Photoabsorption in hot, dense plasmas—the average atom, the spherical cell model and the random phase approximation II

Abstract

This work is a continuation of our earlier work on the finite temperature random phase approximation (FTRPA) for inhomogeneous, finite electron systems. In the earlier work we obtained the fundamental FTRPA eigenvalue equation for the spectral amplitudes of the linear response function via the use of the Matsubara Green's function technique arrived at earlier by des Cloizeaux via the density matrix technique. In this work we show that the normalization requirement for the FTRPA spectral amplitudes obtainable via the Matsubara Green's function technique is the same as the one obtained by des Cloizeaux. Thus, the two techniques in every respect give identical equations and formulas for the FTRPA. We also derive the fundamental equations for the actual linear responses of finite temperature inhomogeneous finite electron systems to specific external perturbations in the FTRPA. This side steps the problem of normalization by the use of an inhomogeneous integro–differential equation.