Minimally coupled N-particle scattering integral equations
Journal Article
·
· Phys. Rev., C; (United States)
A concise formalism is developed which permits the efficient representation and generalization of several known techniques for deriving connected-kernel N-particle scattering integral equations. The methods of Kouri, Levin, and Tobocman and Bencze and Redish which lead to minimally coupled integral equations are of special interest. The introduction of channel coupling arrays is characterized in a general manner and the common base of this technique and that of the so-called channel coupling scheme is clarified. It is found that in the Bencze-Redish formalism a particular coupling array has a crucial function but one different from that of the arrays employed by Kouri, Levin, and Tobocman. The apparent dependence of the proof of the minimality of the Bencze-Redish integral equations upon the form of the inhomogeneous term in these equations is eliminated. This is achieved by an investigation of the full (nonminimal) Bencze-Redish kernel. It is shown that the second power of this operator is connected, a result which is needed for the full applicability of the Bencze-Redish formalism. This is used to establish the relationship between the existence of solutions to the homogeneous form of the minimal equations and eigenvalues of the full Bencze-Redish kernel.
- Research Organization:
- Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106
- OSTI ID:
- 7304307
- Journal Information:
- Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 16:1; ISSN PRVCA
- Country of Publication:
- United States
- Language:
- English
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