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Recent observation of the 6$^+$ seniority isomers and measurements of theB${(E2)}$ values in the $^{134-138}$Sn isotopes lying close to the neutron dripline have raised some questions about the validity of the currently usedeffective interactions in the neutron-rich region. Simpson $\it{et}$ $\it{al.}$[Phys. Rev. Lett. $\textbf{113}$, 132502 (2014)] had to modify the diagonal andnon-diagonal ${\nu}f_{7/2}^2$ two body matrix elements of the "${Vlk}$"interaction by ${\sim150}$ keV in their shell model calculations in order toexplain the data of $^{136}$Sn. In contrast, we are able to explain theobserved energy levels and the B${(E2)}$ values after marginal reduction of thesame 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 dueto the seniority mixing. Further, we do not find it necessary to consider thecore excitations, and the "RCDB" interaction seems better suited to explain thedata beyond N$=82$ magic number.

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