A Note on the Ground State Energy of an Assembly of Interacting Electrons

The ground state energy of an assembly of charged particles of density rho imbedded in a continuum of charge of the other sign in an electrically neutral system is considered. Asymptotic formulae for the ground state energy of such systems are known in the high- and low-density regimes. An interpolation formula covering the entire density range is derived using the method of two-point Padé approximants. A phase transition from an electron lettice to an electron gas seems to occur at r(3) congruent with 14, r(3) being the radius of a sphere which, on the average, contains a single charge, in units of the Bohr radius of the electron in a hydrogen atom.