Dispersion (asymptotic) theory of charged particle transfer reactions at low energies and nuclear astrophysics: II. the asymptotic normalization coefficients and their nuclear-astrophysical application

Abstract

Within the asymptotic theory proposed by authors R. Yarmukhamedov and K.I. Tursunmakhatov [Phys. Rev. C (submitted 2019)] for the peripheral sub- and above-barrier transfer $A$($x$, $y$)$B$ reaction in the three-body ($A$, $a$ and $y$) model ($x$= $y$ + $a$ and $B$= $A$ + $a$, and $a$ is a transferred particle), the analysis of the experimental angular distributions of the differential cross sections is performed for the peripheral proton and triton transfer ${}^9\mathrm{Be}{(}^{10}\mathrm{B},{}^9\mathrm{Be}{)}^{10}\mathrm{B}$, ${}^{16}\mathrm{O}{(}^3\mathrm{He},d{)}^{17}\mathrm{F}$ and ${}^{19}\mathrm{F}(p,\alpha {)}^{16}\mathrm{O}$ reactions at above-and sub-barrier projectile energies, respectively. New estimates and their uncertainties are obtained for magnitudes of the asymptotic normalization coefficients (respective the nuclear vertex constants) for ${}^9\mathrm{Be}+p\to {}^{10}\mathrm{B}$, ${}^{16}\mathrm{O}+p\to {}^{17}\mathrm{F}$ and ${}^{16}\mathrm{O}+t\to {}^{19}\mathrm{F}$. They are applied for calculations of the astrophysical $S$ factors for the nuclear-astrophysical ${}^9\mathrm{Be}(p,\gamma {)}^{10}\mathrm{B}$, ${}^{16}\mathrm{O}(p,\gamma {)}^{17}\mathrm{F}$ and ${}^{19}\mathrm{F}(p,\alpha {)}^{16}\mathrm{O})$ reactions at thermonuclear energies. New values and their uncertainties are obtained for the astrophysical $S$ factors at stellar energies.