Stretched excitations and the spin-dependent part of the pion-nucleon interaction

The $p$-wave form of the spin-orbit operator provides the basis for a single scattering model for the excitation of unnatural parity levels in pion-nucleus scattering in the region of the $\Delta$ resonance. The model is found to give a reasonable description of the ${\pi }^{+}$ and ${\pi }^{-}$ experimental cross sections for the excitation of stretched $4^{-}$ and $6^{-}$ states in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. In the calculations the interaction strength was fixed from the free pion-nucleon data and the spin transition densities were determined from recent ($e, e^{\prime }$) and ($p, p^{\prime }$) data. A schematic discussion of possible corrections to the model is also presented.