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arXiv · 1409.1650

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

M. R. Hadizadeh·Ch. Elster·W. N. Polyzou
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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.

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M. R. Hadizadeh, Ch. Elster, W. N. Polyzou. 2014-09-05. The Relativistic Three-Body Bound State in a 3D Formulation. https://doi.org/10.1103/physrevc.90.054002

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