Double-magicity of proton drip-line nucleus ${}^{22}$Si with \textit{ab initio} calculation

Abstract

New magic numbers have been discovered in the neutron-rich region of the nuclear chart. However, there has been a lack of research on proton-rich nuclei. ${}^{22}$O, the mirror nucleus of ${}^{22}$Si, is a double-magic nucleus bearing a high $E(2_1^{+})$. Whether ${}^{22}$Si exhibits double-magic characters is an intriguing topic. To investigate this matter, we utilized \textit{ab initio} valence space in-medium similarity renormalization group for ${}^{22}$Si/${}^{22}$O, and their nearby nuclei. Our \textit{ab initio} calculations provide good descriptions for the double magicity of ${}^{22}$O, as well as the shell evolution of $N=14$ and $Z=14$ through $E(2_1^{+})$. The computed $E(2_1^{+})$ indicate that the closure of $Z=14$ sub-shell in proton-rich nuclei is weaker than the $N=14$ sub-shell closure in their mirror nuclei. Particularly, the calculated $E(2_1^{+})$ of ${}^{22}$Si is 800 keV lower than the one of ${}^{22}$O. To further explore the magicity of ${}^{22}$Si, the mirror energy difference (MED) of ${}^{26}$Si/${}^{26}$Mg, ${}^{24}$Si/${}^{24}$Ne, as well as ${}^{22}$Si/${}^{22}$O are calculated. The results demonstrate that the calculated MEDs agree well with available experimental data, and the $E(2_1^{+})$ values of ${}^{22,24,26}$Si are all lower than their respective mirror nuclei due to the Thomas-Ehrman shift with large $s_{1/2}$ occupation. Moreover, our calculation provides that the many-body configurations of the low-lying state of ${}^{22}$Si/${}^{22}$O are nearly identical despite the fact that the states bearing large MED. In conclusion, our \textit{ab initio} results suggest that ${}^{22}$Si is a double magic nucleus, similar to its mirror nucleus ${}^{22}$O, albeit with a lower $E(2_1^{+})$.

6 Pages, 4 Figures

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