How Many Nucleons are Involved in Pion Absorption in Nuclei?

The proton yields from the interaction of pions on nuclear targets with $12<~A<~181$ were measured in the region of the $\Delta (3, 3)$ resonance. The shift in proton energies with angle is analyzed in terms of the average number of nucleons that have participated in absorbing the pion's momentum and total energy. The effective number of interacting nucleons, for both ${\pi }^{+}$ and ${\pi }^{-}$ incident, is found to be ∼ 3 for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and increasing to ∼ 5.5 for ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$. These effective numbers of nucleons are also consistent with the ratio of proton yields from ${\pi }^{+}$- and ${\pi }^{-}$-induced reactions.