Universality of Low-Energy Scattering in 2+1 Dimensions: The Non Symmetric Case

Abstract

For a very large class of potentials, $V(\vec{x})$, $\vec{x}\in R^2$, we prove the universality of the low energy scattering amplitude, $f({\vec{k}}^{\prime },\vec{k})$. The result is $f=\sqrt{\frac{\pi }{2}}\{1/logk)+O(1/(logk{)}^2)$. The only exceptions occur if $V$ happens to have a zero energy bound state. Our new result includes as a special subclass the case of rotationally symmetric potentials, $V(|\vec{x}|)$.

65 pages, Latex, significant changes, new sections and appendices