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arXiv · 2407.00884

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

J. G. Li·K. H. Li·N. Michel·H. H. Li·W. Zuo
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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.

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J. G. Li, K. H. Li, N. Michel, H. H. Li, W. Zuo. 2024-07-01. 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. https://arxiv.org/abs/2407.00884

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