标题： 展示托马斯-厄尔曼位移状态的镜像能差机制：基于Gamow壳模型的$^{18}$氖/$^{18}$氧和$^{19}$钠/$^{19}$氧案例研究 显示英文标题

标题： 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

摘要： 镜像态的能量差（MED）特别是对于存在托马斯-厄尔曼位移的态，是同位旋对称性破缺的一个灵敏探针。 我们采用包含核子关联和连续谱耦合的Gamow壳模型，以Ne/$^{18}$和O/$^{18}$的镜像核以及Na/$^{19}$和O/$^{19}$的镜像核为例，研究了$sd$壳层核的MED。 我们的GSM模型对Ne/$^{18}$与O/$^{18}$以及Na/$^{19}$与O/$^{19}$的激发能和MED值给出了很好的描述。此外，我们的计算还表明镜像态的大MED值是由弱束缚或非束缚的$s_{1/2}$波显著占据引起的，这使得质子丰度核中的态的径向密度分布比深束缚中子丰度核中的镜像态更扩展。此外，我们的GSM计算显示，对于质子丰度核中的低激发态，库仑效应的贡献不同，这显著影响了镜像态的MED值。此外，对于具有Thomas-Ehrman位移的质子丰度核态，核子-核子相互作用的贡献也不同，这也导致了由于大MED值而产生的显著同位旋对称性破缺。 显示英文摘要

摘要： 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.