Construction of the scattering amplitude from the differential cross-sections

• DOI: 10.1007/bf02756351
• Publication Date: 2007-11-22T14:14:30Z
• Authors: A. Martin

We establish rigorously a sufficient condition for the existence of a scattering amplitude corresponding to a given angular distribution for scalar particles in the elastic region. The condition is max [(1/4π) · e|F(13)||F(23)|dΩ3/|F (12)|]=sinµ<1. We show that if |sinµ|<0.79 the amplitude is unique, except for one obvious ambiguity. Further, by examining the case of a finite, but arbitrarily large number of partial waves, we show that it is very likely that the solution is still unique for 0.79<sinµ<1. We also discuss the number of solutions in other situations.