Pion Absorption Cross Section for ^2H and ^3He in the Delta-Isobar Region: A Phenomenological Connection

Abstract

The absorption of π^+ on ^3He in the $Δ$-region is evaluated with exact inclusion of the final state interaction among the three emerging protons. The absorption is described by a $πN \to Δ$ vertex and a $NΔ- NN$ transition t-matrix which are calculated from a phenomenological model for NN and πd reactions. In a calculation where the initial pion scattering effects are neglected, the predicted peaks of the pion absorption cross sections for ^2H and ^3He 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 ^3He. We demonstrate that the adjustment of the peak position for the deuteron cross section by small modifications of the $Δ$-parameters, automatically leads to the correct peak position in ^3He.