Pion interaction with the trinucleon up to the eta production threshold

Pion elastic, charge exchange scattering, and induced eta production on the trinucleon systems are investigated in a coupled-channels approach in momentum space with Faddeev wave functions. The channel πN→ηN is included using an isobar model with S-, P-, and D-wave resonances. While the coherent reactions like ${}_{}{}^3{}_{}{}^{}\mathrm{He}$(π,π${)}^3$He can be reasonably well reproduced up to ${\mathit{T}}_{\mathrm{\pi }}$=500 MeV, large discrepancies appear for the incoherent processes ${}_{}{}^3{}_{}{}^{}\mathrm{He}$(${\mathrm{\pi }}^{\mathrm{-}}$,${\mathrm{\pi }}^0$ ${)}^3$H and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$(${\mathrm{\pi }}^{\mathrm{-}}$,η${)}^3$H at backward angles and energies above Δ resonance. In the forward direction, the (π,η) calculations underestimate the experimental measurements very close to threshold, but agreement with the data improves with increasing pion energy. Predictions are made for the asymmetries of the various reactions on polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.