Minimum Theorem for the Interaction Radius in Two-Body Collisions

A general theorem has been derived for the behavior of a two-body scattering process. It is shown that the phase shift analysis must incorporate at least $\overline{l}$ non-negligible phase shifts, where $\overline{l}$ is determined by the total and elastic cross sections in a simple fashion. For large $\overline{l}$, a minimum value for the interaction radius can be inferred from $\overline{l}$. This result is applied to several scattering experiments which were previously analyzed, and the minimum radius obtained turns out in each case to be quite close to the interaction radius as estimated in the more elaborate discussion.