Variational calculations in a halfspace for the interaction of a ground and excited state helium atom with its mirror image

Correlated trial wave-functions (depending explicitly upon the inter-electronic separation in the helium atom) subjected to boundary conditions excluding the helium electrons from the solid surface are used in half space, to evaluate in a variational approach the holding potential between an helium atom in its ground and metastable³S state with a perfectly imaging metallic conductor limited by a plane surface. Inter-electronic correlation effects are pointed out, and are seen to be non negligible. The holding potential for the helium³S displays a well of nearly an order of magnitude deeper than for the ground state. These results could be useful to determine the distance of closest approach of thermal atoms, and an approximate wave function for an helium atom interacting with a surface.