Microscopic investigation of $E2$ matrix elements in atomic nuclei

TL;DR

This paper systematically analyzes $E2$ matrix elements in several nuclei using the triaxial projected shell model, providing detailed calculations that align well with experimental data and reveal shape transitions.

Contribution

It applies the TPSM approach to a broad set of nuclei, tabulates extensive $E2$ matrix elements, and performs shape analysis with Kumar-Cline sum rules, offering new insights into nuclear shape evolution.

Findings

TPSM describes measured $E2$ transitions well.

Shape analysis indicates a transition from $b3$-rigid to $b3$-soft configurations.

1496 $E2$ matrix elements evaluated and tabulated.

Abstract

A systematic analysis of $E2$ matrix elements of $^{72}$Ge, $^{76}$Ge, $^{168}$Er, $^{186}$Os, $^{188}$Os, $^{190}$Os, $^{192}$Os and $^{194}$Pt nuclides is performed using the beyond mean-field approach of triaxial projected shell model (TPSM). For these nuclei, large sets of $E2$ matrix elements have been deduced from the multi-step Coulomb excitation experiments, and it is shown that TPSM approach provides a reasonable description of the measured transitions. We have evaluated 1496 $E2$ matrix elements up to spin, $I=10$ for the eight nuclei studied, and tabulate them for future experimental and theoretical comparisons. Further, shape invariant analysis has been performed with the calculated $E2$ transitions using the Kumar-Cline sum rules. It is inferred from the analysis that the resulting shape, after configuration mixing of the quasiparticle states, transforms from $\gamma$-rigid to that of $\gamma$-soft for some nuclei, in conformity with the experimental data.