Electron and positron scattering from halogenated methanes: a comparison of elastic cross sections

Abstract

This paper discusses the use of quantum scattering methods for the evaluation of the elastic (rotationally summed) integral and differential cross sections produced in collisions at low energies (E coll 20 eV) of electrons and positrons with polyatomic gaseous targets. The calculations use close-coupled equations and a parameter-free model of electron and positron interactions with the molecules in a single-collision situation. Comparison with existing experiments on the collision processes with the two projectiles helps us to know more detail about the features of the forces in play during the scattering events. Computed results are also found to be in good accord with experiments.

Vibrational excitation of CF4by electron impact: a computational analysis

“…The above SCE representation refers to the µth element of the pth irreducible representation (IR) of the point group of the molecule at the nuclear geometry R. The angular functions X pµ lh (r) are symmetry-adapted angular functions given by a proper combination of spherical harmonics Y lm (r), where the b coefficients have been described in [10,13,14],…”

“…The numerical solutions of the coupled equation (4) will produce the relevant K-matrix elements, which will in turn yield the necessary expression for the elastic (rotationally summed) differential cross sections, obtained for scattering off randomly oriented molecules by averaging the scattering amplitude f(k ·r|α, β, γ) over all the angular values [10]- [14].…”

“…This is chiefly due to the lack of correlation effects in the description of the e − -molecule interaction. We have therefore used a further correction that we had used for electron scattering from large polyatomic nonlinear targets with a good degree of success [11]- [14]. In particular, we have already shown elsewhere [14,15] how the combined effects of simplifying the exchange interaction between the bound electrons and the continuum projectile via a modified semiclassical (local) approach and of treating the correlation-polarization forces using a global density functional model can indeed help us to deal with vibrationally inelastic collisions, at least for the present tetrahedral molecule, with a markedly decreased computational effort and with an acceptable level of accuracy [15,16].…”

“…The long-range part of V ecp is obtained by first constructing a model polarization potential V pol , which asymptotically agrees with the potential obtained from the static dipole polarizability of the target in its ground electronic state. This corresponds to including the dipole term in the second-order perturbation expansion of the polarization potential [11]- [14], [18].…”

“…The coupled equation (3) can now be recast in an integral form [14] using the potential coupling elements defined before, V pµ in (r|R), and using standard Green's function techniques to obtain for the radial functions of the continuum electron…”