Study of the direct ${}^{16}\mathrm{O}(p,\gamma {)}^{17}\mathrm{F}$ astrophysical capture reaction within a potential model approach

Abstract

A potential model is applied for the analysis of the astrophysical direct nuclear capture process ${}^{16}$O(p,$\gamma {)}^{17}$F. The phase-equivalent potentials of the Woods-Saxon form for the p${-}^{16}$O interaction are examined which reproduce the binding energies and the empirical values of ANC for the ${}^{17}$F(5/2${}^{+}$) ground and ${}^{17}$F(1/2${}^{+}$) ($E^{\ast }$=0.495 MeV) excited bound states from different sources. The best description of the experimental data for the astrophysical $S$ factor is obtained within the potential model which yields the ANC values of 1.043 fm${}^{-1/2}$ and 75.484 fm${}^{-1/2}$ for the ${}^{17}$F($5/2^{+}$) ground and ${}^{17}$F($1/2^{+}$) excited bound states, respectively. The zero-energy astrophysical factor $S(0)=9.321$ KeV b is obtained by using the asymptotic expansion method of D. Baye. The calculated reaction rates within the region up to 10${}^{10}$ K are in good agreement with those from the R-matrix approach and the Bayesian model in both absolute values and temperature dependence.

Comments: 6 figures