Low energy behavior of astrophysical S factor in radiative captures to loosely bound final states

Abstract

The low-energy behavior of the astrophysical S-factor for E1 direct radiative captures a(p,gamma)b leading to loosely bound final states (b=a+p) is investigated. We derive a first-order integral representation for S(E) and focus on the properties around zero energy. We show that it is the competition between various effects, namely the remnant Coulomb barrier, the initial and final centrifugal barriers and the binding energy, that defines the behavior of the S(E->0). Contrary to previous findings, we prove that S(E->0) is not determined by the pole corresponding to the bound state. The derivative S'(0) increases with the increase of the centrifugal barrier, while it decreases with the charge of the target. For l_i=l_f+1 the increase of the binding energy of the final nucleus increases the derivative S'(0) while for l_i=l_f-1 the opposite effect is found. We make use of our findings to explain the low energy behavior of the S-factors related to some notorious capture reactions: 7Be(p, gamma)8B, 14N(p,gamma)15O, 16O}(p,gamma)17F, 20Ne(p, gamma)21Na and 22Mg(p, gamma)23Al.