Nucleon charge exchange in the (π,πN) reaction at resonance energies

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.