
pmid: 9952922
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 ${\ensuremath{\Delta}}_{33}$ resonance. The intermediate ${\ensuremath{\Delta}}_{33}$ spectrum is described by a mean spectral energy, ${E}_{\mathrm{ms}}$, where the shift ${E}_{\mathrm{ms}}$ represents the average of the ${\ensuremath{\Delta}}_{33}$-nucleus mean field, ${U}_{\ensuremath{\Delta}}$, 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 \ensuremath{\omega}, assuming that ${U}_{\ensuremath{\Delta}}$ 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.
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