Three-body equations for nuclear reactions

Chao, S H

Title: Three-body equations for nuclear reactions

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Abstract

The problem of calculating three-body differential cross sections for two-body interactions which are local in configuration space is considered. The integral equations of Faddeev and recent modifications are reviewed. The difficulties both in solving and interpreting the various equations are discussed. An alternative set of exact operator equations is proposed. This new set of operator equations involve the two-body potentials directly rather than the two-body t-matrices. The solutions represent quantities different from those of previous equations. The formal structure of the operator equations is similar to but different from the Faddeev equations. It is demonstrated that the equations contain no terms which correspond to disconnected diagrams. The transformation of the equations to the Faddeev equations is given. Integral equations are obtained using the momentum representation. Only Cauchy-type singularities occur in the Green's function, and the equations have unique solutions. No off-energy shell t-matrices are required. Transition amplitudes are obtained from the solutions by quadrature, so that effects which result from the nature of the final state can be separated from the three-body effects. The angular momentum reduction of Omnes is used to obtain two-dimensional coupled integral equations. A method of numerical solution is developed using a generalization of the approximatemore »« less

Authors:: Chao, S H

Publication Date:: Tue Jan 01 00:00:00 EST 1980

Research Org.:: Alabama Univ., Birmingham (USA)

OSTI Identifier:: 5227146

Resource Type:: Thesis/Dissertation

Resource Relation:: Other Information: Thesis (Ph. D.)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; DEUTERON REACTIONS; ELASTIC SCATTERING; STRIPPING; NUCLEAR REACTIONS; THREE-BODY PROBLEM; OXYGEN 16 TARGET; ANALYTICAL SOLUTION; NUMERICAL SOLUTION; DIFFERENTIAL CROSS SECTIONS; FADDEEV EQUATIONS; CHARGED-PARTICLE REACTIONS; CROSS SECTIONS; DIRECT REACTIONS; EQUATIONS; MANY-BODY PROBLEM; SCATTERING; TARGETS; TRANSFER REACTIONS; 653003* - Nuclear Theory- Nuclear Reactions & Scattering; 651315 - Nuclear Properties & Reactions, A=6-19, Theoretical- Nuclear Reactions & Scattering- (-1987)

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                    Chao, S H. Three-body equations for nuclear reactions.  United States: N. p., 1980. 
        Web.

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                    Chao, S H. Three-body equations for nuclear reactions.  United States.

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                    Chao, S H. 1980.  
        "Three-body equations for nuclear reactions".  United States.

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@article{osti_5227146,

  title        = {Three-body equations for nuclear reactions},

  author       = {Chao, S H},

  abstractNote = {The problem of calculating three-body differential cross sections for two-body interactions which are local in configuration space is considered. The integral equations of Faddeev and recent modifications are reviewed. The difficulties both in solving and interpreting the various equations are discussed. An alternative set of exact operator equations is proposed. This new set of operator equations involve the two-body potentials directly rather than the two-body t-matrices. The solutions represent quantities different from those of previous equations. The formal structure of the operator equations is similar to but different from the Faddeev equations. It is demonstrated that the equations contain no terms which correspond to disconnected diagrams. The transformation of the equations to the Faddeev equations is given. Integral equations are obtained using the momentum representation. Only Cauchy-type singularities occur in the Green's function, and the equations have unique solutions. No off-energy shell t-matrices are required. Transition amplitudes are obtained from the solutions by quadrature, so that effects which result from the nature of the final state can be separated from the three-body effects. The angular momentum reduction of Omnes is used to obtain two-dimensional coupled integral equations. A method of numerical solution is developed using a generalization of the approximate product integration method due to Young. Examples corresponding to the reactions /sup 16/O(d,p)/sup 17/O g.s and /sup 16/O(d,d)/sup 16/O in two dimensions and /sup 16/O(d,p)/sup 17/O* (0.87 MeV) in three dimensions for a deuteron enegy of 5 MeV are considered using Gaussian potentials. The convergence of the summation over angular momentum is examined and a comparison is made with experiment to obtain the spectroscopic factor for the 0.87 MeV state of /sup 17/O.},

  doi          = {},

  url          = {https://www.osti.gov/biblio/5227146},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Tue Jan 01 00:00:00 EST 1980},

  month        = {Tue Jan 01 00:00:00 EST 1980}

}

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