Weak interaction rate Coulomb corrections in big bang nucleosynthesis

Abstract

We have applied a fully relativistic Coulomb wave correction to the weak reactions in the full Kawano/Wagoner big bang nucleosynthesis (BBN) code. We have also added the zero-temperature radiative correction. We find that using this higher accuracy Coulomb correction results in good agreement with previous work, giving only a modest $\ensuremath{\sim}0.04%$ increase in helium mass fraction over correction prescriptions applied previously in BBN calculations. We have calculated the effect of these corrections on other light element abundance yields in BBN, and we have studied these yields as functions of electron neutrino lepton number. This has allowed insights into the role of the weak neutron-proton interconversion processes in the setting of the neutron-to-proton ratio during the BBN epoch. We find that the lepton capture processes' contributions to this ratio are only second order in the Coulomb correction.