Weak capture of protons by protons

The cross section for the proton weak capture reaction ${}^1\mathrm{H}{(p,e}^{+}{\nu }_e{)}^2\mathrm{H}$ 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 $\beta$ 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 ${\Lambda }^2\mathrm{}(E=0\mathrm{})\mathrm{}$ 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.