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

It is shown that the s-wave partial amplitude f(k) for scattering on the re al-valued Woods-Saxon potential V(r) = -V-0/[1 + exp((r - R)/d)] has very s pecial analytic properties: the trajectories of the poles of the function k cot delta [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 Yukaw a-like potentials, the scattering length does not vanish here at zero energ y. The results reported in this article were obtained analytically under th e assumption that exp(-R/d) much less than 1. The problem of revealing the poles of the function k cot delta in a partial-wave analysis of neutron sca ttering on nuclei is discussed. (C) 2000 MAIK "Nauka/Interperiodica".