Coulomb deflection in ion-atom collisions

Abstract

The Coulomb-deflection factor, defined as the ratio of the Coulomb to plane-wave Born cross sections, is derived for slow but classically moving ions, and found to be in agreement with the data for $K$-shell ionization. When the half distance of closest approach in a head-on collision, $d$, is comparable to the important impact parameters ($\ensuremath{\sim}\frac{1}{{q}_{0}}$, where ${q}_{0}$ is the minimum momentum transfer), this factor simplifies to $\mathrm{exp}(\ensuremath{-}\ensuremath{\pi}d{q}_{0})$ as it has been employed in the inner-shell-ionization theory. When the impact parameters are small on the scale of the projectile de Broglie wavelength, as they are in nuclear phenomena, the Coulomb-deflection factor tends to $\mathrm{exp}(\ensuremath{-}2\ensuremath{\pi}d{q}_{0})$. An extension of our results to screened Coulomb repulsion gives good agreement with the semiclassical calculations and the data for $K$-shell excitation in ${\mathrm{Ne}}^{+}$-Ne collisions.