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A New Approach to the 3D Faddeev Equation for Three-body Scattering

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Abstract

A novel approach to solve the Faddeev equation for three-body scattering at arbitrary energies is proposed. This approach disentangles the complicated singularity structure of the free three-nucleon propagator leading to the moving and logarithmic singularities in standard treatments. The Faddeev equation is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation for identical bosons, which we are using, is an integral equation in five variables, magnitudes of relative momenta and angles. The singularities of the free propagator and the deuteron propagator are now both simple poles in two different momentum variables, and thus can both be integrated with standard techniques.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Institute of Nuclear and Particle Physics, Ohio University, Athens, OH, 45701, USA

    Ch. Elster

  2. Institute for Theoretical Physics II, Ruhr-University Bochum, 44780, Bochum, Germany

    W. Glöckle

  3. M. Smoluchowski Institute of Physics, Jagiellonian University, 30059, Kraków, Poland

    H. Witała

Authors
  1. Ch. Elster
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  2. W. Glöckle
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  3. H. Witała
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Correspondence to Ch. Elster.

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Elster, C., Glöckle, W. & Witała, H. A New Approach to the 3D Faddeev Equation for Three-body Scattering. Few-Body Syst 45, 1–10 (2009). https://doi.org/10.1007/s00601-008-0003-6

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  • DOI: https://doi.org/10.1007/s00601-008-0003-6

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