Bound States in Coulomb Systems - Old Problems and New Solutions



We analyze the quantum statistical treatment of bound states in Hydrogen considered as a system of electrons and protons. Within this physical picture we calculate analytically isotherms of pressure for Hydrogen in a broad density region and compare to some results from the chemical picture. Our study is restricted to the range of intermediate temperatures 104K < T < 105K and not too high densities n < 1024 protons per cm3, the formation of molecules is neglected. First we resume in detail the two transitions along isotherms:

(i) formation of bound states occurring by increasing the density from low to moderate values,

(ii) the destruction of bound states in the high density region, modelled here by Pauli-Fock effects. Avoiding chemical models we will show, why bound states according to a discrete part of the spectra occur only in a valley in the T-p plane. First we study virial expansions in the canonical ensemble and then in the grand canonical ensemble. We show that in fugacity representations the population of bound states saturates at higher density and that a combination of both representations provides quickly converging equations of state. In the case of degenerate systems we calculated first the density-dependent energy levels, and find the pressure in Hartree-Fock-Wigner approximation showing the prominent role of Pauli blocking and Fock effects in the selfenergy (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)