reference system approach

In the frame of non-relativistic approximation, a compact approximate solution of the Schrödinger equation for the ion of $H^{-}$ has been obtained in the form of product for Legendre polynomials and variational functions of the Schull--Löwdin type. The accuracy of calculation of ion energy is of the same order that the results obtained using the multiparametric functions of Hylleraas and Pekeris.

The two- and three-particle correlation functions of degenerate relativistic model of homogeneous electron gas with Coulomb interactions at $T=0$ K in the momentum-frequency presentation in the local field approximation are investigated. These functions are sufficient for a correct calculation of the equation of state for the electron-nuclear model with the densities that correspond to the degenerate dwarfs.