Weak capture of protons by protons

Abstract

The cross section for the proton weak capture reaction ${}^{1}\mathrm{H}{(p,e}^{+}{\ensuremath{\nu}}_{e}{)}^{2}\mathrm{H}$ is calculated with wave functions obtained from a number of modern, realistic high-precision interactions. To minimize the uncertainty in the axial two-body current operator, its matrix element has been adjusted to reproduce the measured Gamow-Teller matrix element of tritium $\ensuremath{\beta}$ decay in model calculations using trinucleon wave functions from these interactions. A thorough analysis of the ambiguities that this procedure introduces in evaluating the two-body current contribution to the $\mathrm{pp}$ capture is given. Its inherent model dependence is in fact found to be very weak. The overlap integral ${\ensuremath{\Lambda}}^{2}(E=0)$ for the $\mathrm{pp}$ capture is predicted to be in the range 7.05--7.06, including the axial two-body current contribution, for all interactions considered.