Detailed calculations are presented of the Pauli blocking correction in $\pi$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ scattering for the energy range $T_{\pi }=24-220\mathrm{}$ MeV. Pion-nucleon partial wave mixing which is due to the Pauli projection operator is taken into account for the first time. The first-order optical potential of Celenza, Liu, and Shakin is used. The nucleon-core interaction is simulated by means of an effective $\pi -N$ subenergy. Satisfactory results are obtained for the cross sections at low energies. However, at intermediate energies the elastic cross sections are overestimated by 30-40%. The partial wave mixing which is introduced by the Pauli principle generates a small correction at low energies but in the resonance region it leads to a clear increase in the cross sections by 10-20%.

NUCLEAR REACTIONS $\pi$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ scattering, $T_{\pi }=24-220\mathrm{}$ MeV, optical potential, Pauli-principle corrections.

• Received 2 April 1981

DOI:https://doi.org/10.1103/PhysRevC.24.1554