Qualitative difference between the angular anisotropy parameters in fast electron scattering and photoionization

It is demonstrated for the first time that in spite of well known big similarities between atomic ionization by photons and fast electrons, a qualitative difference exists in angular anisotropy parameters of electrons knocked out in these processes. The difference is disclosed here and attributed to distinction between normal (transverse) and virtual (longitudinal) photons. Formulas are derived for dipole and non-dipole angular anisotropy parameters in fast electron-atom scattering. The ratio of quadrupole-to-dipole matrix elements is determined by the parameter ω R/v < 1, where ω is the transferred in collision energy, R is the ionized shell radius, and v is the speed of projectile. This factor can be much larger than that in the case of photoionization, where one has the speed of light c that is much higher than v . We illustrate general formulas by concrete results for outer s subshells of noble gas atoms Ar and Xe. Even for very low momentum transfer q , in the so-called optical limit, the deviation from photoionization case is prominent and instructive.