Approximation methods for low-energy potential scattering

Abstract A systematic method is developed for short-range central potentials, to obtain the coefficients of the momentum expansion of wave function and scattering amplitude for any value of the angular momentum. The corresponding effective range solution and Pade approximants for the k -variable expansion of the S -matrix are studied. Both methods are compared as a means to find the analytical behaviour of the scattering function in the complex momentum plane. As an example, numerical calculations have been performed for the S-wave amplitude of a spherical square-well potential. Results show an outstanding ability of diagonal Pade approximants to reproduce in a fastly convergent way the trajectories of the poles in the k -plane.