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On the Uniqueness of the Solution to the Three-Body Problem with Zero-Range Interactions

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Abstract.

We consider the uniqueness of the solution to a three-body problem with zero-range Skyrme interactions in configuration space. With the lowest, k0, two-body term alone the problem is known to have no unique solution as the system collapses – the variational estimate of the energy tends towards negative infinity, the size of the system towards zero. We argue that the next, k2, two-body term removes the collapse and the three-body system acquires finite ground-state energy and size. The three-body interaction term is thus not necessary to provide a unique solution to the problem.

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  1. Department of Physics and Astronomy, University of Aarhus, 8000, Aarhus C, Denmark

    D. V. Fedorov & A. S. Jensen

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  1. D. V. Fedorov
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  2. A. S. Jensen
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Fedorov, D., Jensen, A. On the Uniqueness of the Solution to the Three-Body Problem with Zero-Range Interactions. Few-Body Systems 38, 75–78 (2006). https://doi.org/10.1007/s00601-006-0150-6

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  • DOI: https://doi.org/10.1007/s00601-006-0150-6

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