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

TL;DR

This work uses VS-IMSRG, an ab initio approach, to study shell evolution at $N=14$ and $Z=14$ and to assess the double magicity of the proton-rich nucleus $^{22}$Si via its mirror $^{22}$O. Employing NN+3N interactions (EM 1.8/2.0) with SRG evolution and a valence space in the $sd$ shell above $^{16}$O, the authors reproduce high $E(2_1^+)$ in $^{22}$O indicating robust subshell closures and predict a still-mizable but weaker $N=14$ closure in $^{22}$Si, with $E(2_1^+)$ around 2.4 MeV. The mirror-energy differences (MED) and the Thomas-Ehrman shift (TES) are analyzed across $^{22}$Si/$^{22}$O, $^{24}$Si/$^{24}$Ne, and $^{26}$Si/$^{26}$Mg, showing good agreement with data when using $NN+3N$ forces, while NN-only results fail to capture the observed splittings; ground-state configurations remain similar despite large MED. The study concludes that $^{22}$Si preserves double-magic characteristics akin to $^{22}$O, with TES lowering the $^{22}$Si $E(2_1^+)$, and provides robust ab initio predictions for the structure of proton-rich sd-shell nuclei, informing future experiments on the proton dripline.

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 $E(2_1^+)$.

Figures (4)

• Figure 1: The calculated excitation energy of first $2_1^+$ ($E(2_1^+)$) of oxygen, neon, magnesium and silicon isotopes with VS-IMSRG, along with experimental data ensdf.
• Figure 2: Similar to Fig. \ref{['2+N']}, but for the $E(2_1^+)$ of $N =$ 8, 10, 12, and 14 isotones.
• Figure 3: Ab initio VS-IMSRG calculations of spectra, MED, and average occupations of mirror nuclei $^{22}$Si/$^{22}$O, $^{24}$Si/$^{24}$Ne, and $^{26}$Si/$^{26}$Mg with only $NN$ and $NN + 3N$ interactions, along with experimental data ensdfPhysRevC.101.031303. Shown average occupations correspond to the valence protons and neutrons in proton- and neutron-rich nuclei, respectively.
• Figure 4: Correlation between the energies of the $2_1^+$ excited state in $^{22}$O and $^{22}$Si mirror partner, obtained from the interactions NNLO$_{\rm sat}$(gray square), 1.8/2.0 (EM) (red diamond), NN+3N(lnl) (purple triangle), and NNLO$_{\rm opt}$(blue circle). The error bars estimate uncertainties from enlarging the model space from $N =12$ to $N =14$. The thin horizontal line marks the known energy of the $2_1^+$ state in $^{22}$O. The MED values of the $2_1^+$ are estimated to be approximately $-886$ keV based on the calculated.