Bounds on the rate of 1H(p, e+ν)2H in impulse approximation

Working in impulse approximation, we derive simple bounds on the experimentally inaccessible rate of the proton--proton reaction 1H(p, e+ν)2H, using only a few common and physically plausible assumptions. We evaluate these bounds at the kilovolt energies of interest for hydrogen burning in stars and find that they permit at most a few percent enhancement over currently accepted impulse-approximation rates. Within the framework of the usual nonrelativistic Schrodinger-equation description of the two-nucleon interaction, this result is obtained independent of the specific features of the two-nucleon interaction at distances less than 3 fm, provided that the energy dependence of the interaction may be neglected at the low energies in question