Covariant equations for the three-body bound state

Details Covariant equations for the three-body bound state Covariant equations for the three-body bound state

1997-03-19

arxiv.org/abs/nucl-th/9703043v1

Phys.Rev.C56:2396,1997

Physics

Nuclear Physics

Nuclear Theory

57 pages, RevTeX, 6 figures, uses epsf.sty

Scientific paper

10.1103/PhysRevC.56.2396

The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical solution. The equations are first written in operator form and compared to the Bethe-Salpeter equation, then expanded into plane wave momentum states, and finally expanded into partial waves using the three-body helicity formalism first introduced by Wick. In order to solve the equations, the two-body scattering amplitudes must be boosted from the overall three-body rest frame to their individual two-body rest frames, and all effects which arise from these boosts, including the Wigner rotations and rho-spin decomposition of the off-shell particle, are treated exactly. In their final form, the equations reduce to a coupled set of Faddeev-like double integral equations with additional channels arising from the negative rho-spin states of the off-shell particle.

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