The Mass Action Law in Two‐Component Fermi Systems Revisited Excitons and Electron‐Hole Pairs

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Abstract
Taking up the quantum‐statistical derivation of a mass action law for two‐component Fermi systems with Coulomb interaction given previously an improved density formula for either species is presented. It expresses the densities as a sum of a free quasi‐particle part and a correlated contribution resulting from bound and scattering states. Avoiding the resolvent‐technique for the solution of the T‐matrix equation the correlated density is directly expressed in terms of on‐shell quantities, eventually the scattering phase shifts. The ionisation equilibrium of excitons, electrons, and holes is quantitatively analyzed by model calculations for a cut‐off Coulomb potential. The possibility of Bose‐Einstein condensation of scattering states is inspected.