Abstract
The resonating group model is reformulated by splitting the microscopic interaction into a dominant part and a residual part. In the equal-width oscillator limit, the dominant part leads to a very simple exchange kernel. In norm kernel eigenstate representation, this kernel has a peculiar, fish bone like symmetry. For the evaluation of the residual interaction, only two-body matrix elements are needed. A physical interpretation of the fish bone symmetry is given in terms of the reflection property of a fermi sphere with a diffuse surface. An optical model is proposed in which the influence of partly Pauli-forbidden states on the observables is described by the fish bone symmetry of the interaction. It is speculated that fish bone symmetry might be the key to a better understanding of hadronic interactions.
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References
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Horiuchi, H. has used a similar technique in [12] to derive the resonating group equation in harmonic oscillator representation. The present derivation differs by the special treatment of the noncompact part of the equation and by the splitting of the microscopic interaction into a dominant part and a residual part. The appearance of the fish bone matrixM is a result of this splitting
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Discussions with Professors G. Cattapan, H.P. Noyes and S. Oryu are gratefully acknowledged. I also want to thank my collaborators K. Hahn, R. Kircher, Dr. H. Leeb, Dr. M. Orlowski and G. Spitz, who are currently working on numerical applications of the theory, for discussions and help.
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Schmid, E.W. The two-cluster “fish bone” model. Z Physik A 297, 105–114 (1980). https://doi.org/10.1007/BF01421466
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DOI: https://doi.org/10.1007/BF01421466