Coordinate asymptotics of the wave function for a system of four particles free in the initial state

The coordinate asymptotics of the wave function for a system of four particles in which $4\to4$ processes are taken into account is studied. The main attention is devoted to triple scattering effects. It is established that in the parts of the configuration space in which the formally constructed scattering amplitude becomes infinite, the asymptotic behavior of the wave function can be described by Fresnel type double integrals.