Estimate of theπ−πTotal Cross Section and Diffraction Width

In this note we estimate the total $\pi -\pi$ cross section and diffraction width at high energy via a simple approximation procedure for the reduced residue which was recently noted in potential theory. Results consistent with the present known facts on the $\pi -\pi$ system are obtained, and it is concluded that this approximation procedure may provide a simple and yet accurate means of estimating total high-energy cross sections and diffraction widths once the crossed-channel trajectories are known.