Excitation functions of pion reactions onN14,O16, andF19through the (3,3) resonance

Cross sections for pion-induced reactions of the form ($\pi ,\pi N$) and more complex spallation reactions of the form ($\pi ,X$) have been measured from 50-550 MeV on the target nuclei ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ using the secondary pion beams at the Lawrence Berkeley Laboratory 184-inch synchrocyclotron and the Clinton P. Anderson Meson Physics Facility. The dominance of the (3, 3) free-particle resonance is seen in all excitation functions determined in this work. Relative to the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({\pi }^{\pm },\pi N){}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ reactions, the (${\pi }^{\pm },\pi N$) reactions on ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ have magnitudes of 0.2, 1, and 0.7, respectively. The cross section ratio $R=\frac{\sigma ({\pi }^{-},{\pi }^{-}n)}{\sigma ({\pi }^{+},\pi N)}=1.68\mathrm{}\pm 0.18$ for ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ at 188 ± 15 MeV, 1.68 ± 0.05 for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ at 188 ± 9 MeV, and 1.68 ± 0.03 for ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ at 178 ± 2 MeV incident pion energy. The results from this work are compared to previous pion work, analogous proton-induced reactions, Monte Carlo intra-nuclear cascade-evaporation calculations, and to a semiclassical nucleon charge-exchange model which convincingly explains the ($\pi ,\pi N$) reaction mechanism in the (3, 3) resonance region.