Title: Huygens-Fresnel Picture for Electron-Molecule Elastic Scattering,
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.