We study the early evolution of the electron fraction (or, alternatively, the neutron-to-proton ratio) in the region above the hot proto-neutron star formed after a supernova explosion. We study the way in which the electron fraction in this environment is set by a competition between lepton (electron, positron, neutrino, and antineutrino) capture processes on free neutrons and protons and nuclei. Our calculations take explicit account of the effect of nuclear composition changes, such as formation of alpha particles (the "alpha effect") and the shifting of nuclear abundances in nuclear statistical equilibrium associated with cooling in near-adiabatic outFLow. We take detailed account of the process of weak interaction freezeout in conjunction with these nuclear composition changes. Our detailed treatment shows that the alpha effect can cause significant increases in the electron fraction, while neutrino and anti-neutrino capture on heavy nuclei tends to have a buffering effect on this quantity. We also examine the effect on weak rates and the electron fraction of fluctuations in time in the neutrino and antineutrino energy spectra arising from hydrodynamic waves. Our analysis is guided by the Wilson and Mayle supernova code numerical results for the neutrino energy spectra and density and velocity profiles.
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