Quasiclassical asymptotics of the scattering cross-section for the Schrödinger equation

The author considers scattering with a potential $gq(x)$, $x\in\mathbf R^m$, that decreases as $|x|\to\infty$ as a homogeneous function of degree $-\alpha$. In the domain $gk^{-1}\to\infty$, $gk^{\alpha-2}\to\infty$ the asymptotics of the forward scattering amplitude is found, as well as the total scattering cross-section averaged over a small interval of $k$. This is determined only by the behavior of $q(x)$ as $|x|\to\infty$. Dual results are obtained for strongly singular potentials.
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