Effects of particle structure in the three-body problem

A study is made of an exactly solvable manifestly relativistically invariant model of three particles (hadrons, nuclei) that possess internal structure. The model takes into account not only a potential interaction but also a mechanism associated with the formation of compound systems (of the type of composite quark-gluon bags) in intermediate states. The scattering problem in the system is solved by a method based on introducing a dependence of the state vectors and scattering operators in the three-body space on an additional external parameter. By an analysis of the conditions of two- and three-particle unitarity it is shown that the effects of particle structure due to coupling of three-body (hadronic) and hadron-bag configurations leads to the appearance of certain factors in the cross sections for $2\to 2$ and $2\to 3$ processes. These factors can be expressed in terms of the mean values of the derivatives of the operators of the effective interactions in the three-body space with respect to the invariant masses of the two-body subsystems. Bounds on these factors that follow from the Hermiticity of the mass operator of the system are obtained.