Gaussian estimation of electron scattering cross sections on the basis of a Feynman path integral

Abstract

A version of Gaussian estimation of a Feynman path integral is considered and its validity for a scattering problem is investigated. Test calculations of the differential and total cross sections are performed for the scattering of a plane wave by a three-dimensional spherically symmetric Gaussian potential and for the electron impact excitation of the 1s → 2s transition in the hydrogen atom. The data on the scattering by a potential are compared with the analogous results obtained using the first Born approximation and the method of phase functions (which gives almost exact results). The excitation cross sections for the transition in the hydrogen atom are compared with those obtained by the convergent close-coupling method. The validity of this approach is demonstrated. The accuracy of the method proposed is acceptable for many cases. For total cross sections, the result obtained in terms of the density matrix formalism turned out to be more exact than that derived from differential cross sections. Among all the above approaches using path integration to solve problems of scattering of electrons by atoms, the method proposed here.