Fock–Tani representation for surface-plasmon induced atomic transitions of an ion near a metallic surface

In this work we report a second quantized representation for the collective interaction of a single charged slow ion (or atom) with a nearby metallic surface. The unitary Fock–Tani transformation decomposes the electron–surface plasmon interaction potential into a multicomponent potential operator which contains explicitly all the possible atomic transitions, for both ion–surface and atom–surface systems, induced by the coupling between metal electrons and surface-plasmons. The coefficient of each component corresponds to the matrix element for the given transition. In particular we obtain the ion velocity dependent matrix elements for the process of surface-plasmon ion neutralization at metallic surfaces a result which generalizes not only the one obtained within the fixed ion approximation but also the one obtained with the Galilean transformation approach.