Inhomogeneous electron liquids generated by Coulomb confinement of electrons with and without interparticle repulsions

Abstract

The inhomogeneous electron liquid created through Coulomb confinement by a single-centre potential energy −Ze 2/r remains central to the fundamental 1/Z expansion: a pillar of analytic atomic theory. Therefore, some recent progress in this area of non-relativistic quantum mechanics is first discussed, the main focus being the Feynman propagator. The closely related Slater sum is also treated, differential equations being cited in both three and two dimensions. The effect of interparticle interactions on the density of the electron liquids will next be considered in two areas: (i) for models of He-like atomic ions with nuclear charge Ze where analytic ground state electron densities can be obtained, as well as the exact differential equations they satisfy, and (ii) fine-tuning of Hartree–Fock densities for four spherical atoms, Be, Ne, Mg and Ar. In (ii), a semi-empirical framework is now available in which the experimental ionisation potential replaces that of Koopmans. Densities having almost QMC quality are thereby available. Finally, the inhomogeneous electron liquids in short linear chains of H nuclei stabilised by one electron plus an intense magnetic field along the chain axis will be treated, fields considered being as found at the surfaces of some neutron stars.