Odd tensor E3 transitions and the generalized seniority in Sn-isotopes

In our recent paper [Phys. Lett. B 753, (2016) 122], we have shown that both the odd and even tensor electric transition probabilities exhibit similar behavior within the generalized seniority scheme in a multi-j environment. This microscopic approach was used to show for the first time the occurrence of seniority isomers in the $ {13}^-$ isomers of Sn-isotopes, which decay by odd tensor $E1$ transition to the same seniority ($\Delta v = 0$) state. In this letter, we extend our studies to odd tensor $E3$ transitions connecting different seniority states ($\Delta v = 2$), and show for the first time that the generalized seniority scheme explains reasonably well the systematics of the $B(E3)$ values for the $(0^+ \rightarrow 3_1^-)$ transitions in the Sn-isotopes. Additionally, we support these results by seniority guided Large Scale Shell Model (LSSM) calculations. The generalized seniority results are able to single out the most crucial valence space required in the LSSM calculations.