V. I. Kukulin, O. A. Rubtsova, “Discrete Quantum Scattering Theory”, TMF, 134:3 (2003), 460–486; Theoret. and Math. Phys., 134:3 (2003), 404

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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 134, Number 3, Pages 460–486
DOI: https://doi.org/10.4213/tmf165 (Mi tmf165)

This article is cited in 16 scientific papers (total in 16 papers)

Discrete Quantum Scattering Theory

V. I. Kukulin, O. A. Rubtsova

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Full-text PDF (371 kB) Citations (16)

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DOI: https://doi.org/10.4213/tmf165

Abstract: We formulate quantum scattering theory in terms of a discrete $L_2$-basis of eigen differentials. Using projection operators in the Hilbert space, we develop a universal method for constructing finite-dimensional analogues of the basic operators of the scattering theory: $S$- and $T$-matrices, resolvent operators, and Möller wave operators as well as the analogues of resolvent identities and the Lippmann–Schwinger equations for the $T$-matrix. The developed general formalism of the discrete scattering theory results in a very simple calculation scheme for a broad class of interaction operators.

Keywords: quantum scattering theory, wave packets, Green's function, wave operator, $T$-matrix, discretization of continuum.

Received: 11.03.2002

English version:
Theoretical and Mathematical Physics, 2003, Volume 134, Issue 3, Pages 404–426
DOI: https://doi.org/10.1023/A:1022657607306

Bibliographic databases:

Language: Russian

Citation: V. I. Kukulin, O. A. Rubtsova, “Discrete Quantum Scattering Theory”, TMF, 134:3 (2003), 460–486; Theoret. and Math. Phys., 134:3 (2003), 404–426

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf165

https://doi.org/10.4213/tmf165

https://www.mathnet.ru/eng/tmf/v134/i3/p460

This publication is cited in the following 16 articles:

Miller S.B.S. Ekstrom A. Forssen Ch., “Wave-Packet Continuum Discretisation For Nucleon-Nucleon Scattering Predictions”, J. Phys. G-Nucl. Part. Phys., 49:2 (2022), 024001
Rubtsova O.A. Kukulin V.I. Pomerantsev V.N., “Wave-Packet Continuum Discretization For Quantum Scattering”, Ann. Phys., 360 (2015), 613–654
Kelvich S.A., Kukulin V.I., Rubtsova O.A., “Path Toward Fast Calculations in Quantum Scattering Theory”, Phys. Atom. Nuclei, 77:4 (2014), 438–445
Pupyshev, VV, “Generalizations of the Fock and Kato expansions to systems of three quantum particles”, Physics of Particles and Nuclei, 40:4 (2009), 391
JETP Letters, 90:5 (2009), 402–406
Rubtsova, OA, “Quantum scattering theory on the momentum lattice”, Physical Review C, 79:6 (2009), 064602
Pomerantsev V.N., Kukulin V.I., Rubtsova O.A., “Solving three-body scattering problems in the momentum lattice representation”, Physical Review C, 79:3 (2009), 034001
O. A. Rubtsova, V. I. Kukulin, V. N. Pomerantsev, “Microscopic theory of nuclear reactions based on the wave-packet technique”, Bull. Russ. Acad. Sci. Phys., 73:6 (2009), 750
Rubtsova OA, Kukulin VI, Moro AM, “Continuum discretization methods in a composite particle scattering off a nucleus: Benchmark calculations”, Physical Review C, 78:3 (2008), 034603
V. I. Kukulin, V. N. Pomerantsev, O. A. Rubtsova, “Wave-packet continuum discretization method for solving the three-body scattering problem”, Theoret. and Math. Phys., 150:3 (2007), 403–424
Rubtsova OA, Kukulin VI, “Wave-packet discretization of a continuum: Path toward practically solving few-body scattering problems”, Physics of Atomic Nuclei, 70:12 (2007), 2025–2045
Kukulin VI, Rubtsova OA, “Elastic scattering on a nucleus and the breakup of the composite projectile via wave-packet continuum discretization”, Physical Review C, 76:4 (2007), 047601
The Mathematica GuideBook for Symbolics, 2006, 978
V. I. Kukulin, O. A. Rubtsova, “Solving the Charged-Particle Scattering Problem by Wave Packet Continuum Discretization”, Theoret. and Math. Phys., 145:3 (2005), 1711–1726
V. I. Kukulin, O. A. Rubtsova, “Finite-Dimensional Approximations for Scattering Theory Operators in the Wave-Packet Representation”, Theoret. and Math. Phys., 139:2 (2004), 693–705
Nunes FM, Mukhamedzhanov AM, Rosa CC, et al, “Insight into continuum couplings”, Nuclear Physics A, 736:3–4 (2004), 255–268

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

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