Bulk plasmon assisted electron capture process for ions travelling outside a metal surface

We obtain the interaction Hamiltonian for a charge exchange mechanism at metal surfaces in which a metal electron is captured by an ion travelling at constant velocity outside the solid while a bulk plasmon is emitted. The only work reported so far on this novel process, for the simplest case of an ion at rest, shows a transition probability in the near surface region as important as the one for the surface plasmon assisted charge exchange process. The Bohm–Pines and Fock–Tani theories provide the appropriate mathematical framework to obtain a closed analytical expression for the three-dimensional interaction potential responsible for this collective charge transfer process. Further, we show that the conservation of momentum parallel to the surface is implicitly contained in the matrix elements of such Bohm–Pines Fock–Tani Hamiltonian.