Singularities in Angular Momentum of the Scattering Amplitude for a Class of Soluble Potentials

The analyticity of the scattering amplitude in the variables, energy, and angular momentum is explicitly studied for square well and a class of continuous potentials having a $\frac{1}{r^2}$ type of core or tail. The trajectories of the poles in the $l$ plane and their residues have been determined numerically.