Abstract
We propose modified Faddeev-Merkuriev integral equations for solving the 2→2, 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.
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Dedicated to the memory of Academician S. P. Merkuriev, who would have been 65 in 2010
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 163, No. 2, pp. 314–327, May, 2010.
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Yakolev, S.L., Papp, Z. The three-body Coulomb scattering problem in a discrete Hilbert-space basis representation. Theor Math Phys 163, 666–676 (2010). https://doi.org/10.1007/s11232-010-0049-8
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DOI: https://doi.org/10.1007/s11232-010-0049-8