The semiclassical trajectory model of Benioff, which treats the nuclear structure of the target by means of the harmonic oscillator model, has been adapted to the ($\pi$,$\pi N$) reaction in the (3,3) resonance region. Excitation functions have been calculated for comparison with the experimental results on the following reactions: ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${\pi }^{\pm }$,${\pi }^{\pm }n$), ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$(${\pi }^{\pm }$,${\pi }^{\pm }p$), and ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$(${\pi }^{\pm }$,${\pi }^{\pm }n$). The nucleon charge exchange probability $P$ was treated as an adjustable parameter and found to decrease from ∼0.2 for light elements to ≲0.05 for heavy elements. The value of $P$ for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is supported by a parameter-free estimate on the basis of a modified free nucleon-nucleon scattering model. The decrease in $P$ with increasing target $A$ is attributed to nuclear size and structure effects. The calculated excitation functions are in good agreement with the experimental results for both light and heavy target nuclei. Experiments that would constitute a more stringent test of various aspects of the model are proposed.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${\pi }^{\pm }$,${\pi }^{\pm }n$), ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$(${\pi }^{\pm }$,${\pi }^{\pm }p$), ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$(${\pi }^{\pm }$,${\pi }^{\pm }n$), $T_{\pi }=100-300\mathrm{}$ MeV; calculated excitation functions and and nucleon charge exchange probability.

• Received 18 November 1981

DOI:https://doi.org/10.1103/PhysRevC.25.2638