Relativistic three-body calculations are presented for the real part of the $\pi$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ scattering length. The effects of the nucleon binding and the exclusion principle are studied in the framework of a covariant three-body model (pion, nucleon, and core) of the optical potential. The present theory is a natural generalization of the optical potential model of Celenza, Liu, and Shakin who consider only the single-triangle diagram, ignoring the nucleon rescattering. We find that the nucleon binding and the exclusion principle each have a large effect on the scattering length. However, the combined effect of both medium corrections is much smaller. Depending on the model for the $\pi N$ $t$ matrix, the single-triangle diagram alone accounts for 15% and 33% of the scattering length. With medium correction included, these numbers are 25% and 40%, respectively. Finally, we determined the $s$ wave strength parameter $B_0$ in a phenomenological ${\rho }^2$ term.

NUCLEAR REACTIONS Three-body model, nucleon binding effects, exclusion-principle corrections, pion-nucleus optical potential, pion-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ scattering length.

• Received 1 March 1982

DOI:https://doi.org/10.1103/PhysRevC.26.570