Complex angular momentum in three-particle potential scattering

Abstract

The continuation of three-particle partial wave scattering amplitudes 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. A non-rigorous construction of such a continuation is given for an amplitude which describes a scattering in which a given pair of the particles is bound in the initial and final states. Except for simple kinematic factors, the only singularities of this continuation are poles and possibly isolated essential singularities. The results are generalized to cases 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. The behavior of Regge trajectories near two- and three-particle thresholds is explored.