\begin{document}$\gamma$\end{document}-ray. This is a potential astronomical observable, whose occurrence is suspected in classical novae. The \begin{document}$^{22}{{\rm{Mg}}}(p,\,\gamma)^{23}{{\rm{Al}}}$\end{document} reaction is relevant to the nucleosynthesis of 22Na in Ne-rich novae. In this study, employing the adiabatic distorted wave approximation and continuum discretized coupled channel methods, the squared neutron asymptotic normalization coefficients (ANCs) for the virtual decay of \begin{document}$^{23}{{\rm{Ne}}}$\end{document} \begin{document}$\to$\end{document} \begin{document}$^{22}{{\rm{Ne}}}$\end{document} + n were extracted, and determined as \begin{document}$(0.483\pm0.060)$\end{document} fm−1 and \begin{document}$(9.7\pm2.3)$\end{document} fm−1 for the ground state and the first excited state from the experimental angular distributions of \begin{document}${}^{22}{{\rm{Ne}}}(d,\,p){}^{23}{{\rm{Ne}}}$\end{document} populating the ground state and the first excited state of \begin{document}$^{23}{{\rm{Ne}}}$\end{document}, respectively. Then, the squared proton ANC of \begin{document}${}^{23}{{\rm{Al}}}_{\rm{g.s.}}$\end{document} was obtained as \begin{document}$C_{d5/2}^{2}({}^{23}{{\rm{Al}}})=(2.65\pm0.33)\times10^{3}$\end{document} fm−1 according to the charge symmetry of the strong interaction. The astrophysical S-factors and reaction rates for the direct capture contribution in \begin{document}${}^{22}{{\rm{Mg}}}(p,\,\gamma){}^{23}{{\rm{Al}}}$\end{document} were also presented. Furthermore, the proton width of the first excited state of \begin{document}$^{23}{{\rm{Al}}}$\end{document} was derived to be \begin{document}$(57\pm14)$\end{document} eV from the neutron ANC of its mirror state in \begin{document}$^{23}{{\rm{Ne}}}$\end{document} and used to compute the contribution from the first resonance of \begin{document}$^{23}{{\rm{Al}}}$\end{document}. This result demonstrates that the direct capture dominates the \begin{document}$^{22}{{\rm{Mg}}}(p,\,\gamma)^{23}{{\rm{Al}}}$\end{document} reaction at most temperatures of astrophysical relevance for \begin{document}$0.33 < T_9<0.64$\end{document}."> Astrophysical <sup>22</sup>Mg(<i>p</i>, <i>γ</i>)<sup>23</sup>Al reaction rates from asymptotic normalization coefficient of <sup>23</sup>Ne→<sup>22</sup>Ne+<i>n</i> -
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