The production of ${}^{22}\mathrm{Na}$ in ONe novae can be influenced by the ${}^{22}\mathrm{Mg}$$(p,\gamma )$${}^{23}\mathrm{Al}$ reaction. To investigate this reaction rate at stellar energies, we have determined the asymptotic normalization coefficient (ANC) for ${}^{22}\mathrm{Mg}$$+p\to$${}^{23}\mathrm{Al}$ through measurements of the ANCs in the mirror nuclear system ${}^{22}\mathrm{Ne}$$+n\to$${}^{23}\mathrm{Ne}$. The peripheral neutron-transfer reactions ${}^{13}\mathrm{C}$(${}^{12}\mathrm{C}$,${}^{13}\mathrm{C}$)${}^{12}\mathrm{C}$ and ${}^{13}\mathrm{C}$(${}^{22}\mathrm{Ne}$,${}^{23}\mathrm{Ne}$)${}^{12}\mathrm{C}$ were studied. The identical entrance and exit channels of the first reaction make it possible to extract independently the ground-state ANC in ${}^{13}\mathrm{C}$. Our experiment gives $C_{p_{1/2}}^2$(${}^{13}\mathrm{C}$)$=2.24\pm 0.11$ fm${}^{-1}$, which agrees with the value obtained from several previous measurements. The weighted average for all the obtained $C_{p_{1/2}}^2$ is $2.31\pm 0.08$ fm${}^{-1}$. This value is adopted to be used in obtaining the ANCs in ${}^{23}\mathrm{Ne}$. The differential cross sections for the reaction ${}^{13}\mathrm{C}$(${}^{22}\mathrm{Ne}$,${}^{23}\mathrm{Ne}$)${}^{12}\mathrm{C}$ leading to the $J^{\pi }=5/2^{+}$ and $1/2^{+}$ states in ${}^{23}\mathrm{Ne}$ have been measured at 12 MeV/u. Optical model parameters for use in the DWBA calculations were obtained from measurements of the elastic scatterings ${}^{22}\mathrm{Ne}+{}^{13}\mathrm{C}$ and ${}^{22}\mathrm{Ne}+{}^{12}\mathrm{C}$. The extracted ANC for the ground state in ${}^{23}\mathrm{Ne}$, $C_{d_{5/2}}^2=0.86\pm 0.08\pm 0.12$ fm${}^{-1}$, is converted to its corresponding value in ${}^{23}\mathrm{Al}$ using mirror symmetry to give $C_{d_{5/2}}^2$(${}^{23}\mathrm{Al}$)$=(4.63\pm 0.77)\times {10}^3$ fm${}^{-1}$. The astrophysical $S$ factor $S(0)$ for the ${}^{22}\mathrm{Mg}$($p,\gamma$) reaction was determined to be $0.96\pm 0.11$ keV b. The consequences for nuclear astrophysics are discussed.

• Received 25 August 2009

DOI:https://doi.org/10.1103/PhysRevC.81.035802