Effect of finite nucleon mass on primordial nucleosynthesis

By numerically evaluating five-dimensional phase-space integrals, we have calculated the small effect of finite nucleon mass on the weak-interaction rates that interconvert protons and neutrons in the early Universe. We have modified the standard code for primordial nucleosynthesis to include these corrections and find a small, systematic increase in the ${}^{4}$He yield, $\ensuremath{\Delta}Y/Y\ensuremath{\simeq}(0.47\ensuremath{-}0.50)%$, depending slightly on the value of the baryon-to-photon ratio $\ensuremath{\eta}$. The fractional changes in the abundances of $\mathrm{D}$, ${}^{3}\mathrm{He}$, and ${}^{7}\mathrm{Li}$ range from 0.06 to $2.8%$ for ${10}^{\ensuremath{-}11}l~\ensuremath{\eta}l~{10}^{\ensuremath{-}8}$.