An ab initio method of taking Fermi motion effects in pion scattering into account combined with proper antisymmetrization of the two nucleon final state in $d({\pi }^{\pm } {\pi }^{\pm }, p)n$ shows that the reaction amplitude consists of not only a contribution from pion scattering on a proton, but also pion scattering on a neutron, and that the two amplitudes differ considerably in their $\pi -N$ c.m. energies. The neutron scattering contribution to the differential cross section exceeds 10% in as many as 51 out of 195 ${\pi }^{-}$ events recorded in a recent kinematically complete experiment by Hoftiezer et al. in the $\Delta$-resonance region. In several kinematical situations the neutron contribution exceeds 100% and could even be as high as ∼400%.

NUCLEAR REACTIONS $d({\pi }^{\pm }, {\pi }^{\pm } p)n$, ab initio method for Fermi motion effects, Pauli principle, effective mass, exchange amplitude.

• Received 24 May 1982

DOI:https://doi.org/10.1103/PhysRevC.27.2198