Effect of dense plasmas on exchange-energy shifts in highly charged ions: An alternative approach for arbitrary perturbation potentials

Abstract

An alternative method of calculation of dense plasma effects on exchange-energy shifts $\ensuremath{\Delta}{E}_{x}$ of highly charged ions is proposed which results in closed expressions for any plasma or perturbation potential. The method is based on a perturbation theory expansion for the inner atomic potential produced by charged plasma particles employing the Coulomb Green function method. This approach allows us to obtain analytic expressions and scaling laws with respect to the electron temperature T, density ${n}_{e}$, and nuclear charge Z. To demonstrate the power of the present method, two specific models were considered in detail: the ion sphere model (ISM) and the Debye screening model (DSM). We demonstrate that analytical expressions can be obtained even for the finite temperature ISM. Calculations have been carried out for the singlet $1s2p{}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ and triplet $1s2p{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ configurations of He-like ions with charge Z that can be observed in dense plasmas via the He-like resonance and intercombination lines. Finally we discuss recently available purely numerical calculations and experimental data.