Stellar weak interaction rates for intermediate-mass nuclei. IV - Interpolation procedures for rapidly varying lepton capture rates using effective log (ft)-values

Abstract

Simple expressions for continuum electron and positron capture phase space factors and the associated neutrino energy loss integrals are presented in terms of standard Fermi integrals. Continuous approximations to the relevant Fermi integrals and their first derivatives are made. These allow the computation of effective log (ft)-values, at each temperature and density point, for the continuum lepton capture rates considered in the earlier papers in this series. Since the effective log (ft)-values have most of the rapid temperature and density dependence associated with the phase space integrals removed, interpolation in temperature and density to obtain stellar rates is greatly facilitated in speed and accuracy. Computer simulations of stellar evolution will be able to implement more accurately the calculations of the stellar nuclear weak interaction rates of intermediate-mass nuclei. Generalization of the Fermi integral expressions for the lepton continuum capture phase space factors are given for astrophysical environments where there exists an equilibrium distribution of electron-type neutrinos. These allow rough estimates of the effect of neutrino blocking on the tabulated rates and estimates of total neutrino capture rates.