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 identify the pole contribution to the S-factor without any explicit consideration of the asymptotic behavior of the bound-state wave function. This allows us to calculate $S_{17}$ in terms of purely short-range integrals involving the two-body potential. Much of the discussion is relevant to other radiative capture processes with weakly bound final states.

• Received 1 October 1999

DOI:https://doi.org/10.1103/PhysRevC.62.027602