Special analytic properties of the amplitude for scattering on the Woods-Saxon potential

Abstract

It is shown that the s-wave partial amplitude f(k) for scattering on the real-valued Woods-Saxon potential V(r)=−V0/[1+exp((r−R)/d)] has very special analytic properties: the trajectories of the poles of the function k cotδ [of the zeros of the amplitude f(k)] coincide with the lines of the dynamical singularities [spurious poles of f(k)], so that the zeros and the poles compensate each other. In contrast to what is obtained for Yukawa-like potentials, the scattering length does not vanish here at zero energy. The results reported in this article were obtained analytically under the assumption that exp(-R/d)≪1. The problem of revealing the poles of the function k cotδ in a partial-wave analysis of neutron scattering on nuclei is discussed.