Quenching of Glory Undulations for Scattering from Polyatomic Molecules: Clover-Leaf Model for Spherical-Top Molecules

Abstract

A formula is derived which describes the quantum-mechanical analog to Huygens' principle in optics. From this the quantum-mechanical analog to Kirchhoff–Fraunhofer diffraction is formulated and is used to calculate small-angle differential cross sections and total cross sections. Complex scattering phase shifts (optical potentials) are easily accommodated. The method is applied to the case of glory quenching, employing potential models (“breathing sphere,” “clover leaf,” and certain combinations) which can be carried through analytically. As an example, the clover-leaf model was chosen for comparison with experimental data. By applying some suitable approximations the quenching effect can be expressed in simple known terms, both as far as quenched glory amplitudes as well as “misplaced” and “distorted” glory extrema are concerned. For glory scattering from spherical-top molecules (tetrahedral molecules) the clover-leaf model seems to offer a reasonable approximation. It can be used to derive potential parameters and anisotropy parameters.