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Nuclear Theory

arXiv:1606.02259 (nucl-th)
[Submitted on 7 Jun 2016 (v1), last revised 7 Dec 2016 (this version, v3)]

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

Authors: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.
Comments: 7 pages, 3 figures; v3: figures slightly changed, minor changes to match version published in EPJ A
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)
Cite as: arXiv:1606.02259 [nucl-th]
  (or arXiv:1606.02259v3 [nucl-th] for this version)
  https://doi.org/10.48550/arXiv.1606.02259
Journal reference: Eur. Phys. J. A 52, 358 (2016)
Related DOI: https://doi.org/10.1140/epja/i2016-16358-8

Submission history

From: Vakhid Gani [view email]
[v1] Tue, 7 Jun 2016 18:47:32 UTC (19 KB)
[v2] Tue, 21 Jun 2016 06:51:16 UTC (19 KB)
[v3] Wed, 7 Dec 2016 16:28:52 UTC (31 KB)
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