Quasiclassical integral representations of the scattering amplitude for rearrangement processes

A quasiclassical representation is obtained for the amplitude of rearrangement reactions in the three-body problem in terms of exact classical trajectories and wave functions of the bound states of the particles. Variables convenient for expressing the wave functions and two-body potentials are employed. The conservation laws and Hamilton function are given in the necessary variables. There is a discussion of the physical meaning of the obtained representation and the method of calculating the increment of the action in the channels in angle-action variables. At high energies, the obtained representation goes over into the eikonal expression obtained earlier from the Lippmann–Schwinger equations. An eikonal expression is found for the amplitude of two-particle rearrangement, and this can be generalized to the case of redistribution of an arbitrary number of particles in a two-body collision.