Elastic scattering by spherically-symmetric r-2 and r-3 potentials

N. N. Khuri

Eyvind H. Wichmann

The elastic scattering of spinless particles from a spherically symmetric stationary target is considered. The main idea is to describe the incident beam of particles as a certain statistical ensemble of one-particle wave packets, and to define the differential cross section in terms of the average scattering of the particles in this ensemble. The physical significance of this mode of description is discussed, and arguments are presented as to why it should be regarded as a realistic description of typical scattering experiments. The discussion is general, and not restricted to potential scattering. It is based on the notion of the S matrix, and the most basic ideas of the S matrix are discussed. A simple derivation of the partial wave expansion is given within the framework of S matrix theory. The aim of this paper is mainly pedagogical, and the final results obtained are old and well established.

Peter Fröbrich, R. Lipperheide

Abstract Potential scattering is the scattering of two collision partners whose mutual interaction is described by a static potential. This potential depends in general on the structure of the collision partners, in particular, on their size and shape (usually taken as spherical), but once the potential is specified and the centre-of-mass motion is separated out, the scattering problem in the remaining relative coordinate reduces to the description of the motion of a point-particle with a mass equal to the reduced mass of the two collision partners in the static field of the interaction potential. Only elastic scattering can be described in this way.

P. R. Berman

E. I. Dashevskaya, Françoise Masnou-Seeuws, E. E. Nikitin

A quasiclassical theory is presented for scattering of atoms in a spinless P state by a spherical target. The scattering amplitudes can be expressed analytically as a function of a few parameters which are not only the phaseshifts for elastic scattering along the and molecular potentials, but also the locking angles and the slipping probabilities. Interference effects, for one scattering angle, occur between contributions of classical trajectories corresponding to different potentials. The locking angle appears explicitly in the amplitude of the high-frequency oscillations. It turns out that this type of interference survives the statistical averaging over initial substates, resulting in an oscillating pattern of the differential cross section for scattering of unpolarized atoms. It is shown that the existence of the locking phenomenon is a necessary condition to the observation of such an effect.