Low Energy Behavior of the \protect(^{7}\protect) Be \protect( (p,\gamma)^{8}\protect) B reaction

Abstract

Three related features of the astrophysical S-factor, (S_{17}), for low energies are an upturn as the energy of the proton goes to zero, a pole at the proton separation energy and a long ranged radial integral peaking at approximately 40 fm. These features, particularly the last, mean (S_{17}) at threshold is largely determined by the asymptotic normalization of the proton bound-state wave function. In this paper we show that by taking the pole explicitly into account, (S_{17}) can be calculated in terms of purely short range integrals involving the two-body potential. Much of the discusion is relevant to other radiative capture processes especially those wth weakly bound final states.