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TMF, 2007, Volume 150, Number 3, Pages 473–497 (Mi tmf5991)  

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: PDF file (658 kB)
References: PDF file   HTML file

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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\paper Wave-packet continuum discretization method for solving the~three-body
scattering problem
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\pages 473--497
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\pages 403--424
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  • http://mi.mathnet.ru/eng/tmf/v150/i3/p473

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  crossref  adsnasa  isi  scopus
    2. 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.  crossref  adsnasa  isi  elib  scopus
    3. 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.  crossref  adsnasa  isi  elib  scopus
    4. 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.  crossref  adsnasa  isi  elib  scopus
    5. JETP Letters, 90:5 (2009), 402–406  mathnet  crossref  isi  elib
    6. Stroe M., Fifirig M., “Electron-induced dissociation in $H_2^+$, $HD^+$ and $HT^+$”, Phys. Lett. A, 373:45 (2009), 4152–4157  crossref  zmath  adsnasa  isi  elib  scopus
    7. 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.  crossref  adsnasa  isi
    8. 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  isi
    9. 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  crossref  adsnasa  isi  scopus
    10. 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  crossref  adsnasa  isi  elib  scopus
    11. 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  crossref  adsnasa  isi  elib  scopus
    12. 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  crossref  adsnasa  isi  scopus
    13. 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  crossref  mathscinet  adsnasa  isi  scopus
    14. 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  crossref  adsnasa  isi  scopus
    15. Papadimitriou G., Vary J.P., “Nucleon-Nucleon Scattering With the Complex Scaling Method and Realistic Interactions”, Phys. Rev. C, 91:2 (2015), 021001  crossref  adsnasa  isi  scopus
    16. Rubtsova O.A. Kukulin V.I. Pomerantsev V.N., “Wave-Packet Continuum Discretization For Quantum Scattering”, Ann. Phys., 360 (2015), 613–654  crossref  mathscinet  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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