pd↔π+treaction around theΔresonance

The $\mathrm{pd}\leftrightarrow {\pi }^{+}t$ process has been calculated in the energy region around the $\Delta$ resonance with elementary production/absorption mechanisms involving one and two nucleons. The isobar degrees of freedom have been explicitly included in the two-nucleon mechanism via $\pi$- and $\rho$-exchange diagrams. No free parameters have been employed in the analysis since all the parameters have been fixed in previous studies on the simpler $\mathrm{pp}\leftrightarrow {\pi }^{+}d$ process. The treatment of the few-nucleon dynamics entailed a Faddeev-based calculation of the reaction, with continuum calculations for the initial $p$-$d$ state and accurate solutions of the three-nucleon bound-state equation. The integral cross section was found to be quite sensitive to the $\mathrm{NN}$ interaction employed while the angular dependence showed less sensitivity. Approximately a 4% effect was found for the one-body mechanism, for the three-nucleon dynamics in the $p$-$d$ channel, and for the inclusion of a large, possibly converged, number of three-body partial states, indicating that these different aspects are of comparable importance in the calculation of the spin-averaged observables.