Geodesic
Quasiclassical integral representations of the scattering amplitude for rearrangement processes
Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 426-433 
A. V. Bogdanov; G. V. Dubrovskiy. Quasiclassical integral representations of the scattering amplitude for rearrangement processes. Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 426-433. http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a10/
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     author = {A. V. Bogdanov and G. V. Dubrovskiy},
     title = {Quasiclassical integral representations of the scattering amplitude for rearrangement processes},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a10/}
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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.

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