The helium atom in metallic electron gases: a comparative study based on screened Schrödinger Hamiltonians

Abstract

In the presence of an environment of mobile charges, the bound-state Schrödinger Hamiltonian for an embedded He atom differs from its vacuum form. The central problem of incorporating screening in the nucleus–bound-electron and bound-electron–bound-electron terms of this Hamiltonian is investigated here for the He ground state in a comparative manner by using two models, and the same product form of 1s-type parametric hydrogenic functions to perform exploratory variational calculations. Both models employ induced charge densities in the corresponding Poisson equations with a fixed point-like nucleus, but the underlying charge-density response of the host system is generated by differently chosen perturbations. These are the point-charge nucleus and the nucleus–bound-electron charge distribution as external perturbations. The repulsive bound-electron–bound-electron interaction in the Hamiltonian is modelled by a parametric Yukawa-type potential. Using the consistent variational results for the binding energies and wavefunctions, the charge-state-dependent stopping power of a metallic target for slowly moving He is briefly discussed.