Geodesic
The~three-body Coulomb scattering problem in a~discrete Hilbert-space basis representation
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 314-327

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We propose modified Faddeev–Merkuriev integral equations for solving the $2\to2,3$ quantum three-body Coulomb scattering problem. We show that the solution of these equations can be obtained using a discrete Hilbert-space basis and that the error in the scattering amplitudes due to truncating the basis can be made arbitrarily small. The Coulomb Green's function is also confined to the two-body sector of the three-body configuration space by this truncation and can be constructed in the leading order using convolution integrals of two-body Green's functions. To evaluate the convolution integral, we propose an integration contour that is applicable for all energies including bound-state energies and scattering energies below and above the three-body breakup threshold.
Keywords: Coulomb scattering problem, quantum scattering problem, Faddeev–Merkuriev integral equations. 
@article{TMF_2010_163_2_a6,
     author = {S. L. Yakovlev and Z. Papp},
     title = {The~three-body {Coulomb} scattering problem in a~discrete {Hilbert-space} basis representation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {314--327},
     publisher = {mathdoc},
     volume = {163},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a6/}
}
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S. L. Yakovlev; Z. Papp. The~three-body Coulomb scattering problem in a~discrete Hilbert-space basis representation. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 314-327. http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a6/