Pion absorption cross section for {sup 2}H and {sup 3}He in the {Delta}-isobar region: A phenomenological connection

The absorption of {pi}{sup +} on {sup 3}He in the {Delta} region is evaluated with exact inclusion of the final state interaction among the three emerging protons. The absorption is described by a {pi}N{r_arrow}{Delta} vertex and an N{Delta}-NN transition t matrix which are calculated from a phenomenological model for NN and {pi}d reactions. In a calculation where the initial pion scattering effects are neglected, the predicted peaks of the pion absorption cross sections for {sup 2}H and {sup 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 {sup 3}He. We demonstrate that the adjustment of the peak position for the deuteron cross section by small modifications of the {Delta} parameters automatically leads to the correct peak position in {sup 3}He. {copyright} {ital 1997} {ital The American Physical Society}