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

TL;DR

This paper extends the generalized seniority scheme to odd tensor E3 transitions in Sn-isotopes, demonstrating its effectiveness in explaining systematics of transition probabilities and guiding shell model calculations.

Contribution

It is the first to analyze E3 transitions within the generalized seniority framework in Sn-isotopes, linking theory with shell model calculations.

Findings

Generalized seniority explains E3 transition systematics in Sn-isotopes.

The approach identifies key valence spaces for shell model calculations.

Results support the occurrence of seniority isomers in $^{13}$- isomers.

Abstract

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.