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TMF, 2015, Volume 182, Number 2, Pages 315–337 (Mi tmf8738)  

This article is cited in 2 scientific papers (total in 2 papers)

Effective-radius approximation in the problem of two-dimensional scattering by a central short-range potential

V. V. Pupyshev

Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

Abstract: We study the role of weakly bound and near-threshold resonance states of a quantum particle in its two-dimensional elastic low-energy scattering. The energies of such states are determined in the effective-radius approximation using the roots of transcendental equations. The same approximation is used to analyze scattering. We obtain and study the explicit low-energy asymptotic forms of all partial phases and cross sections. These asymptotic forms contain energies of weakly bound or near-threshold resonance states.

Keywords: two-dimensional scattering, short-range potential, weakly bound resonance state, near-threshold resonance state

DOI: https://doi.org/10.4213/tmf8738

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English version:
Theoretical and Mathematical Physics, 2015, 182:2, 264–283

Bibliographic databases:

Received: 19.06.2014
Revised: 12.08.2014

Citation: V. V. Pupyshev, “Effective-radius approximation in the problem of two-dimensional scattering by a central short-range potential”, TMF, 182:2 (2015), 315–337; Theoret. and Math. Phys., 182:2 (2015), 264–283

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf8738
  • https://doi.org/10.4213/tmf8738
  • http://mi.mathnet.ru/eng/tmf/v182/i2/p315

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    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:
    1. V. V. Pupyshev, “Two-dimensional Coulomb scattering of a quantum particle: Wave functions and Green's functions”, Theoret. and Math. Phys., 186:2 (2016), 213–230  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. V. Pupyshev, “The method of amplitude functions in two-dimensional scattering theory”, Theoret. and Math. Phys., 191:1 (2017), 499–523  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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