The Relativistic Three-Body Bound State in a 3D Formulation

Abstract

Background: The relativistic three-body problem has a long tradition in few-nucleon physics. Calculations of the triton binding energy based on the solution of the relativistic Faddeev equation in general lead to a weaker binding than the corresponding non-relativistic calculation. Purpose: In this work we solve for the three-body binding energy as well as the wave function and its momentum distribution. The effect of the different relativistic ingredients are studied in detail. Method: Relativistic invariance is incorporated within the framework of Poincar{é} invariant quantum mechanics. The relativistic momentum-space Faddeev equation is formulated and directly solved in terms of momentum vectors without employing a partial-wave decomposition. Results: The relativistic calculation gives a three-body binding energy which is about 3% smaller than its non-relativistic counterpart. In the wave function, relativistic effects are manifested in the Fermi motion of the spectator particle. Conclusions: Our calculations show that though the overall relativistic effects in the three-body bound state are small, individual effects by themselves are not necessarily small and must be taken into account consistently.

arXiv comment20 pages, 1 table and 6 figures

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Cited by in corpus (12)

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• The charge and mass symmetry breaking in the $KK\bar{K}$ system
• The Relativistic Three-Body Bound State in Three-Dimensions
• Representations of relativistic particles of arbitrary spin in Poincaré, Lorentz, and Euclidean covariant formulations of relativistic quantum mechanics
• Relativistic nucleon-nucleon potentials in a spin-dependent three-dimensional approach
• Four-body bound states in momentum space: the Yakubovsky approach without two-body $t-$matrices
• Relativistic Faddeev 3D Equations for Three-Body Bound States Without Two-Body $t-$Matrices
• Comment on "Three-dimensional study of the six-body bound-state for the case of effective three-body configuration model" [Int. J. Mod. Phys. E 25, 9 (2016) 1650072]
• Three-boson stability for boosted interactions towards the zero-range limit