The ground state of the proton-rich nucleus ${}^{23}$Al has been studied by one-proton removal on a carbon target at about 50 MeV/nucleon using the EXOGAM $+$ SPEG experimental setup at GANIL. Longitudinal momentum distributions of the ${}^{22}$Mg breakup fragments, inclusive and in coincidence with $\gamma$ rays de-exciting the residues, were measured. The ground-state structure of ${}^{23}$Al is found to be a configuration mixing of a $d$-orbital valence proton coupled to four core states—0${}_{\text{gs}}^{+}$, 2${}_1^{+}$, 4${}_1^{+}$, 4${}_2^{+}$. We confirm the ground state spin and parity of ${}^{23}$Al as $J^{\pi }=5/2^{+}$. The measured exclusive momentum distributions are compared with extended Glauber model calculations to extract spectroscopic factors and asymptotic normalization coefficients (ANCs). The spectroscopic factors are presented in comparison with those obtained from large-scale shell model calculations. We determined the asymptotic normalization coefficient of the nuclear system ${}^{23}$Al${}_{\text{gs}}$ $\to$ ${}^{22}$Mg(0${}^{+}$) $+$ $p$ to be $C_{d_{5/2}}^2{(}^{23}{\text{Al}}_{\text{gs}})=(3.90\pm 0.44)\times {10}^3{\text{fm}}^{-1}$, and used it to infer the stellar reaction rate of the direct radiative proton capture ${}^{22}$Mg($p$,$\gamma$)${}^{23}$Al. Astrophysical implications related to ${}^{22}$Na nucleosynthesis in ONe novae and the use of one-nucleon breakup at intermediate energies as an indirect method in nuclear astrophysics are discussed.

• Received 3 March 2011

DOI:https://doi.org/10.1103/PhysRevC.84.015803