6$^+$ isomers in neutron-rich Sn-isotopes beyond N$=82$ and effective interaction

Recent observation of the 6$^+$ seniority isomers and measurements of the B${(E2)}$ values in the $^{134-138}$Sn isotopes lying close to the neutron drip line have raised some questions about the validity of the currently used effective interactions in the neutron-rich region. Simpson $\it{et}$ $\it{al.}$ [Phys. Rev. Lett. $\textbf{113}$, 132502 (2014)] had to modify the diagonal and non-diagonal $νf_{7/2}^2$ two body matrix elements of the "${Vlk}$" interaction by ${\sim150}$ keV in their shell model calculations in order to explain the data of $^{136}$Sn. In contrast, we are able to explain the observed energy levels and the B${(E2)}$ values after marginal reduction of the same set of matrix elements by ${25}$ keV in the "RCDB" (Renormalized CD-Bonn) interaction. The observed mismatch in reproducing the data of $^{136}$Sn is due to the seniority mixing. Further, we do not find it necessary to consider the core excitations, and the "RCDB" interaction seems better suited to explain the data beyond N$=82$ magic number.

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