Inverse problem in atom-atom scattering in WKB approach

The WKB phase of a scattering problem including high angular momenta can be written as a Jeffreys-Born integral, $${}^{delta WKB}(beta ,K) = - frac{A}{{2K}}intlimits_beta ^infty {frac{{Q(t,K)tdt}}{{sqrt {t^2 - beta ^2 } }}} $$ where β=(l+1/2)/A is the reduced collision parameter. The quasipotential Q(t, K) defined by this formula is connected with the potential in an easily understandable way. Its introduction allows the solution of the inversion problem (in WKB approximation) by treating this formula as an integral equation forQ. It further permits to investigate the relation between potential and phase function. The evaluation of experimental atom-atom-scattering data, using a phase function with seven parameters is given as an example how potential parameters can be used. Potentials leading to observed differential cross sections thus can easily be computed. Computation times are about a factor 50 smaller than in conventional methods.