Higher-order terms and the apparent non-convergence of the perturbation expansion for the effective interaction in finite nuclei

Bruce R. Barrett, Michael W. Kirson

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Abstract

We have calculated all significant terms through third order in the reaction matrix G which contribute to the perturbation series for the J = 0, T = 1 effective interaction between two valence nucleons in the mass-18 nuclei and also a few selected fourth-order terms. We have shown that the perturbation series does not converge order-by-order to third order in G and that certain large third-order terms tend to cancel the second-order contribution. An intuitive physical picture of the process giving rise to this effect and to analogous effects in related calculations of the effective charge is given. This picture suggests a rearrangement of the perturbation series into physically significant groups of diagrams, so that each group converges order-by-order in G. However, one must then find some way to sum all these groups of diagrams. We conclude that simple perturbation theory is not a reliable method for calculating the effective two-nucleon interaction in mass-18 nuclei, when currently standard calculational techniques are used, and that the success of first- plus second-order perturbation theory in fitting experimental spectra for these nuclei is unexplained.

Original languageEnglish (US)
Pages (from-to)145-180
Number of pages36
JournalNuclear Physics, Section A
Volume148
Issue number1
DOIs
StatePublished - Jun 8 1970

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ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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