Second-order pion-nucleus optical potential

The second-order pion-nucleus optical potential is expressed in momentum space in terms of the πN off-shell t matrix and the NN correlation function. The dependence of the πN t matrix on the total πN momentum is determined within the framework of relativistic particle quantum mechanics. Numerical results are presented for π-4He scattering. It is found that the NN correlations tend to decrease the forward elastic cross sections by a factor of about 1.5 at low energy, E/sub π/MeV. At higher energies the main effect of the NN correlations is to increase the differential cross section at large angles. The effect of NN correlations on the total cross section and the pion wave function is also found to be important. A study of the dependence of the calculated cross sections on the range parameters of the πN t matrix and of the NN correlations suggests that the low-energy pion-nucleus scattering data cannot be adequately described by an optical model constructed from the first- and second-order terms in an expansion in terms of the πN t matrix