Evaluation of the S matrix for a class of potentials
Giulio Paiano, Stefano L. Paveri-Fontana · Journal of Physics A Mathematical and General · 1980
The S-matrix problem is studied for the radial potential V(r)=-( mu + lambda /r)exp(-r). The Schrodinger equation is Laplace transformed. Then results on the asymptotics of the Laplace transformation are used to express the S-matrix element S l as a linear combination of the values of the transformed function and of its first l+1 derivatives at one point in the complex plane. By a change of variables, the evaluation of S l and of the phase shift sigma l is then reduced to the numerical solution of a non-singular neutral functional differential equation (on a finite interval) followed by a finite recursive procedure. A convergent numerical scheme is implemented.