Lower Limit for the Energy Derivative of the Scattering Phase Shift

Abstract

It is shown that the derivative of the scattering phase shift with respect to energy, $\frac{d\ensuremath{\eta}}{\mathrm{dE}}$, must exceed a certain limit if the interaction of scattered particle and scatterer vanishes beyond a certain distance. This limitation of $\frac{d\ensuremath{\eta}}{\mathrm{dE}}$ is, fundamentally, a consequence of the principle of causality; it is derived, however, from a property of the derivative matrix $R$.