Variational derivation of the adiabatic time-dependent Hartree-Fock formalism and generalized Hamiltonian dynamics

The three-particle collision process 3 → 3 with relative high-energy motion of each pair of particles described by a model with eikonal Hamiltonian is investigated. No additional restrictions on the motion of the particles (such as fixed scattering centre approximation) are imposed. It is shown that the three-particle problem in this case can be solved analytically. An explicit expression for 3 → 3 amplitude off the energy shell is obtained as the result of the exact summation of the multiple scattering series in the considered model. On the energy shell this series breaks off (there are no terms higher than triple). The formula for the mutual cancellation of the higher-order terms of the series is derived.