Mean-electric-field approximation to multiple ionization in distant collisions

The description of ion-atom collisions in a mean-electric-field approximation is discussed. In this method the sum of the interactions between the projectile and the electrons of the target is expressed as the sum of the Coulomb field acting on the center of charge of the target electrons and a residual interaction. For distant (high-energy) collisions the residual interaction can be neglected. The calculation of the scattering amplitude corresponding to the mean electric field is performed within the framework of the first Born approximation. It is shown that for high-energy collisions the scattering amplitude is a product of single-electron scattering amplitudes and the cross sections of the multiple ionization follow the binomial distribution. A simple expression is derived for the cross section of n-vacancy production. The calculated ionization cross sections and mean numbers of outer-shell vacancies in the presence of an inner-shell vacancy are in satisfactory agreement with experimental values for high projectile energies.