Geodesic
Analytic solution to the problem of three-particle collisions in a~model with eikonal Hamiltonian
Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 1, pp. 73-88

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The three-particle eikonal model of the process $3\to3$ is investigated in the case when the relative motions of the particles of each pair correspond to high energies. No other restrictions (such as in the fixed-center approximation) are imposed on the motion of the particles. It is shown that in this case the three-particle problem admits an analytic solution. An explicit expression is found for the off-shell amplitude of the $3\to3$ process; it is obtained by exact summation of the multiple scattering series in a model with eikonal Hamiltonian. On the mass shell, this series terminates (there are no terms with multiplicity higher than three). A formula is obtained that describes the mutual canceling of the terms of higher multiplicity in the series. 
@article{TMF_1981_47_1_a5,
     author = {V. E. Kuz'michev and V. F. Kharchenko},
     title = {Analytic solution to the problem of three-particle collisions in a~model with eikonal {Hamiltonian}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {73--88},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_47_1_a5/}
}
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V. E. Kuz'michev; V. F. Kharchenko. Analytic solution to the problem of three-particle collisions in a~model with eikonal Hamiltonian. Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 1, pp. 73-88. http://geodesic.mathdoc.fr/item/TMF_1981_47_1_a5/