Optical potentials for elastic heavy ion scattering

The zero-field level crossing effect in selective reflection from an atomic vapour is calculated for normally incident radiation using a theory which, unlike the conventional dispersion theory, includes the effect of transient polarization behaviour due to diffuse wall collisions of vapour atoms. Both longitudinal and transverse magnetic fields are considered. At low vapour densities we find a narrowing of the level crossing curve in selective reflection relative to its width in the conventional dispersion theory. The narrowing is calculated as a function of the ratio of the homogeneous and inhomogeneous line width of the vapour for a Maxwellian velocity distribution of the vapour atoms and spectrally uniform incident radiation. The theory of this paper offers an explanation for recent observations of narrowing of level crossing curves in selective reflection.