Watson-Sommerfeld Transformation for Many-Particle Scattering Amplitudes

Abstract

The continuation of many-particle partial-wave scattering amplitude to complex values of the total angular momentum is discussed in the framework of potential scattering. We show that if there is a continuation for which a Watson-Sommerfeld transformation of the full scattering amplitude can be made, then it is unique and determines the behavior of the amplitude for large values of any single scattering angle. The continuation of the partial-wave Schrödinger equation to complex values of the angular momentum is discussed, and the results are generalized to the case when exchange forces are present. As a simple application of the results, we discuss a crude nuclear model to illustrate how sequences of rotational levels can be described by Regge trajectories.