Asymptotic theory of charged particle transfer reactions at low energies and nuclear astrophysics

Abstract

A new asymptotic theory is proposed for the peripheral sub- and above-barrier transfer $A$($x$, $y$)$B$ reaction within the three-body ($A$, $a$ and $y$) model, where $ x$= $y$ + $a$, $B$= $A$ + $a$ and $ a$ is a transferred particle. In the asymptotic theory, the allowance of the contribution of the three-body ($A$, $a$ and $y$) Coulomb dynamics of the transfer mechanism to the peripheral partial amplitudes for the partial wave $l_i>>$ 1 and of the Coulomb-nuclear distorted effects in the entrance and exit channels is done in a correct manner within the framework of the dispersion theory and the conventional distorted-wave Born approximation (DWBA), respectively. It is shown that the proposed asymptotic theory makes it possible to test the accuracy of taking into account the the three-body Coulomb dynamics of the transfer mechanism in the modified DWBA. The results of the analysis of the differential cross sections of the specific proton and triton transfer reactions at above- and sub-barrier energies are presented. New estimates and their uncertainties are obtained for values of the asymptotic normalization coefficients for ${\rm{^9Be}} \,+p \to\,{\rm{^{10}B}}$, ${\rm{^{11}B}}\,+\,p\to\,{\rm{^{12}C}}$, ${\rm{^{16}O}} \,+\,p \to\, {\rm{^{17}F}}$ and ${\rm{^{19}F}}\to\, {\rm{^{16}O}} \,+\,t$ as well as for the direct astrophysical $S$ factors at stellar energy of the radiative capture ${\rm{^9Be(}}p,\,\gamma{\rm{)^{10}B}} $, ${\rm{^{11}B(}}p,\,\gamma{\rm{)^{12}C}} $ and ${\rm{^{16}O(}}p,\,\gamma{\rm{)^{17}F}}$ reactions.