Effect of parallel velocity on the formation of a Kondo resonance in the atom-surface interaction

The interesting phenomena that may arise in the context of impurity states in a metal are well established. In certain parameter ranges there exist collective many-body states, which exhibit unusual low-energy behavior. In particular there appear resonances in the electronic spectral functions near the Fermi level associated with the screening of the spin of the impurity ~the Kondo effect! or with slow fluctuations between the local charge configurations ~mixed-valent behavior! induced by the interactions of the impurity state with the continuum of many-body excitations in the metal. Recently, direct experimental evidence for the formation of a Kondo resonance when a magnetic atom is chemisorbed on a metal surface has been presented. The analogous collective many-body effects will also occur in the problem of an atom moving outside a metal surface, provided that the motion of the atom is slow enough. In a recent paper, we demonstrated that in an atomsurface scattering experiment involving appropriately chosen atoms and substrates, there will be time for such a correlated state to form when the atom is near the surface. Some of the characteristics of this state will survive as the atom leaves the surface and can be detected. Specifically, we have shown that it is possible to probe the dramatic temperature dependence of the population of the atomic level when the atom is in the strongly correlated mixed-valent state near the surface. This phenomenon can simply be detected by measuring the ionization probability ~charge-transfer probability! of atoms scattered against a substrate as a function of substrate temperature. This prediction has also been verified using an alternative calculational method. Indeed, these findings indicate that measuring charge transfer in atom-surface scattering experiments may provide an ideal way to probe these states, because of the wide range of parameters that can be varied. The dramatic temperature dependence of the population of the atomic level in the mixed-valent regime arises from the formation of a Kondo resonance located just above the Fermi energy. This resonance is typically very narrow. Energy fluctuations larger than the width of this resonance are expected to weaken its contribution to the population of the atomic level and thus reduce the temperature dependence of the charge transfer between the atom and the substrate. Such energy fluctuations can come from recoil caused by electron tunneling, large amplitude vibrations of the substrate atoms, or the Doppler smearing, vW i•kW i , of the Fermi-Dirac distribution caused by parallel velocity vW i of the scattered atom. 9 Simple estimates of the two first mechanisms show that they can be neglected in the relevant hyperthermal scattering experiments. However, due to the construction of the instruments used in typical atom-surface scattering experiments, it is not always possible to keep the parallel velocity of the scattered atom low. The purpose of this paper is to investigate quantitatively how the effects of parallel velocity will influence the proposed temperature dependence of charge transfer. The present calculation shows that the temperature dependence is considerably less sensitive to the effect of parallel velocity than our previous crude estimates indicated. However, more importantly, the present calculation shows that, by measuring the parallel velocity dependence of the charge transfer while keeping the substrate temperature constant, it is also possible to probe the mixed-valent state formed when the atom is close to the surface.