Pion absorption cross section for2H and3He in theΔ-isobar region: A phenomenological connection

Abstract

The absorption of ${\ensuremath{\pi}}^{+}$ on ${}^{3}$He in the $\ensuremath{\Delta}$ region is evaluated with exact inclusion of the final state interaction among the three emerging protons. The absorption is described by a $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\Delta}$ vertex and an $N\ensuremath{\Delta}$-$\mathrm{NN}$ transition $t$ matrix which are calculated from a phenomenological model for $\mathrm{NN}$ and $\ensuremath{\pi}d$ reactions. In a calculation where the initial pion scattering effects are neglected, the predicted peaks of the pion absorption cross sections for ${}^{2}$H and ${}^{3}$He lie too high in energy in relation to the data. The effect of the final-state three-nucleon interaction turns out to be too small for changing the magnitude and shifting the peak position of the total absorption cross section for ${}^{3}$He. We demonstrate that the adjustment of the peak position for the deuteron cross section by small modifications of the $\ensuremath{\Delta}$ parameters automatically leads to the correct peak position in ${}^{3}$He.