Weak capture of protons by protons

The cross section for the proton weak capture reaction {sup 1}H(p,e{sup +}{nu}{sub e}){sup 2}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 pp capture is given. Its inherent model dependence is in fact found to be very weak. The overlap integral {Lambda}{sup 2}(E=0) for the pp capture is predicted to be in the range 7.05--7.06, including the axial two-body current contribution, for all interactions considered