General expansions of a scattering amplitude

Valentin N. Ostrovsky

Alex Grossmann

The results of the preceding paper are used to indicate procedures of calculation of the scattering amplitude, obtain several expansions, find bounds on the variation of the amplitude under a change in the potential, and study multiple scattering.

Moriyasu Murai, Yujiro Kakudo, Moriyasu Murai +1 more

The amplitude for diffraction scattering due to an absorbing corpuscle is calculated by using Kirchhoff's formula in optics and the spherical wave expansion. The relationship between the amplitude obtained by us and the usual one used in the general theory of scattering is investigated.

P.V. Landshoff

R. T. Ling

The concept of a generalized scattering amplitude is introduced and applied to quantum potential scatterings. After an outgoing spherical wave is factored out from a wave function, the remaining wave envelope is defined as the generalized scattering amplitude. The transformed Schr\"odinger equation, in terms of the generalized scattering amplitude, can be solved numerically by using a finite-difference method over the entire scattering domain. Example problems of scatterings by a spherical potential well and the (${\mathit{e}}^{\mathrm{\ensuremath{-}}}$,H) static field interaction potential are solved to validate the theoretical formulation and numerical method. The far-field solutions for the ordinary scattering amplitude and differential cross section agree very well with those obtained from the partial-wave analysis. The radial profiles of the generalized scattering amplitude and particle density function over the entire scattering region are also presented, and their properties are discussed. These results demonstrate that the method can be used to yield a complete and accurate solution to scattering problems involving arbitrary interaction potentials.