Three-Body Calculation ofπdElastic Scattering at 142 MeV

We calculate the pion-deuteron elastic scattering at $E_{\pi }=142\mathrm{}$ MeV using nonrelativistic three-body equations in which relativistic kinematics are retained only for the pion. The $\mathrm{NN}$ tensor force is taken into account, and, for the first time, all $S$ and $P$ $\pi N$ partial waves are included in an exact way. The coupling between $l=J\pm 1$ $\pi d$ channels is found to be not negligible, and we establish the large interference effects of all other than $P_{33}$ $\pi N$ channels leading to a rather good description of the experimental data at $E_{\pi }=142\mathrm{}$ MeV.