  The rates of electron neutrino capture on neutron, electron anti-neutrino
capture on proton, and their reverse processes are important for understanding
the production of heavy elements in the supernova environment above the
protoneutron star. Observations and theoretical considerations suggest that
some protoneutron stars may be born with strong magnetic fields. We develop a
numerical method to calculate the above rates in supernova environments with
magnetic fields up to 10^16 G. This method is accurate to the order of one over
nucleon mass. We show that our results have the correct behavior in the limit
of high neutrino energy or small magnetic field. Based on comparison of our
results with various approximations, we recommend efficient estimates of the
above rates for use in models of supernova nucleosynthesis in the presence of
strong magnetic fields.
