Dependence of asymptotic properties of the $S$-matrix in the angular momentum plane on the distribution of Regge poles in nonrelativistic scattering

A study is made of the asymptotic properties of the scattering phase in the left half-plane of angular monientum in the nonrelativistic case. In contrast to the existing approaches, a given distribution of Regge poles is taken as the starting point. The class of functions describing this distrilmtlon is chosen on the basis of an analysis of the Born terms and soluble models. It is shown that for this class the scattering phase in the left-plane of the complex angular momentum increases faster than any polynomial.