Book Description

An attempt is made to clarify the structure of pion-nucleus scattering taking into account the fact that the pions in scattering and in nuclear forces are identical. To understand the essential points, a simple pion plus two- nucleon system is chosen. The processes considered are $pi$NN $Yields$ $pi$NN and $pi$NN reversible NN. Both relativistic and nonrelativistic approaches are adopted. In the relativistic approach Taylor's method is used, whereas in the nonrelativistic approach a Hamiltonian (Schroedinger equation) method is utilized together with a projection technique. Both approaches give a finite set of amplitude equations respectively, and the formal correspondence between these sets of equations is observed. Due to the proper consideration of pions, the problem of pion overcounting does not occur and the amplitudes are shown to satisfy at least two- and three-particle unitarity. Through the study of the scattering in the $pi$NN system, several important aspects common in general pion- nucleus scattering have been observed. For instance, this observation gives some new insight into the proper structure of pion-nucleus optical potentials. For practical applications the non-relativistic $pi$NN amplitudes are reduced in angular momentum-isospin eigenstates together with the inclusion of bound states. The reduced amplitudes are then used to study the pion absorption effect on the pion--deuteron scattering length. The result is consistent with experiment. Some possible future applications of the formulations developed are discussed. 10 tables, 2 figures, 65 references. (auth).