Differential scattering of electrons from atoms and molecules: I. General and exact binary-encounter approximation cross sections for three-dimensional transfer of energy and linear momentum from the incident electron to the electrons of the target

Abstract

Two general and exact (within the formalism of the binary-encounter approximation) doubly differential cross sections for three-dimensional scattering of an incident electron from electrons of a target atom (molecule) are derived from first principles. The first cross section is for an electron-target collision in which the incident electron loses a specific amount of energy while being scattered into a specific direction. The second cross section describes a collision in which one of the target electrons gains some specific amount of energy and is ejected from the target into some specific direction. The cross sections can be averaged over any distribution of energy of the target electrons participating in the scattering of the incident electron from the target particle. This allows one to apply the cross sections to study a broad range of inelastic collisions of electrons with heavy particles, including excitation and ionization of atoms and molecules, and molecular dissociation caused by electronic excitation to repulsive molecular states. The cross sections derived can also be used to study three-dimensional binary interactions of free electrons in fusion and astrophysical plasmas.