Abstract The steady equilibrium conditions for a mixed gas of neutrons, protons, electrons, positrons and radiation fields (abbreviated as npe± gas) with or without external neutrino flux are investigated, and a general chemical potential equilibrium equation μn = μp + Cμe is obtained to describe the steady equilibrium at high temperatures (T > 109 K). An analytic fitting formula of coefficient C is presented for the sake of simplicity, when neutrinos and antineutrinos are transparent. It is a simple method to estimate the electron fraction for the steady equilibrium npe± gas that adopts the corresponding equilibrium condition. As an example, we apply this method to the GRB accretion disk and confirm that the composition in the inner region is approximately in equilibrium when the accretion rate is low. For the case with external neutrino flux, we calculate the initial electron fraction of neutrino-driven wind from the proto-neutron star model M15-l1-r1. The results show that the improved equilibrium condition makes the electron fraction decrease significantly more than the case μn = μp + μe when the time is less than 5 s post bounce, which may be useful for r-process nucleosynthesis models.

Keywords nuclear reactions — nucleosynthesis, weak-interaction GRB accretion disk — neutrino-driven wind

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