Huygens–Fresnel picture for electron-molecule elastic scattering

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Part of the following topical collections:
  1. Topical Issue: Low Energy Positron and Electron Interactions

Abstract

The elastic scattering cross sections for a slow electron by C2 and H2 molecules have been calculated within the framework of the non-overlapping atomic potential model. For the amplitudes of the multiple electron scattering by a target the wave function of the molecular continuum is represented as a combination of a plane wave and two spherical waves generated by the centers of atomic spheres. This wave function obeys the Huygens–Fresnel principle according to which the electron wave scattering by a system of two centers is accompanied by generation of two spherical waves; their interaction creates a diffraction pattern far from the target. Each of the Huygens waves, in turn, is a superposition of the partial spherical waves with different orbital angular momenta l and their projections m. The amplitudes of these partial waves are defined by the corresponding phases of electron elastic scattering by an isolated atomic potential. In numerical calculations the s- and p-phase shifts are taken into account. So the number of interfering electron waves is equal to eight: two of which are the s-type waves and the remaining six waves are of the p-type with different m values. The calculation of the scattering amplitudes in closed form (rather than in the form of S-matrix expansion) is reduced to solving a system of eight inhomogeneous algebraic equations. The differential and total cross sections of electron scattering by fixed-in-space molecules and randomly oriented ones have been calculated as well. We conclude by discussing the special features of the S-matrix method for the case of arbitrary non-spherical potentials.

Graphical abstract

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Arifov Institute of Ion-Plasma and Laser TechnologiesTashkentUzbekistan
  2. 2.Center for Theoretical Studies of Physical Systems, Clark Atlanta UniversityAtlantaUSA

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