Nonrelativistic S-Matrix Poles for Complex Angular Momenta

Abstract

Regge's introduction of complex angular momenta is studied in more detail. The shape and number of trajectories of S-matrix poles as functions of the energy is investigated, with particular attention to the way they leave the real axis, and to their ends at E → ± ∞. The conditions are found under which the S matrix is meromorphic even in Re l < −1/2. Some properties of the S matrix in the left half-plane are discussed and so are its symmetry between left and right half-planes, its branch point at E = 0, and the residues at its poles.