Ground-state energy shift of He close to a surface and its relation with the scattering potential: A confinement model

Abstract

The relation between scattering potential and ground-state energy shift of a helium atom (ion) close to a surface is investigated through use of a model of spatial limitation whereby the surface is represented by an infinitely rigid planar boundary. The model of an atom confined in a semi-infinite space with a plane boundary allows the variational evaluation of the ground-state energies and wave functions for He and ${\mathrm{He}}^{+}$ at different positions from the surface. The respective Born-Oppenheimer energy curves serve to model the ground-state energy shift for the elastic scattering channel in atom (ion) surface interactions. Independent calculations for the He-graphite and He-Al (111), (110), and (100) continuous planar potentials are carried out using high-quality ab initio calculations reported in the literature for the lowest He-C and He-Al binary interaction potentials. It is shown in this case that the He ground-state energy shift obtained within this model corresponds to an upper limit to the usual continuous planar potential. A discussion on the physical origin of this agreement is presented in terms of the static nature for the surface considered in both the hard-wall model and the atomic binary interactions used to construct the planar potentials, i.e., no account of the dynamic surface response is allowed as the projectile approaches. This is done by taking a reference pilot calculations based on electron nuclear dynamics for $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ He $({\mathrm{He}}^{+})$-benzene $({\mathrm{C}}_{6}{\mathrm{H}}_{6})$ interactions by considering the benzene molecule as a rough approximation to a local graphitic surface sector. It is found that the static planar potential provides a reasonable average representation of the interaction for neutral He, and supporting evidence for the use of the static O'Connor-Biersack potential is given. Finally, the effective scattering potential for $\mathrm{He}∕{\mathrm{He}}^{+}\text{\ensuremath{-}}\mathrm{Al}$ (111) is constructed through the use of the static planar potential for He-Al (111) considering the energy shift due to the classical image interaction for ${\mathrm{He}}^{+}$ approaching a perfectly Al (111) conducting plane before charge neutralization takes place. It is concluded that this scattering potential is directly related with the ground-state energy shift of the emerging already neutralized He atoms in $\mathrm{He}∕{\mathrm{He}}^{+}\text{\ensuremath{-}}\mathrm{Al}(111)$ grazing scattering experiments.