Quantum theory of neutral-atom scattering at long range from solid cylinders

Abstract

Qualitative arguments suggest that diffraction effects might be important for the interpretation of the experiments of Shih et al. We derive a tractable quantum theory to describe the scattering of neutral atoms at long range by van der Waals forces from solid cylinders. The theory is based on an angular-momentum expansion and evaluates the scattered intensity close to the cylinder in the geometrical shadow region. The formal quantum theory indicates that one is far from the conventional classical limit, in the sense that WKB and stationary-phase approximations are not valid. Yet an essentially exact evaluation appears to agree with the classical prediction, at least over the range of deflections that have been experimentally studied. This surprising classical-quantum correspondence is clarified by a Regge-pole analysis. Finally we also set limits on the extent of specular reflection from the cylinder surfaces. The discrepancy between theory and experiment remains unresolved.