Pion absorption cross section for 2H and 3He in the Δ-isobar region: A phenomenological connection

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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→Δ vertex and an 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.

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