π4He scattering in the (3.3)-resonance range and the problems of multiple scattering theory

The π4He scattering in the vicinity of the (3.3) resonance s studied in the multiple scattering theory by the first-order optical potential method using two different formulations of the theory, viz., Watson formulation and that of Kerman, McManus and Thaler. Difference between the impulse approximation results obtained in both formulations is used to choose the best form of the impulse approximation. It is shown that the Galilean invariant impulse approximation is obviously better than the usual Galilean non-invariant approximation. The applicability of the optical potential factorization approximation in the vicinity of the (3.3) resonance is studied. It is shown that this approximation may lead to incorrect picture of the pion-nuclear dynamics