Born-Hartree-Bethe approximation in the theory of inelastic electron-molecule scattering

Abstract

We propose a new approximation in the theory of inelastic electron–atom and electron–molecule scattering. Taking into account the completeness property of atomic and molecular wavefunctions, considered in the Hartree approximation, and using Bethe’s parametrization for electronic excitations during inelastic collisions via the mean excitation energy, we show that the calculation of the inelastic total integral cross-sections (TICS), in the framework of the first Born approximation, involves only the ground-state wavefunction. The final analytical formula obtained for the TICS, i.e. for the sum of elastic and inelastic ones, contains no adjusting parameters. Calculated TICS for electron scattering by light atoms and molecules (He, Ne, and H₂) are in good agreement within the experimental data; results show asymptotic coincidence for heavier ones (Ar, Kr, Xe and N₂)