with a gate on an electron-γ time difference of −0.5 ≤ ∆t eγ ≤ 0.5 µs.Contaminants from the granddaughter 126 Cd are marked with filled circles.The inset magnifies the energy region from 230 to 310 keV measured with −4.0 ≤ ∆t eγ ≤ 0.5 µs (red) and −0.5 ≤ ∆t eγ ≤ 50 µs (blue).(d): γ rays measured with −4.0 ≤ ∆t eγ ≤ 0.5 µs, and additionally, with a gate on the electron peak marked with "I" in the inset, where the spectrum depicted with the red line (multiplied by a factor of ten) is obtained with a sum of gates on the γ rays below the (5 − ) isomer in 126 Pd, while the blue line represents an electron spectrum without γ-ray gates.