A first-order pion-nucleus optical potential which is convenient for the analysis of pion-nucleus data is presented. This configuration-space potential incorporates a number of important theoretical features. A Lorentz transformation of the pion-nucleon interaction from the pion-nucleon to the pion-nucleus center-of-mass system is shown to yield a first-order potential which is almost local in coordinate space, and which differs from the originally proposed gradient potential, by containing an additional term proportional to the Laplacian of the density. We then show how this form is modified by off-shell and high-energy considerations. It is emphasized that proper off-shell and threshold behavior can be included and that energy and momentum variables must be treated carefully in deriving the optical potential. Typical numerical results are given and the new potential is shown to yield significant build-up of large-angle cross sections.

[NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\pi ,\pi )$, $E=120-280\mathrm{}$ MeV; calculated $\sigma \left(\theta \right)$: Optical potential deduced from multiple-scattering theory.]

• Received 3 August 1973

DOI:https://doi.org/10.1103/PhysRevC.9.188