A diagrammatic approach to ion neutralization at surfaces: On the validity of first-order perturbation calculations

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Abstract
A theoretical investigation of ion neutralization from positive-ion scattering from surfaces is presented. Based on the time-dependent Fano–Anderson potential, a diagrammatic expansion of the reduced density matrix elements of the neutralized atom is given. Strictly speaking, the formalism holds only for systems in which the conduction band is completely empty, i.e., insulators, but conditions are given under which the formalism can be used for ion neutralization at metals. Calculations are performed for the simple case in which the atomic level is not degenerate. The validity of the first-order approximation is analyzed and its contribution to the neutralization probability is found to be dominant provided: (1) the discrete energy level of the atomic projectile is not embedded in the continuum of the valence band of the solid; and (2) the duration of the interaction is sufficiently short, i.e., the collision energy is high enough.