  In the present paper, we propose a variational average-atom model of
electron-ion plasma performing a quantum treatment of bound electrons and
accounting for correlations (VAAQBEC). This model addresses the correlation
functions in a weakly-coupled plasma, while also accounting self-consistently
for the ion average shell structure. This is done at the price of treating the
free electrons classically, whereas bound electrons are treated
quantum-mechanically. When ions are approximated by point-like particles, the
present approach yields the usual Debye-H\"{u}ckel corrections to the orbital
energies and chemical potential. If one disregards the interactions of
continuum electrons, the present approach yields ion-ion correlation
corrections through a self-consistent one-component-classical-plasma
contribution. Comparisons are presented with the broadly-used
continuum-lowering approach of Stewart and Pyatt and with the dense-plasma
average-atom models INFERNO and VAAQP, on warm silicon and hot iron cases.

Plasma Physics