Image-induced surface states on metals: the effects of spatial dispersion

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Abstract
The ground-state energy E, including all plasmon-excitation (non-adiabatic) effects, is estimated for an idealised surface polaron which consists of an electron or positron bound to an impenetrable half-space representing a metal by the standard quantised spatially dispersive hydrodynamic model. A unitary transformation that is in effect a non-relativistic gauge transformation leads to a new form of the Hamiltonian, for which E is shown to lie between explicitly calculated upper and lower bounds; these bounds are separated only by 4% rising to 22% as the inverse electron-concentration parameter rs rises through the metallic range from 2 to 6. A good approximation is shown to be embodied in the Schrodinger equation for the particle alone, subject to an ordinary static potential first given by Newns (1969), plus a correction, also effectively a static potential, which capture most of the effects that in other gauges would be classed as non-adiabatic. The success of this approach depends wholly on the presence of spatial dispersion. A brief discussion considers how far the methods developed here are likely to be useful in calculations on more realistic models.