Beta equilibrium

Beta equilibrium is a condition in which weak reactions interconverting neutrons and protons produce no net change of composition. For matter where neutrinos are thermally trapped, the reaction $n+{\nu }_e\rightleftharpoons p+e^{-}$ gives the chemical equilibrium conditionwhere each $\mu$ is the corresponding chemical potential. In cold neutrino-transparent neutron star matter, one usually takes ${\mu }_{{\nu }_e}=0$, giving ${\mu }_n={\mu }_p+{\mu }_e$. The escaping neutrinos do not form an equilibrated thermal bath in that approximation.^[ref]

Charge neutrality in matter containing only neutrons, protons and electrons additionally requires $n_p=n_e$. Given a total baryon density, these relations and an equation of state determine the composition. As an illustrative chemical-potential check, ${\mu }_n=1000$ MeV and ${\mu }_p=900$ MeV require ${\mu }_e=100$ MeV in the transparent approximation. At finite temperature, balancing emission and capture rates is the more general kinetic condition; nuclear statistical equilibrium under strong reactions alone does not impose beta equilibrium.