Pion-Oxygen Elastic Scattering in the 3-3 Resonance Region

Abstract

The total and differential cross sections for ${\pi }^{-}$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ elastic scattering in the 3-3 resonance region are calculated using the first-order optical potential derived from the multiple-scattering theory of Kerman, McManus, and Thaler. In order to include the 3-3 resonance and generate a reasonable off-shell behavior of the $\pi$-nucleon transition matrix, a separable model is used to construct the $\pi$-nucleon transition matrix. The optical potential also includes a proper transformation of the $\pi$-nucleon transition matrix from the $\pi$-nucleon to the $\pi$-nucleus c.m. frames. The results are compared with recent ${\pi }^{-}$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ elastic-scattering data and with earlier ${\pi }^{-}$-${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ calculations.