Three-body scattering problem in the fixed center approximation: the case of attraction
arXiv:1606.02259 · doi:10.1140/epja/i2016-16358-8
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.
7 pages, 3 figures; v3: figures slightly changed, minor changes to match version published in EPJ A
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