Dispersive effects in pion-nucleus scattering

The influence of dispersive, medium effects on pion-nucleus elastic scattering is investigated in a simple model. The pion-nucleus interaction in the impulse approximation is represented by an optical potential whose form is motivated by field-theoretic considerations and the properties of the ${\Delta }_{33}$ resonance. The intermediate ${\Delta }_{33}$ spectrum is described by a mean spectral energy, $E_{\mathrm{ms}}$, where the shift $E_{\mathrm{ms}}$ represents the average of the ${\Delta }_{33}$-nucleus mean field, $U_{\Delta }$, over the nucleon and pion wave functions. We calculate the real part of $E_{\mathrm{ms}}$ as a function of mass number A and pion energy ω, assuming that $U_{\Delta }$ is numerically the same as the nucleon-nucleus shell-model potential. We compare our theory to more conventional ones, showing that the mean spectral energy is an important correction for pion-nucleus elastic scattering.