Coupled channel formulation of the perturbed finite-temperature atomic random phase approximation: single channel approximation

We present the spin and angular momentum analysis of the inhomogeneous coupled partial integro-differential equation formulation of the finite-temperature random phase approximation of an atom in a plasma. We demonstrate the cancellation of the direct and exchange self-interaction terms in the three-dimensional form of the equations. The direct self-interaction terms are also shown to cancel for each partial wave in the radial equations obtained from the spin and angular momentum analysis. We discuss how this inhomogeneous formulation avoids normalization difficulties encountered in our previous homogeneous eigenvalue formulation. Finally, the photoabsorption of the atom is given in terms of its polarizability