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.