Mechanisms of mirror energy difference for states exhibiting Thomas-Ehrman shift: Gamow shell model case studies of $^{18}$Ne/$^{18}$O and $^{19}$Na/$^{19}$O

TL;DR

This study uses the Gamow shell model to analyze mirror energy differences in nuclei exhibiting Thomas-Ehrman shifts, revealing the roles of weakly bound states, Coulomb effects, and nucleon interactions in isospin symmetry breaking.

Contribution

It applies the Gamow shell model to accurately describe MEDs in $sd$-shell mirror nuclei, highlighting the impact of weakly bound states and Coulomb interactions on isospin symmetry breaking.

Findings

Large MEDs caused by occupation of weakly bound $s_{1/2}$ waves.

Radial density distributions are more extended in proton-rich nuclei.

Coulomb and nucleon-nucleon interactions significantly influence MEDs.

Abstract

The mirror energy difference (MED) of the mirror state, especially for states bearing the Thomas-Erhman shift, serves as a sensitive probe of isospin symmetry breaking. We employ the Gamow shell model, which includes the inter-nucleon correlation and continuum coupling, to investigate the MED for $sd$-shell nuclei by taking the $^{18}$Ne/$^{18}$O and $^{19}$Na/$^{19}$O as examples. Our GSM provides good descriptions for the excitation energies and MEDs for the $^{18}$Ne/$^{18}$O and $^{19}$Na/$^{19}$O. Moreover, our calculations also reveal that the large MED of the mirror states is caused by the significant occupation of the weakly bound or unbound $s_{1/2}$ waves, giving the radial density distribution of the state in the proton-rich nucleus more extended than that of mirror states in deeply-bound neutron-rich nuclei. Furthermore, our GSM calculation shows that the contribution of Coulomb is different for the low-lying states in proton-rich nuclei, which significantly contributes to MEDs of mirror states. Moreover, the contributions of the nucleon-nucleon interaction are different for the mirror state, especially for the state of proton-rich nuclei bearing the Thomas-Erhman shift, which also contributes to the significant isospin symmetry breaking with large MED.