Microscopic investigation of $E2$ matrix elements in atomic nuclei -- II

TL;DR

This paper extends previous microscopic calculations of $E2$ matrix elements in nuclei using the triaxial projected shell model, now including six additional nuclides and comparing results with experimental data.

Contribution

It systematically applies the TPSM approach to new nuclides, demonstrating its effectiveness and contrasting it with phenomenological models regarding shape invariants.

Findings

TPSM provides good agreement with experimental data for most nuclides.

Most investigated nuclides exhibit $$ soft behavior.

No clear correlation between $\u03b3$ band energy staggering and shape invariants was found.

Abstract

The present work is a continuation of our earlier investigation with the primary objective to systematically calculate the $E2$ matrix elements using the microscopic approach of the triaxial projected shell model (TPSM). In the earlier work, we studied nine nuclides of $^{72}$Ge, $^{76}$Ge, $^{104}$Ru, $^{168}$Er, $^{186}$Os, $^{188}$Os, $^{190}$Os, $^{192}$Os, and $^{194}$Pt. In the present work six more nuclides of $^{70}$Ge, $^{76,78,80,82}$Se, and $^{100}$Mo have been investigated. The Coulomb excitation data has recently become available for $^{70}$Ge and other nuclides were inadvertently omitted in our earlier investigation. It is demonstrated that TPSM approach provides a good description of the available experimental data and most of the nuclides, except for $^{76}$Se and $^{100}$Mo, are shown to have $\gamma$ soft behaviour. Further, it is demonstrated that in contrast to the predictions of the phenomenological collective model, TPSM calculations depict no clear correlation between the energy staggering pattern of the $\gamma$ band and the deduced shape invariant quantities using the Kumar-Cline sum rules.