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Three-body scattering problem in the fixed center approximation: The case of attraction

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Abstract.

We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous --they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, introducing a finite cut-off. We show that all three approaches are equivalent. We also discuss how our approach to the problem matches with the introduction of three-body contact interaction as done by other authors.

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Authors and Affiliations

  1. Institute for Theoretical and Experimental Physics, National Research Center Kurchatov Institute, 117218, Moscow, Russia

    Alexander E. Kudryavtsev & Vakhid A. Gani

  2. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Moscow, Russia

    Vakhid A. Gani & Alexander I. Romanov

Authors
  1. Alexander E. Kudryavtsev
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  2. Vakhid A. Gani
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  3. Alexander I. Romanov
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Corresponding author

Correspondence to Vakhid A. Gani.

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Communicated by A. Ramos

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Kudryavtsev, A.E., Gani, V.A. & Romanov, A.I. Three-body scattering problem in the fixed center approximation: The case of attraction. Eur. Phys. J. A 52, 358 (2016). https://doi.org/10.1140/epja/i2016-16358-8

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  • DOI: https://doi.org/10.1140/epja/i2016-16358-8

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