Additional Quantum Effects in Atom–Atom Scattering: Higher-Order Glory Scattering

In atomic scattering theory the phase shift η has often been treated as a continuous function of angular momentum l, in order to replace summation over l by integration. However, because l is quantized, additional (higher-order) forward and backward glories may occur. The effect is most pronounced in like-particle scattering, where “hard-sphere” glories show up in total cross section. General formulas are derived and applied to like particles. For comparison, exact quantum calculations are presented. A criterion for the applicability of the continuous phase approximation is derived. Construction of phase-shift curves from experimental data only is discussed.