Perturbation theory for the effective interaction in nuclei |
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Authors: | Thomas H Schucan Hans A Weidenmüller |
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Affiliation: | Schweizerisches Institut für Nuklearforschung, Zürich, Switzerland;Seminar für Theoretische Physik, Swiss Federal Institute of Technology, Zürich, Switzerland |
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Abstract: | Starting from a decomposition of the Hamiltonian H(x) of the nuclear many-body problem in the form H(x) = H0 + xV, where H0 is a shell-model Hamiltonian, V the residual interaction, and x a strength parameter, we introduce a general effective interaction W(x) describing the interaction of nucleons within a shell, and the associated effective operators . We display some properties of these operators. From a particular choice of W(x) we obtain the expressions introduced earlier by several authors. The convergence of the expansions for W(x) and in powers of x is investigated. It is shown that W(x) and are holomorphic in a domain of the complex x-plane including the point x = 0. With the help of a generalization of the von Neumann-Wigner noncrossing rule, we exhibit the nature of the common singularity of W(x) and which is closest to the origin and thus defines the radius r0 of convergence of the expansions of W and . It is shown that r0 is unaffected by the cancellation of unlinked diagrams. A criterion of consistency is established, which shows that most of the practical calculations of W lead to results which are inconsistent with the definition of W. |
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