Precision Rates for Nucleon Weak Interactions in Primordial Nucleosynthesis and He-4 Abundance

We report the results of a detailed calculation of nucleon weak interactions relevant for the neutron to proton density ratio at the onset of primordial nucleosynthesis. Radiative electromagnetic corrections, finite nucleon mass terms, thermal radiative effects on weak processes and on neutrino temperature are taken into account to reduce the theoretical uncertainty on $n \leftrightarrow p $ rates to 1%. This translates into a sensitivity in $^4 He$ mass fraction $Y_p$ prediction up to $10^{-4}$. We find a positive total correction to the Born prediction $\delta Y_p \simeq 0.004$.