Analysis of the antineutrino capture on protons

Corrections to the zeroth-approximation cross-section formula for antineutrino capture on protons at nuclear reactors are evaluated. They include recoil corrections $\frac{1}{M}$ of three kinds. The true recoil correction to the cross section is negligible. The weak-magnetism—axial-vector interference is sizable, decreasing the cross section by ∼2% for 5-MeV positrons. One also has to include the recoil-neutron energy in relating the positron and antineutrino energies in order to evaluate the antineutrino flux. That effect decreases the positron yield by as much as 6% for 5-MeV positrons. The radiative corrections of order $\alpha$ have been also evaluated; they increase the cross section by ∼1.5% near threshold and by ∼0.7% at 5MeV. Formulas and a table of numerical values of all corrections are presented.