$1p_{3/2}$ Proton-Hole State in ${}^{132}\mathrm{Sn}$ and the Shell Structure Along $N=82$

A low-lying state in ${}^{131}{\mathrm{In}}_{82}$, the one-proton hole nucleus with respect to double magic ${}^{132}\mathrm{Sn}$, was observed by its $\gamma$ decay to the $I^{\pi }=1/2^{-}$ $\beta$-emitting isomer. We identify the new state at an excitation energy of $E_x=1353\mathrm{keV}$, which was populated both in the $\beta$ decay of ${{}^{131}\mathrm{Cd}}_{83}$ and after $\beta$-delayed neutron emission from ${{}^{132}\mathrm{Cd}}_{84}$, as the previously unknown $\pi p_{3/2}$ single-hole state with respect to the ${}^{132}\mathrm{Sn}$ core. Exploiting this crucial new experimental information, shell-model calculations were performed to study the structure of experimentally inaccessible $N=82$ isotones below ${}^{132}\mathrm{Sn}$. The results evidence a surprising absence of proton subshell closures along the chain of $N=82$ isotones. The consequences of this finding for the evolution of the $N=82$ shell gap along the $r$-process path are discussed.

Figure 1

(a) Experimental energies of the first excited $2^{+}$ states, $E(2^{+})$ and (b) proton gaps, ${\mathrm{\Delta }}_{2p}$, in even $N=50$ isotones (filled black boxes) compared to the results of the shell-model calculations of Ref. [15] (blue asterisks). The results of new SM calculations (present work), using realistic interactions derived in the same way as the ones used in the calculations for the $N=82$ isotones, are shown as filled red circles. (c) Energies of the first excited $2^{+}$ states, $E(2^{+})$, and (d) proton gaps, ${\mathrm{\Delta }}_{2p}$, for the $N=82$ isotones as calculated in the present work (filled red circles). The experimental $2^{+}$ energies in ${}^{130}\mathrm{Cd}$ and ${}^{128}\mathrm{Pd}$ (filled black boxes) are included for comparison [9, 10]. The black lines (solid, dashed, and dotted) represent the results of SM calculations assuming an increase of the $1p$ splitting by 0.5, 1.0, and 1.5 MeV, respectively.

Figure 2

Spectra of $\gamma$-rays detected in prompt coincidence with the $\beta$ decay of ${}^{132}\mathrm{Cd}$ (upper panel) and ${}^{131}\mathrm{Cd}$ (lower panel). The lines labeled with symbols correspond to known transitions in ${}^{130}\mathrm{In}$ (#), populated after $\beta$-delayed neutron emission from ${}^{131}\mathrm{Cd}$, in ${}^{131}\mathrm{Sn}$ (&), populated in the $\beta$ decay of the daughter nucleus ${}^{131}\mathrm{In}$, and the annihilation of positrons from the pair creation of high-energy $\gamma$-rays in the Ge detectors (@). The inset shows a schematic decay scheme for ${}^{131,132}\mathrm{Cd}$.

Figure 3

Energy systematics of several $1p$, $1d$, and $1f$ spin-orbit partner orbitals in the vicinity of the neutron-rich double magic nuclei ${}^{78}\mathrm{Ni}$, ${}^{132}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$ compared to the position of the neighboring $0f_{5/2}$, $0g_{7/2}$, and $0h_{9/2}$ SPOs (see text for details). Experimental (calculated) values from Ref. [23] are shown as solid (dashed) lines. For ${}^{78}\mathrm{Ni}$, shell-model extrapolated energies are replacing the unknown experimental ones. (Note that for $1p_{3/2}$ both lines coincide.)