Three-body equations for nuclear reactions
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.
- Research Organization:
- Alabama Univ., Birmingham (USA)
- OSTI ID:
- 5227146
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
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)