S. L. Yakovlev, Z. Papp, “The three-body Coulomb scattering problem in a discrete Hilbert-space basis representation”, TMF, 163:2 (2010), 314–327; Theoret. and Math. Phys., 163:2 (2010), 666

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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 163, Number 2, Pages 314–327
DOI: https://doi.org/10.4213/tmf6502 (Mi tmf6502)

This article is cited in 12 scientific papers (total in 12 papers)

The three-body Coulomb scattering problem in a discrete Hilbert-space basis representation

S. L. Yakovlev^a, Z. Papp^b

^a Saint-Petersburg State University, St. Petersburg, Russia
^b Department of Physics and Astronomy, California State University, Long Beach, California, USA

Full-text PDF (440 kB) Citations (12)

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DOI: https://doi.org/10.4213/tmf6502

Abstract: We propose modified Faddeev–Merkuriev integral equations for solving the

2 \to 2, 3

$2\to2,3$ 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.

Received: 01.10.2009
Revised: 17.11.2009

English version:
Theoretical and Mathematical Physics, 2010, Volume 163, Issue 2, Pages 666–676
DOI: https://doi.org/10.1007/s11232-010-0049-8

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: S. L. Yakovlev, Z. Papp, “The three-body Coulomb scattering problem in a discrete Hilbert-space basis representation”, TMF, 163:2 (2010), 314–327; Theoret. and Math. Phys., 163:2 (2010), 666–676

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Linking options:

https://www.mathnet.ru/eng/tmf6502

https://doi.org/10.4213/tmf6502

https://www.mathnet.ru/eng/tmf/v163/i2/p314

This publication is cited in the following 12 articles:

V. A. Gradusov, V. A. Roudnev, E. A. Yarevsky, S. L. Yakovlev, “Theoretical study of antihydrogen formation reactions in the three body ${{e}^{ + }}{{e}^{ - }}\bar {p}$ system via Faddeev–Merkuriev equations in total orbital momentum representation”, Izvestiya Rossiiskoi akademii nauk. Seriya fizicheskaya, 87:8 (2023), 1191
V. A. Gradusov, V. A. Roudnev, E. A. Yarevsky, S. L. Yakovlev, “Theoretical Study of Antihydrogen Formation Reactions in the Three Body ${{e}^{ + }}{{e}^{ - }}\bar {p}$ System via Faddeev–Merkuriev Equations in Total Orbital Momentum Representation”, Bull. Russ. Acad. Sci. Phys., 87:8 (2023), 1200
V. A. Gradusov, V. A. Roudnev, E. A. Yarevsky, S. L. Yakovlev, Communications in Computer and Information Science, 1868, Parallel Computational Technologies, 2023, 63
V. A. Gradusov, V. A. Roudnev, E. A. Yarevsky, S. L. Yakovlev, “Theoretical study of reactions in the $e^-e^+\bar{p}$ three body system and antihydrogen formation cross sections”, JETP Letters, 114:1 (2021), 11–17
Gradusov V.A., Roudnev V.A., Yarevsky E.A., Yakovlev S.L., “Solving the Faddeev-Merkuriev Equations in Total Orbital Momentum Representation Via Spline Collocation and Tensor Product Preconditioning”, Commun. Comput. Phys., 30:1 (2021), 255–287
Gradusov V.A., Roudnev V.A., Yarevsky A., Yakovlev S.L., “High Resolution Calculations of Low Energy Scattering in E(-)E(+)P(-) and E(+)E(-)He(++) Systems Via Faddeev Merkuriev Equations”, J. Phys. B-At. Mol. Opt. Phys., 52:5 (2019), 055202
Gradusov V.A., Roudnev V.A., Yakovlev S.L., “Merkuriev Cut-off in e+ H Multichannel Scattering Calculations”, Atoms, 4:1 (2016)
M. V. Volkov, E. A. Yarevsky, S. L. Yakovlev, “Potential splitting approach to the three-body Coulomb scattering problem”, EPL, 110:3 (2015), 30006
S. L. Yakovlev, “Quantum $N$ -body problem: Matrix structures and equations”, Theoret. and Math. Phys., 181:1 (2014), 1317–1338
Mengoue M.S., “Three-Body-Continuum Coulomb Problem Using a Compact-Kernel-Integral-Equation Approach”, Phys. Rev. A, 87:2 (2013), 022701
Popov Yu.V., Zaytsev S.A., Vinitsky S.I., “J-matrix Method for Calculations of Three-Body Coulomb Wave Functions and Cross Sections of Physical Processes”, Physics of Particles and Nuclei, 42:5 (2011), 683–712
Mengoue M.S., Njock M.G.K., Piraux B., Popov Yu.V., Zaytsev S.A., “Electron-impact double ionization of He by applying the Jacobi matrix approach to the Faddeev-Merkuriev equations”, Phys Rev A, 83:5 (2011), 052708

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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