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Journal of Physics B Atomic Molecular and Optical Physics

The locking phenomenon in scattering of P-state atoms: I. Quasiclassical theory of interference effects for waves scattered by two different potentials

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

Published Feb 14, 1996• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/29/3/008

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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.
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.
The effective-mass method for treating scattering by nonlocal potentials described in a previous publication. is applied to some problems in atomic collision theory. The applications are based on an effective equation for scattering in the elastic channel when coupling with other channels is included, giving rise to a nonlocal effective potential. We use the effective-mass theory to analyze the influence of coupling with closed channels on the elastic scattering in atom-atom collisions and point out that this may lead to a new type of rainbow effect. We show that strong interchannel coupling results in the appearance of poles and zeros in the effective mass and that the latter may lead to compound-state resonances and orbiting effects. It is observed that the occurences of Fesbach resonances in molecular encounters is always reflected in the presence of zeroes in the corresponding effective mass. We also employ the effective-mass method to deal briefly with the familiar problem of curve crossing and nonadiabatic transitions in atomic collisions.
The quasiclassical theory of the Landau-Zener resonance arising because of the atomic motion in the field of a strong standing light wave is developed. A resonance atom in a spatially inhomogeneous field as two effective potentials and two trajectories of motion. The Landau-Zener (LZ) transitions from one trajectory to the other take place in the regions of quasi-intersection of the terms (standing-wave nodes). This effect leads to the appearance of strong quantum fluctuations which break the potential character of the atomic motion and result in the interference of the translational motion states. Therefore a number of the features of the atomic dispersion in the standing-wave field arise (anomalous widths of the forbidden gaps and allowed bands in the under-barrier energetic region and oscillations of the density of states in the over-barrier energetic region). The manifestation of LZ resonance in non-linear spectroscopy and for bipotential scattering of atoms by light is considered.
The time delay, as defined via phase shifts, does not apply to atom-atom collisions because of the semiclassical nature of the system. In this limit the contribution of one partial wave to the cross section is negligible. Therefore, we analyze time delay for the scattering amplitude and show that some new phenomena may occur, which cannot be explained by the time delay for a single phase shift. The time delay, which is averaged over all scattering angles, shows structure corresponding to several delay mechanisms. We also show that the lifetime of a resonance state, formed in a collision, may be considerably shorter than expected from the theory of resonance scattering.
The scattering of a monoenergetic beam of atoms by a hard hemisphere on a hard flat surface is formulated quantum mechanically. Differential and integral cross sections are calculated as a function of incident beam energy and incident angle and compared with the familiar results of scattering from a free hard sphere. Two types of interference processes are identified. In addition to the previously discussed off-specular reflection symmetry interferences, Rayleigh oscillations are found in the integral cross sections. They result from the interference of specular scattering from the hemisphere and from the flat surface. Their phases are found to be independent of the angle of incidence when plotted versus the normal component of the incident wave vector.
Polarization phenomena in collisions between one-electron (alkali-like) atoms are calculated with density-matrix techniques. The kinetic energies for which this treatment is valid are limited from above by the use of the Born-Oppenheimer approximation, and from below by the assumed degeneracy of the hyperfine states. The basic mechanism for polarization changes is the electron-exchange effect, as suggested by Purcell and Field and by Wittke and Dicke. The special situation of unpolarized targets is treated in some detail. In this case, there are two numbers which characterize the scattering through any angle: the absolute values of certain direct and exchange scattering amplitudes, Fd{F}_{d}Fd​ and Fx{F}_{x}Fx​. All cross sections must be expressible in terms of ∣Fd∣|{F}_{d}|∣Fd​∣ and ∣Fx∣|{F}_{x}|∣Fx​∣, and this is explicitly carried out in two cases of special interest. One refers to the case in which only the electron-spin polarization is measured, and the other to measurements of the polarization of the hyperfine states of the scattered atom. Effects of the identity of the atoms are also studied in detail.