Impact-parameter dependence for collisions of atoms with projectiles carrying electrons.

A method is proposed for studying collisions between two atoms or ions with one or more electrons each. An effective charge density as a function of a physically unobservable impact parameter [ital [rvec b]][prime] is introduced to describe the spatial nonlocalization of the electron cloud of the projectile atom. It is shown that the probability amplitude at a given (real) impact parameter may be reduced to a convolution over [ital [rvec b]][prime] of the effective charge density with target excitation amplitude per unit charge. This method, which we call the virtual-impact-parameter method, enables one to identify in a physical way in impact-parameter space the contribution of the electron-electron interaction as well as that of the electron-nucleus interaction. A node structure in the target excitation probability amplitude is found due to the electron-electron interaction. Generalization of the method to the description of many-electron transitions is discussed within the independent-electron approximation.