Inversion of molecular scattering data

Practical solutions of the inverse problem of scattering in molecular physics are reviewed. Methods are presented both for extracting the interaction potential from the S-matrix or its semiclassical analogue the deflection function and for inverting the cross sections to these functions. Exact quantum mechanical methods and methods in the semiclassical or the high energy approximation are available for elastic scattering data. Procedures for inelastic cross sections are discussed for symmetric exchange processes, electronic and rotational excitation. Finally the computational procedures for the preparation of the input data including necessary deconvolution processes and for the construction of the S-matrix and the potential are presented. Only methods which were applied to real data or for which at least simulated examples are available are discussed and illustrated by suitable examples.