Theoretical problems of the pion multiple scattering on nuclei

The general theory of pion multiple scattering (TPMS) on nuclei is expounded on the basis of the relativistic potential theory. In the framework of general theory the problem of the relation pion-nucleon scattering t-matrix in their c.m.f. with the same matrix in an arbitrary frame is considered. The general expression (as a series) for the πA-scattering amplitude is obtained in the fixed-scatterer approximation (FSA) on the basis of the Lippmann-Schwinger equation for T-matrix and the different solvable models are considered in this approximation. The approximation methods which exist at present for the solving πA-scatteting on the basis of the first-order optical potential are considered in detail and the problem of taking into account different effects letting one us to go beyond the FSA are considered. The results of first attempts to obtain the second order optical potential and the problem of the account the genuine pion absorption by nuclei in the πA-scattering processes are discussed as well. The pion-deuteron scattering is considered separetely. The consideration is carried out on the basis of threebody relativistic equations. The TPMS is concluded to be of practical use in studying the πA-scattering