On the linear dynamic response of average atom in plasma

The theory of linear response of an average atom (AA) in plasma is considered. It is assumed that the model of the AA is of the density functional theory (DFT) type, i.e., can be characterized by an equilibrium electron density in terms of a complete set of bound and free one-electron wave functions of a screened self-consistent-field (SCF) potential. The starting point in the linear response theory is the cluster expansion of the energy extinction coefficient. This coefficient expresses the rate of extinction of the energy due to an external potential irradiating a plasma composed if ions and electrons. As shown in previous publications the first-order term in the cluster expansion correctly gives the linear response of the AA. The first-order formula for the extinction coefficient is directly related to the AA photo-absorption cross-section. The cluster expansion technique shows how the homogeneous plasma contribution shall be correctly subtracted from the response of the AA and its surrounding plasma. The linear response is considered in the dipole approximation and in the framework of the random phase approximation which can be viewed as a version of a time-dependent DFT with local density approximation to the exchange-correlation potential. In the paper, we discuss a possible practical scheme for calculation of the dipole linear response and obtain some theoretical results that allow one to reduce the theoretical and numerical difficulties of the approach. We show formally how in the dipole approximation the homogeneous plasma contribution to the induced potential results in the appearance of the cold-plasma dielectric function. We also derive a new sum rule which allows one to calculate the induced dipole using the localized density and potential gradients of the AA in equilibrium. We further propose a change of variables that allows us to eliminate the leading dipole divergence in the first-order Schrödinger equations. We next discuss some aspects of a simplified case in which the induced potential is neglected. Finally, we present and comment on the radial equations for the SCF frequency-dependent induced density and potential.