Abstract
The Coulomb shift is analyzed for the mirror cluster systems of $^{18}\mathrm{O}=\ensuremath{\alpha}+^{14}\mathrm{C}$ and $^{18}\mathrm{Ne}=\ensuremath{\alpha}+^{14}\mathrm{O}$ by applying the orthogonality condition model (OCM). The OCM calculation clearly predicts the suppressed excitation energy of the higher ${0}^{+}$ states in the proton-rich system of $^{18}\mathrm{Ne}$. This results can be interpreted in terms of the extension of the Thomas-Ehrman shift (TES), which is discussed in $^{17}\mathrm{O}=^{16}\mathrm{O}+N$ and $^{17}\mathrm{F}=^{16}\mathrm{O}+P$, to the cluster degrees of freedom. A combination of the cluster TES and the monopole transition is proposed as an experimental probe to identify the cluster structure in mirror systems.
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