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

TL;DR

This paper presents a relativistic three-body bound state calculation using a 3D momentum-space approach, revealing small overall effects but significant individual relativistic contributions in the wave function.

Contribution

It introduces a direct 3D formulation of the relativistic Faddeev equation without partial-wave decomposition, providing new insights into relativistic effects in three-body systems.

Findings

Relativistic binding energy is about 3% smaller than non-relativistic.

Relativistic effects manifest in the Fermi motion of the spectator.

Individual relativistic effects are significant despite small overall impact.

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{\'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 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.