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The three-boson system with short-range interactions
Open accessAbstract
Abstract We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be summed, which leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in one local three-body force counterterm and compute the running of the three-body force with the cutoff. This allows a calculation of the scattering of a particle and the two-particle bound state if the corresponding scattering length is used as input. We also obtain a model-independent relation between binding energy of a shallow three-body bound state and this scattering length. We comment on the power counting that organizes higher-order corrections and on relevance of this result for the effective field theory program in nuclear and molecular physics.
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Citations
Cited by
Modern theory of nuclear forces
Epelbaum, E., Hammer, H.-W., & Meißner, U.-G. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.1773 · Cited by 1,883
Self-citationUniversality in few-body systems with large scattering length
Braaten, E., & Hammer, H.-W. (2006) · Physics Reports · doi:10.1016/j.physrep.2006.03.001 · Cited by 1,313
Self-citationNaidon, P., & Endo, S. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa50e8 · Cited by 474
θ -dependence of light nuclei and nucleosynthesis
Lee, D., Meißner, U.-G., Olive, K. A., Shifman, M., & Vonk, T. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033392 · Cited by 29
Metadata
- Authors
- Bedaque, P. F., Hammer, H.-W., & van Kolck, U.
- Venue
- Nuclear Physics A
- Publisher
- Elsevier BV
- Published
- 1999-02
- Volume
- 646
- Issue
- 4
- Pages
- 444-466
- ISSN
- 0375-9474 (ISSN-L)
- OpenAlex
- W2000930495
- Cited by
- 381
- References
- 0
- FWCI
- 9.71
- Type
- journal article
- Language
- en
- Open access
- green
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- Bedaque, P. F., Hammer, H.-W., & van Kolck, U. (1999). The three-boson system with short-range interactions. Nuclear Physics A. https://doi.org/10.1016/s0375-9474(98)00650-2
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