A simple and effective method to include the nucleon binding effect in pion-nucleus elastic scattering by using the three-body kinematics is proposed. It will be shown that the binding effect can be incorporated into the usual form of the first order optical potential calculation by making the two-body energy argument a variable parameter depending not only on the energy, but also on the nucleon Fermi momentum. Numerical examinations of the binding effect are carried out by $\pi$-${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ elastic scattering and the binding effect will be shown to have significant implications over the entire energy range considered, from low through resonance to above resonance regions.

NUCLEAR REACTIONS Calculated $\sigma \left(\theta \right)$ for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\pi , \pi )$, $E=50-250\mathrm{}$ MeV. Binding effect. Three-body kinematics. Importance of the Fermi motion.

• Received 2 February 1982

DOI:https://doi.org/10.1103/PhysRevC.26.1628