An efficient method for performing the Fermi integration required in the construction of the first order pion-nucleus optical potential is derived. The corrections to a factorized approximation are found to arise predominantly from the energy dependence of the pion-nucleon amplitude. The exact magnitude of these corrections and the quantitative features of cross sections are found to depend sensitively on the particular choice made for the dependence of the two-body energy on the pion and nucleon momenta.

NUCLEAR REACTIONS $\pi$-nucleus elastic scattering, Fermi integration.

• Received 24 January 1983

DOI:https://doi.org/10.1103/PhysRevC.27.2733