Exchange and polarization effects in the elementary excitation spectrum of a hydrogen atom immersed in a hot plasma

Abstract

The one-particle hydrogenic Green's function has been calculated for a partially ionized plasma consisting of hydrogen atoms, electrons, and protons at high temperatures. The theoretical method extends a previous publication and involves an evaluation of the mass operator in the Dyson equation to include proper self-energy parts to "all orders" in the screened interaction. This mass operator characterizes the effective micropotential felt by the atom in the plasma and determines all of the one-particle properties and some two-particle properties associated with the atomic subsystem. The first-order mass operator is nonzero only for exchange scattering, which leads to a frequency-independent exchange shift. This temperature- and density-dependent theory of the exchange shift replaces the usual semiphenomenological schemes based on the Slater-Kohn-Sham type of theory. The exchange-shifted Green's functions are used in evaluating the higher-order contributions. Computer calculations and the resolution of the poles of the Green's function lead to level shifts, widths, and spectral functions. These are calculated within both the second-order and the all-order theory. The second-order theory, which may be valid at sufficiently high densities and in turbulent plasmas, overemphasises the atom-plasmon coupling and shows new structures. The inclusion of contributions beyond second order removes these structures and produces a more "conventional" spectral-intensity function. The effects of center-of-mass motion on the level shifts and level profiles are investigated and the onset of plasma instabilities touched upon. These calculations make contact with the work on "plasma-polarization shifts" and provide an approach to $q$,$\omega$-dependent plasma microfields.