Yrast 6${}^{+}$ Seniority Isomers of ${}^{136,138}$Sn

Delayed $\gamma$-ray cascades, originating from the decay of $(6^{+})$ isomeric states, in the very neutron-rich, semimagic isotopes ${}^{136,138}$Sn have been observed following the projectile fission of a ${}^{238}$U beam at RIBF, RIKEN. The wave functions of these isomeric states are proposed to be predominantly a fully aligned pair of $f_{7/2}$ neutrons. Shell-model calculations, performed using a realistic effective interaction, reproduce well the energies of the excited states of these nuclei and the measured transition rates, with the exception of the $B(E2;6^{+}\to 4^{+})$ rate of ${}^{136}$Sn, which deviates from a simple seniority scheme. Empirically reducing the $\nu f_{7/2}^2$ orbit matrix elements produces a $4_1^{+}$ state with almost equal seniority 2 and 4 components, correctly reproducing the experimental $B(E2;6^{+}\to 4^{+})$ rate of ${}^{136}$Sn. These data provide a key benchmark for shell-model interactions far from stability.

Figure 1

Plot of nuclear charge $Z$ versus mass-to-charge ratio $A/q$ for ions produced, identified, and implanted into the WAS3ABi active stopper.

Figure 2

Delayed $\gamma$ rays in coincidence with (a) ${}^{136}$Sn and (b) ${}^{138}$Sn ions, obtained using high-resolution analogue timing electronics and digital electronics for better low-energy efficiency, respectively. The insets show the summed ion-$\gamma$ time distributions for the three observed transitions of each isotopes.

Figure 3

Spectra of $\gamma$ rays observed in coincidence with the (a) 216-keV, (b) 391-keV, and (c) 688-keV transitions in ${}^{136}$Sn.

Figure 4

Proposed level schemes of ${}^{136}$Sn and ${}^{138}$Sn, along with the neighboring even-even isotope ${}^{134}$Sn [8] and the results of shell-model calculations using $V_{\text{low-}k}$ (vlk) [11] and modified $V_{\text{low-}k}$ (vlkm) interactions (see text for details).

Figure 5

Reduced transition rates for $6_1^{+}\to 4_1^{+}$ transitions in ${}^{134-138}$Sn. In addition to the experimental values (black squares), results are reported for calculations using the realistic $V_{\text{low-}k}$ interaction (red filled circles), a pairing-modified $V_{\text{low-}k}$ interaction (blue open circles), and the diagonalization of only the $f_{7/2}$ orbit (grey curve), which corresponds to the pure seniority scheme.