Models of atoms in plasmas based on common formalism for bound and free electrons

Atom-in-plasma models: Thomas-Fermi (TF) and INFERNO, AJCI and VAAQP, that use the same formalism for all electrons are briefly described and analyzed from the point of view of their thermodynamic consistence. While the TF and VAAQP models may be derived from variational principle and respect the virial theorem, it appears that two earlier quantum extensions of the quasi-classical TF model, INFERNO and AJCI, are not fully variational. The problems of the two latter approaches are analyzed from the point of view of the VAAQP model. However all quantum models seem to give unrealistic description of atoms in plasma at low temperature and high plasma densities. These difficulties are connected with the Wigner-Seitz cavity approach to non-central ions that is present in all considered models. Comparison of some equation-of-state data from TF, INFERNO and VAAQP models are shown on a chosen example. We report also on the status of our research on the frequency-dependent linear-response theory of atoms in plasma. A new Ehrenfest-type sum rule, originally proposed in the quantum VAAQP model, was proven in the case of the response of the TF atom with the Bloch hydrodynamics (TFB) and checked by numerical example. The TFB case allows one to have a direct insight into the rather involved mathematics of the self-consistent linear response calculations in situations when both the central atom and its plasma vicinity are perturbed by an electric field.