A convergent expression for the partition function of a partially ionized hydrogen plasma

Abstract

The partition function of a hydrogen plasma is derived, partly classically and partly quantum-mechanically, avoiding in this way at the same time the close distance and the high orbit divergences. Our result is exact in the small density and infinite temperature limit, but can be considered as a good approximation also for conditions, where the ionization is incomplete. From this a Saha equation is derived, which contains an effective lowering of the ionization potential. An expression is obtained for the pressure, which is not simply the sum of the known pressures of the neutral and ionized parts, but has a correction from the transitions between these parts.