Angular distributions of secondary electrons in fast particle-atom scattering

We present the angular distribution of electrons knocked out from an atom in a fast charge particle collision at small momentum transfer. Not only dipole, but also quadrupole transitions determine this distribution. The contribution of these transitions can be considerably enhanced as compared to the case of photoionization. In photoionization angular distribution, the nondipole parameters are suppressed, as compared to the dipole ones, by the factor omega R/c << 1, where omega is the photon energy, R is the ionized shell radius, and c is the speed of light. In fast electron-atom collisions this suppression can be considerably reduced, since the corresponding expansion parameter omega R/v << 1 is much bigger than in photoionization, because the speed of the incoming electron vis much smaller than c. In formation of the angular distribution, it is decisively important that the ionizing field in the collision process is longitudinal, while in photoionization-it is transversal. We demonstrate that contrary to the case of cross sections, the angular anisotropy parameters for secondary electrons in fast charge particle-atom collisions and in photoionization are essentially different. We illustrate the general formulas by concrete results for outer s, p, and some nd subshells of multielectron noble gas atoms Ar, Kr, and Xe, at several transferred momentum values: q = 0.0, 0.1, 1.1, and 2.1. Even for very small transferred momentum q, i.e., in the so-called optical limit, the deviations from the photoionization case are prominent.