Analytic solution for kinetic equilibrium of beta-processes in nucleonic plasma with relativistic pairs

TL;DR

This paper derives an analytic solution for the kinetic equilibrium of beta-processes in nucleonic plasma with relativistic pairs, applicable under high temperature or density conditions, simplifying the understanding of such astrophysical environments.

Contribution

It provides a novel analytic approach linking electron chemical potential and nucleon number in relativistic plasma, enhancing modeling of astrophysical phenomena.

Findings

Analytic expressions for electron chemical potential as functions of density and temperature.

Explicit relations between nucleon number and plasma conditions.

Simplified modeling of beta-process equilibrium in relativistic plasma.

Abstract

The analytic solution is obtained describing kinetic equilibrium of the $\beta$-processes in the nucleonic plasma with relativistic pairs. The nucleons $(n,p)$ are supposed to be non-relativistic and non-degenerate, while the electrons and positrons are ultra-relativistic due to high temperature $(T>6\cdot 10^9$K), or high density $(\rho>\mu 10^6$g/cm$^3$), or both, where $\mu$ is a number of nucleons per one electron. The consideration is simplified because of the analytic connection of the density with the electron chemical potential in the ultra-relativistic plasma, and Gauss representation of Fermi functions. Electron chemical potential and number of nucleons per one initial electron are calculated as functions of $\rho$ and $T$.