Analytic solution for kinetic equilibrium with respect to β-processes in nucleon plasmas with relativistic pairs

An analytic solution is obtained for kinetic equilibrium with respect to β-processes in nucleon plasmas with relativistic pairs. The nucleons (n, p) are assumed to be nonrelativistic and nondegenerate (their mass is taken to be infinite), while the electrons and positrons are assumed to be ultrarelativistic because of a high temperature (T > 6∙10⁹ K) or high density (ρ > μ10⁶ g/cm³), or both, where μ is the number of nucleons per electron. The analysis can be simplified because of the analytic relationship of the density and chemical potential of the electrons in an ultrarelativistic plasma, as well as by the use of a modified gaussian method for calculating the Fermi functions. The electron chemical potential and the number of nucleons per initial electron are calculated as functions of ρ and T.