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

TL;DR

This paper reveals a fundamental qualitative difference in angular anisotropy parameters between atomic ionization by photons and fast electrons, attributed to the nature of the photon type, with derived formulas and specific examples for noble gases.

Contribution

It introduces the first demonstration of qualitative differences in angular anisotropy parameters between photoionization and fast electron scattering, highlighting the role of photon type and deriving relevant formulas.

Findings

Angular anisotropy parameters differ qualitatively between photon and electron ionization.

Derived formulas for dipole and non-dipole anisotropy parameters in electron scattering.

Prominent deviations from photoionization even at small momentum transfer.

Abstract

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 electronatom scattering. The ratio of quadrupole-to-dipole matrix elements is determined by the parameter \omega R/v << 1 where \omega is the transferred in collision energy, R is the ionized shell radius and v is the speed of projectile. This factor can be much bigger than in the case of photoionization, where one has the speed of light c that is much bigger than v . We illustrate general formulas by concrete results for outer s-subshells of noble gas atoms Ar and Xe. Even for very small transferred momentum q, in the so-called optical limit, the deviation from photoionization case is prominent and instructive.