Many-body theory of charge transfer in hyperthermal atomic scattering

Abstract

We use the Newns-Anderson Hamiltonian to describe many-body electronic processes that occur when hyperthermal alkali atoms scatter off metallic surfaces. Following Brako and Newns, we expand the electronic many-body wave function in the number of particle-hole pairs (we keep terms up to and including a single particle-hole pair). We extend their earlier work by including level crossings, excited neutrals, and negative ions. The full set of equations of motion is integrated numerically, without further approximations, to obtain the many-body amplitudes as a function of time. The velocity and work-function dependence of final-state quantities such as the distribution of ion charges and excited atomic occupancies are compared with experiment. In particular, experiments that scatter alkali ions off clean Cu(001) surfaces in the energy range 5–1600 eV constrain the theory quantitatively. The neutralization probability of ${\mathrm{Na}}^{+}$ ions shows a minimum at intermediate velocity in agreement with the theory. This behavior contrasts with that of ${\mathrm{K}}^{+}$, which shows virtually no neutralization, and with ${\mathrm{Li}}^{+}$, which exhibits a monotonically increasing neutral fraction with decreasing velocity. Particle-hole excitations are left behind in the metal during a fraction of the collision events; this dissipated energy is predicted to be quite small (on the order of tenths of an electron volt). Indeed, classical trajectory simulations of the surface dynamics account well for the observed energy loss, and thus provide some justification for our truncation of the equations of motion at the single particle-hole pair level. ${\mathrm{Li}}^{+}$ scattering experiments off low work-function surfaces provide qualitative information on the importance of many-body effects. At sufficiently low work function, the negative ions predicted to occur are in fact observed. Excited neutral Li atoms (observed via the optical 2p→2s transition) also emerge from the collision. A peak in the calculated Li(2p)→Li(2s) photon intensity occurs at an intermediate work function in accordance with measurements.