CONSTRUCTION OF SCATTERING AMPLITUDE FROM DIFFERENTIAL CROSS-SECTIONS

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 [(1/4 π) · ε|F(13)||F(23)|d Ω 3/|F (12)|]=sin μ<1. We show that if |sin μ|<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<sin μ<1. We also discuss the number of solutions in other situations. © 1969 Società Italiana di Fisica.