The inverse scattering problem

In scattering theory one assumes that the interaction between particles may be represented by a potential V(q,r) which in general is dependent on the velocity and separation of the particles. The problem of course is to determine that interaction. The traditional approach to this problem is to assume some form for the interaction, calculate cross sections, polarizations, etc., and then compare with experimental data. The interaction is then modified until agreement is reached. The inverse problem is posed in the opposite direction. Given information obtained from scattering experiments one tries directly to deduce the interparticle forces.