Covariant equations for the three-body bound state

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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, ... continued below

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Stadler, A.; Gross, F. & Frank, M. March 1997.

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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 Wigner rotations and p-spin decomposition of the 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 p-spin states of the off-shell particle.

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1461 Kilobytes pages

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  • Report No.: DOE/ER/40150-1545
  • Report No.: JLAB-THY-97-09
  • Report No.: WM-97-105
  • Report No.: CNFUL-97-01
  • Report No.: nucl-th/9703043
  • Grant Number: AC05-84ER40150
  • Office of Scientific & Technical Information Report Number: 756284
  • Archival Resource Key: ark:/67531/metadc702218

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Office of Scientific & Technical Information Technical Reports

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Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • March 1997

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  • Sept. 12, 2015, 6:31 a.m.

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  • Feb. 5, 2016, 8:47 p.m.

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Stadler, A.; Gross, F. & Frank, M. Covariant equations for the three-body bound state, article, March 1997; Newport News, Virginia. (digital.library.unt.edu/ark:/67531/metadc702218/: accessed October 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.