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

TL;DR

This study uses a potential model to analyze the astrophysical $^{16}$O(p,$ extgamma)^{17}$F capture reaction, accurately reproducing experimental data and providing reaction rates consistent with other models.

Contribution

It introduces a potential model approach with phase-equivalent Woods-Saxon potentials to analyze the reaction and determine astrophysical S-factors and reaction rates.

Findings

Best fit to experimental S-factor data achieved.

Reaction rates agree with R-matrix and Bayesian models.

Provides specific ANC and S(0) values for the reaction.

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$^+$) ($E^*$=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.