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../sub 33/ resonance. The intermediate ..delta../sub 33/ spectrum is described by a mean spectral energy, E/sub ms/, where the shift E/sub ms/ represents the average of the ..delta../sub 33/-nucleus mean field, U/sub ..delta../, over the nucleon and pion wave functions. We calculate the real part of E/sub ms/ as a function of mass number A and pion energy ..omega.., assuming that U/sub ..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.