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arXiv · 1606.02259

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

Alexander E. Kudryavtsev·Vakhid A. Gani·Alexander I. Romanov
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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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Alexander E. Kudryavtsev, Vakhid A. Gani, Alexander I. Romanov. 2016-12-07. Three-body scattering problem in the fixed center approximation: the case of attraction. https://doi.org/10.1140/epja%2Fi2016-16358-8

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