The ${}^{20}\mathrm{Ne}$$(p,\gamma )$${}^{21}\mathrm{Na}$ reaction rate at stellar energies is dominated by capture to the ground state through the tail of a subthreshold resonance state at an excitation energy of 2425 keV in ${}^{21}\mathrm{Na}$. Both resonant and direct capture contribute to the reaction rate while direct captures to other bound states are negligible. The overall normalization of direct capture to the subthreshold state is determined by the asymptotic normalization coefficient (ANC). Simultaneously this ANC determines the proton partial width of the subthreshold resonance state. To determine the ANC, the ${}^{20}\mathrm{Ne}$(${}^3\mathrm{He}$$,d)$${}^{21}\mathrm{Na}$ proton transfer reaction has been measured, at an incident energy of 25.83 MeV. Angular distributions for proton transfer to the ground and first three excited states were measured, and ANCs were then extracted from comparison with distorted-wave Born approximation calculations. Using these ANCs, we calculated the astrophysical factor for ${}^{20}\mathrm{Ne}$$(p,\gamma )$${}^{21}\mathrm{Na}$. Our total astrophysical factor is $S(0)=5900\pm 1200$ keV b. Our analysis confirms that only nonresonant and resonant captures through the subthreshold state are important.

• Received 8 August 2005

DOI:https://doi.org/10.1103/PhysRevC.73.035806