Abstract
Using Fefferman's analysis of the quantum electron-proton gas, we give a rigorous proof of ionization equilibrium in this system. Ionization equilibrium phases are obtained as low-density and low-temperature limits, letting the chemical potentialμ(T) approach the ground-state energy of the hydrogen atom as the temperatureT tends to zero. The rate of ionization is determined by the slope ofμ(T) atT=0 and is correctly given by the Saha formula. We also discuss a simpler model where a single quantum particle interacts with a classical gas of hard spheres.
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Macris, N., Martin, P.A. Ionization equilibrium in the electron-proton gas. J Stat Phys 60, 619–637 (1990). https://doi.org/10.1007/BF01025985
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DOI: https://doi.org/10.1007/BF01025985