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.
Keywords:
Coulomb scattering problem, quantum scattering problem, Faddeev–Merkuriev integral equations.
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
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 \(e+e−¯p\) 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−¯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+¯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