Schrodinger-Poisson model for very-high-pressure cold helium - art. no. 042505

An alternative numerical solution of the Hartree-Fock integro-differential equations is reported that consists of reformulating the self-consistent an satz as a nonlinear set of coupled Schrodinger and Poisson equations. In th e simple case of helium, this yields an amazingly simple dynamical system w hose statistical properties are constrained by the virial theorem. This app roach leads to an equation of state for helium at zero temperature and very high densities, covering the whole range of astrophysical interest, up to the pressure ionization phase transition that is predicted around 44 Mbar b y the present model.