Boundary-Condition Constraints for the Shell Model: A Method for Nuclear Structure and Nuclear Reactions

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Abstract
It is proposed that the asymptotic boundary conditions be used as constraints for shell-model calculations. Two formalisms which permit this to be done are presented. In one formalism the boundary conditions are introduced as constraints in a variational principle. In the other formalism Green's theorem is used to make the dependence on the boundary conditions explicit. The use of boundary-condition constraints permits the use of the shell-model method for scattering and reactions as well as for nuclear-structure calculations. It is suggested that the constrained-shell-model method will improve the representation of the nuclear surface and will provide the basis for a truly unified treatment of nuclear reactions. In such a unified treatment compound-nucleus resonances, direct-reaction transitions, and optical-model scattering will be generated from a single, fairly fundamental model.

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