TY - JOUR

T1 - Higher-order terms and the apparent non-convergence of the perturbation expansion for the effective interaction in finite nuclei

AU - Barrett, Bruce R.

AU - Kirson, Michael W.

PY - 1970/6/8

Y1 - 1970/6/8

N2 - 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.

AB - 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.

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U2 - 10.1016/0375-9474(70)90617-2

DO - 10.1016/0375-9474(70)90617-2

M3 - Article

AN - SCOPUS:0001707788

SN - 0375-9474

VL - 148

SP - 145

EP - 180

JO - Nuclear Physics, Section A

JF - Nuclear Physics, Section A

IS - 1

ER -