Covariant equations for the three-body bound state
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 {ital 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. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 365350
- Journal Information:
- Physical Review, C, Journal Name: Physical Review, C Journal Issue: 5 Vol. 56; ISSN 0556-2813; ISSN PRVCAN
- Country of Publication:
- United States
- Language:
- English
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