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This article is cited in 16 scientific papers (total in 16 papers)
Wave-packet continuum discretization method for solving the three-body
scattering problem
V. I. Kukulin, V. N. Pomerantsev, O. A. Rubtsova
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University
Abstract:
We generalize the wave-packet continuum discretization method previously
developed for the scattering problem to the three-body system. For each
asymptotic channel, we construct a basis of three-body wave packets
given by square-integrable functions. We show that the projections of
the channel resolvents on the subspace of three-body wave packets are
determined by diagonal matrices, whose eigenvalues we find explicitly. We
express the amplitudes of $2\to 2$ processes explicitly in terms of
"wave-packet" finite-dimensional projections of the full resolvent. To illustrate
our formalism, we calculate the differential cross section of elastic
deuteron scattering on a heavy nucleus above the three-body breakup
threshold and the $s$-wave quartet $(n-d)$-scattering amplitude.
The results of the calculations agree well with the results obtained by other
methods. In terms of complexity, the proposed scheme for solving
the three-body scattering problem is comparable to solving a similar problem
for bound states.
Keywords:
quantum scattering theory, few-body system, discretization of the continuum
DOI:
https://doi.org/10.4213/tmf5991
 Full text:
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English version:
Theoretical and Mathematical Physics, 2007, 150:3, 403–424
Bibliographic databases:
     
Received: 22.04.2005
Revised: 19.05.2006
Citation:
V. I. Kukulin, V. N. Pomerantsev, O. A. Rubtsova, “Wave-packet continuum discretization method for solving the three-body
scattering problem”, TMF, 150:3 (2007), 473–497; Theoret. and Math. Phys., 150:3 (2007), 403–424
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/tmf5991https://doi.org/10.4213/tmf5991 http://mi.mathnet.ru/eng/tmf/v150/i3/p473
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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Rubtsova O.A., Kukulin V.I., “Wave-packet discretization of a continuum: Path toward practically solving few-body scattering problems”, Physics of Atomic Nuclei, 70:12 (2007), 2025–2045
-
Kukulin V.I., Rubtsova O.A., “Elastic scattering on a nucleus and the breakup of the composite projectile via wave-packet continuum discretization”, Phys. Rev. C, 76:4 (2007), 047601, 4 pp.
-
Rubtsova O.A., Kukulin V.I., Moro A.M., “Continuum discretization methods in a composite particle scattering off a nucleus: Benchmark calculations”, Phys. Rev. C, 78:3 (2008), 034603, 9 pp.
-
Pomerantsev V.N., Kukulin V.I., Rubtsova O.A., “Solving three-body scattering problems in the momentum lattice representation”, Phys. Rev. C, 79:3 (2009), 034001, 6 pp.
-
JETP Letters, 90:5 (2009), 402–406
 -
Stroe M., Fifirig M., “Electron-induced dissociation in $H_2^+$, $HD^+$ and $HT^+$”, Phys. Lett. A, 373:45 (2009), 4152–4157
-
Rubtsova O.A., Pomerantsev V.N., Kukulin V.I., “Quantum scattering theory on the momentum lattice”, Phys. Rev. C, 79:6 (2009), 064602, 17 pp.
-
Rubtsova O.A., Kukulin V.I., Pomerantsev V.N., “Solving few-body scattering problems in the momentum lattice basis”, 19th International IUPAP Conference on Few-Body Problems in Physics, EPJ Web of Conferences, 3, 2009
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Rubtsova O.A., Kukulin V.I., Pomerantsev V.N., “Quantum scattering theory on the momentum lattice”, Physics of Particles and Nuclei, 41:7 (2010), 1123–1126
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Rubtsova O.A., Kukulin V.I., Pomerantsev V.N., “Validity of the coupled-channel reduction in three-body scattering”, Phys Rev C, 84:4 (2011), 044002
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Rubtsova O.A., Pomerantsev V.N., Kukulin V.I., Faessler A., “Three-Body Breakup Within the Fully Discretized Faddeev Equations”, Phys. Rev. C, 86:3 (2012), 034004
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Konobeevski E.S., Zuyev S.V., Mordovskoy M.V., Potashev S.I., Sharapov I.M., “Neutron-Deuteron Breakup Reaction as a Tool for Studying Neutron-Neutron Interactions”, Phys. Atom. Nuclei, 76:11 (2013), 1398–1402
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Carbonell J., Deltuva A., Fonseca A.C., Lazauskas R., “Bound State Techniques to Solve the Multiparticle Scattering Problem”, Prog. Part. Nucl. Phys., 74 (2014), 55–80
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Pomerantsev V.N., Kukulin V.I., Rubtsova O.A., “New General Approach in Few-Body Scattering Calculations: Solving Discretized Faddeev Equations on a Graphics Processing Unit”, Phys. Rev. C, 89:6 (2014), 064008
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Papadimitriou G., Vary J.P., “Nucleon-Nucleon Scattering With the Complex Scaling Method and Realistic Interactions”, Phys. Rev. C, 91:2 (2015), 021001
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Rubtsova O.A. Kukulin V.I. Pomerantsev V.N., “Wave-Packet Continuum Discretization For Quantum Scattering”, Ann. Phys., 360 (2015), 613–654
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