Proton Shell Evolution below ${}^{132}\mathrm{Sn}$: First Measurement of Low-Lying $\beta$-Emitting Isomers in ${}^{123,125}\mathrm{Ag}$

The $\beta$-delayed $\gamma$-ray spectroscopy of neutron-rich ${}^{123,125}\mathrm{Ag}$ isotopes is investigated at the Radioactive Isotope Beam Factory of RIKEN, and the long-predicted $1/2^{-}$ $\beta$-emitting isomers in ${}^{123,125}\mathrm{Ag}$ are identified for the first time. With the new experimental results, the systematic trend of energy spacing between the lowest $9/2^{+}$ and $1/2^{-}$ levels is extended in Ag isotopes up to $N=78$, providing a clear signal for the reduction of the $Z=40$ subshell gap in Ag towards $N=82$. Shell-model calculations with the state-of-the-art $V_{\mathrm{MU}}$ plus M3Y spin-orbit interaction give a satisfactory description of the low-lying states in ${}^{123,125}\mathrm{Ag}$. The tensor force is found to play a crucial role in the evolution of the size of the $Z=40$ subshell gap. The observed inversion of the single-particle levels around ${}^{123}\mathrm{Ag}$ can be well interpreted in terms of the monopole shift of the $\pi 1g_{9/2}$ orbitals mainly caused by the increasing occupation of $\nu 1h_{11/2}$ orbitals.

Figure 1

Systematics of experimental energy differences between the lowest-lying $1/2^{-}$ and $9/2^{+}$ states in Ag isotopes. Data are taken from Refs. [24, 31] (black filled circles) and the present work (red filled circles). The dashed blue arrows are drawn to guide the eye. The range of the shaded region for ${}^{119}\mathrm{Ag}$ corresponds to the uncertainties of the experimental data.

Figure 2

(a) $\beta$-delayed $\gamma$-ray spectra measured within 300 ms after the ${}^{123}\mathrm{Pd}$ implantation. The peaks marked with asterisks are new transitions in ${}^{123}\mathrm{Ag}$ but not included in the partial level scheme in Fig. 4, and the peaks marked with # are known contaminants. (b) Coincident $\gamma$-ray spectra gated on the 611.0-keV $\gamma$ ray. The $\gamma$-ray spectra in $\beta$-delayed coincidence with the sum of (c) the 713.6-, 629.7-, and 685.3-keV transitions and (d) 383.1-, 325.1-, and 594.0-keV transitions. Inset in (c): The $\gamma$-ray spectrum in $\beta$-delayed coincidence with the 1009.2-keV transition.

Figure 3

(a) $\beta$-delayed $\gamma$-ray spectra measured within 180 ms after the ${}^{125}\mathrm{Pd}$ implantation. The peaks marked with asterisks are new transitions in ${}^{125}\mathrm{Ag}$ but not included in the partial level scheme in Fig. 4, and the peaks marked with # are known contaminants. (b) Coincident $\gamma$-ray spectra gated on the 625.4-keV $\gamma$ ray. The $\gamma$-ray spectra in $\beta$-delayed coincidence with the sum of (c) the 714.3-, 670.0-, and 728.6-keV transitions and (d) 415.1-, 361.1-, and 606.3-keV transitions. Inset in (c): The $\gamma$-ray spectrum in $\beta$-delayed coincidence with the 1118.5-keV transition.

Figure 4

Partial level schemes of ${}^{123}\mathrm{Ag}$ and ${}^{125}\mathrm{Ag}$ constructed in this work in comparison with the shell-model calculations. The experimental information of $17/2^{-}$ isomeric states in ${}^{123,125}\mathrm{Ag}$, which are not or weakly populated in the present work due to the selection rule, are taken from Ref. [27]. The arrow widths are proportional to their absolute intensities.

Figure 5

(a) Proton effective single-particle energies in Ag isotopes calculated by the $V_{\mathrm{MU}}+\mathrm{LS}$ interaction. The dashed lines are obtained only with the central and spin-orbit forces, while the solid lines include the central, spin-orbit, and tensor forces. (b) Neutron occupation number in the $1h_{11/2}$ shell.