dorsal/arxiv
View SchemaCovariant equations for the three-body bound state
| Authors | Alfred Stadler, Franz Gross, Michael Frank |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9703043 |
| URL | https://arxiv.org/abs/nucl-th/9703043 |
| DOI | 10.1103/PhysRevC.56.2396 |
| Journal | Phys.Rev.C56:2396,1997 |
Abstract
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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"abstract": "The covariant spectator (or Gross) equations for the bound state of three\nidentical spin 1/2 particles, in which two of the three interacting particles\nare always on shell, are developed and reduced to a form suitable for numerical\nsolution. The equations are first written in operator form and compared to the\nBethe-Salpeter equation, then expanded into plane wave momentum states, and\nfinally expanded into partial waves using the three-body helicity formalism\nfirst introduced by Wick. In order to solve the equations, the two-body\nscattering amplitudes must be boosted from the overall three-body rest frame to\ntheir individual two-body rest frames, and all effects which arise from these\nboosts, including the Wigner rotations and rho-spin decomposition of the\noff-shell particle, are treated exactly. In their final form, the equations\nreduce to a coupled set of Faddeev-like double integral equations with\nadditional channels arising from the negative rho-spin states of the off-shell\nparticle.",
"arxiv_id": "nucl-th/9703043",
"authors": [
"Alfred Stadler",
"Franz Gross",
"Michael Frank"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.56.2396",
"journal_ref": "Phys.Rev.C56:2396,1997",
"title": "Covariant equations for the three-body bound state",
"url": "https://arxiv.org/abs/nucl-th/9703043"
},
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