Image-induced surface states on electrically dense metals

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Abstract
In estimating non-adiabatic corrections to the energy E of a particle bound to an impenetrable surface by the image potential (a surface polaron), the trial state-vectors used hitherto become inadequate for metals with high electron-concentration parameters 1/rs, because they cannot behave reasonably in or near the perfect-mirror limit where rs vanishes and the surface-plasmon frequency omega becomes infinite. In this limit the problem is proved to reduce exactly to the Schroedinger equation for the particle governed by the electrostatic image potential, giving (for electrons or positrons) the well-known result E0=-1/32 au. Since for omega to infinity the problem is solvable analytically, high omega points to perturbation theory, and a trial state-vector is constructed, closely related to the first-order perturbed state, yet simple enough for calculations in closed form. For particles that cannot penetrate the mirror, the resultant variational estimate tends to the correct perfect-mirror limit as rs to 0, and for rss.