$E(5)$-like emerging $\gamma$-softness in $^{82}$Kr

TL;DR

This paper demonstrates that an $E(5)$-like $eta$-softness can emerge in the interacting boson model with higher-order $SU(3)$ interactions, specifically in $^{82}$Kr, providing new insights into nuclear shape transitions.

Contribution

It introduces a novel $SU(3)$ fourth-order interaction in the IBM that produces $E(5)$-like $eta$-softness, connecting it to realistic nuclei and transitional behaviors.

Findings

The $E(5)$-like $eta$-softness appears with the $SU(3)$ fourth-order interaction.

Calculated spectra and $B(E2)$ values agree well with experimental data for $^{82}$Kr.

The model offers a new perspective on shape phase transitions in nuclei.

Abstract

Recently the interacting bosom model with $SU(3)$ higher-order interactions was proposed by one of the authors, wherein unexpected $\gamma$-softness can be emerged in this new model. This stimulates further discussion on the connections of the new $\gamma$-softness and the realistic $\gamma$-soft nuclei. In this paper, $E(5)$-like $\gamma$-softness arises when the $SU(3)$ fourth-order interaction $\hat{C}_{2}^{2}[SU(3)]$ is considered. And the corresponding transitional behaviors are similar to that from the $U(5)$ limit to the $O(6)$ limit in previous IBM-1, which provides a novel perspective for understanding the new model. Low-lying spectra, $B(E2)$ values between the low-lying states and quadrupole moment of the first $2_{1}^{+}$ state are investigated. Experimental data of the $E(5)$-like nucleus $^{82}$Kr are compared with the calculated theoretical results, where the calculated low-lying level energies and the associated $B(E2)$ values fit very well with the experimental data.