Phase analysis in the problem of scattering by a radial potential

Let (k,g) be the total scattering cross section of a three-dimensional quantum particle of energy K² by a radial potential. Under the assumption it is shown that in the domain one has the asymptotics where the coefficient is is expressed explicitly in terms of the Gamma function. For nonnegative potentials, the domain of validity of this asymptotic is even larger. For potentials with a strong positive singularity, it is established that as. Similar results are obtained for the forward scattering amplitude.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 155–178, 1985.