Saha Equation Normalized to Total Atomic Number Density
Abstract
The Saha equation describes the relative number density of consecutive ionization levels of a given atomic species under conditions of thermodynamic equilibrium in an ionized gas. Because the number density in the denominator may be very small, special steps must be taken to ensure numerical stability. In this paper we recast the equation into a form in which each ionization fraction is normalized by the total number density of the atomic species, analogous to the Boltzmann equation describing the distribution of excitation states for a given ion.
Cite
@article{arxiv.1209.1111,
title = {Saha Equation Normalized to Total Atomic Number Density},
author = {John W. Fowler},
journal= {arXiv preprint arXiv:1209.1111},
year = {2012}
}
Comments
4 pages; Revisions: Title revised to clarify that "atomic number" does not mean number of protons but rather number density of atoms; Clarification added that the ideal gas law for electrons is not needed for the derivation, but only added as an illustration