Asymptotic Properties of theSMatrix for Singular Potentials

In this paper, two theorems on scattering by singular potentials will be proved. First, the scattering amplitude possesses an essential singularity for small coupling constant $g$ and for fixed energy $k$. Second, for a fixed value $g$ the $S$ matrix has an essential singularity for large values of energy $k$. We give the explicit form for the asymptotic behavior in $\mathrm{}\left|k\right|\mathrm{}$.