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

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 ${\rm{^9Be(^{10}B,\,^9Be)^{10}B}}$, ${\rm{^{16}O(^3He}},\,d{\rm{)^{17}F}}$ and ${\rm{^{19}F(}}p,\,α{\rm{)^{16}O}}$ 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 ${\rm{^9Be}} \,+p \to\,{\rm{^{10}B}}$, ${\rm{^{16}O}} \,+\,p \to\, {\rm{^{17}F}}$ and ${\rm{^{16}O}} \,+\,t\to{\rm{^{19}F}}$. They are applied for calculations of the astrophysical $S$ factors for the nuclear-astrophysical ${\rm{^9Be(}}p,\,γ{\rm{)^{10}B}} $, ${\rm{^{16}O(}}p,\,γ{\rm{)^{17}F}}$ and ${\rm{^{19}F(}}p,\,α{\rm{)^{16}O)}}$ reactions at thermonuclear energies. New values and their uncertainties are obtained for the astrophysical $S$ factors at stellar energies.