Coulomb excitation of an atom by a screened ion

Collisions of atoms with screened ions differ in several respects from collisions with bare ions. According to ordinary perturbation theory, the screening of an incident ion (with N electrons, screening parameter lambda, and nuclear charge Z) amounts essentially to a dependence of the ion charge on the momentum transferred to an electron in the target material: Z/sub q/ = Z[1-ν/(1+q2lambda2)], where ν = N/Z. This has the following consequences: 1) the dependence of the ionization and excitation probabilities on the impact parameter and relative collision velocity is altered; 2) the spectral distribution of the ejected electrons is changed; 3) we must replace kappa/sub Bethe/ in the Bethe equation for the effective deceleration for a screened ion by kapparoughly-equal(1-ν+ν2/2)kappa/sub Bethe/. In this paper the time evolution operator is calculated analytically to lowest order in perturbation theory (assuming the perturbation turns on instantaneously), which makes it possible to study the excitation of targets by fast multiply charged ions and find bounds on the magnitude of the interaction for which ordinary perturbation theory is valid. The transition probabilities and cross sections are analyzed in detail for ionization and excitation of a light hydrogen-like atom. The ratios sigma(ν)/sigma(0) of the cross sections for different ν and for ν = 0 are monotonic at high energies and are insensitive to the collision velocity; they depend primarily on ν and the relative diameter of the incident ion