Improved calculation of total scattering cross sections in the glory region

The usual formula for the decomposition of the total scattering cross section into a slowly-varying average part plus an undulating glory part is not accurate enough for the analysis of recent experiments. A modified uniform approximation is used to derive an improved formula for the undulations. The correction depends on the shape of the potential well, and can be determined experimentally. An improved method for calculating the slowly-varying part is also suggested, and is used to discuss the interparticle distance probed by the measurements. Numerical examples are given for several potentials, and comparisons are made with detailed JWKB phase-shift calculations of the cross section.