Magnus approximation forK-shell ionization by heavy-ion impact

The Magnus approximation (or sudden approximation) is applied to derive the transition amplitude and the cross section for $K$-shell ionization of atoms by heavy-ion impact. The target electron is described by a hydrogenic wave function and the projectile as a point charge moving along a straight-line trajectory. The transition amplitude for each partial wave of the ejected electron is expressed as an infinite (but rapidly converging) sum over hypergeometric functions. To obtain the total cross section, only integrals over impact parameter and the final electron momentum have to be evaluated numerically. The approach, because it is nonperturbative, should be particularly useful for treating collisions of light atoms with much heavier projectile ions. It also allows the study of the impact-parameter dependence of the ionization process. The connection with the Glauber approximation is pointed out.