• DOI:10.1140/epjd/e2017-80421-2
• Corpus ID: 119357765

Huygens–Fresnel picture for electron-molecule elastic scattering

@article{Baltenkov2017HuygensFresnelPF,
  title={Huygens–Fresnel picture for electron-molecule elastic scattering},
  author={Arkadiy S. Baltenkov and Alfred Z. Msezane},
  journal={The European Physical Journal D},
  year={2017},
  volume={71},
  pages={1-13}
}

• A. Baltenkov, A. Msezane
• Published 30 September 2017
• Physics
• The European Physical Journal D

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