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 nonrelativistic 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 is studied in detail.Method: Relativistic invariance is incorporated within the framework of Poincar\'e 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 nonrelativistic 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.