Converged values of second-order core-polarization diagrams with orthogonalized-plane-wave intermediate states

C. L. Kung, T. T. S. Kuo, and K. F. Ratcliff
Phys. Rev. C 19, 1063 – Published 1 March 1979
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Abstract

We carry out an extended study of the Vary-Sauer-Wong effect on the second-order core-polarization diagrams G3p1h and G3p1hT in the effective interaction between two valence nucleons. As in Vary-Sauer-Wong, we first calculate G3p1h using a harmonic oscillator propagator for the intermediate particle states p, including particle-hole excitations with energies up to 22ω. Results are in close agreement with those of Vary-Sauer-Wong. We then calculate G3p1hT where a free particle propagator for p is used. This is obtained by including the U, the oscillator one-body potential, insertions of all orders to p of G3p1h. Although the resulting matrix elements are generally smaller in magnitude than those of Vary-Sauer-Wong, the qualitative feature of the Vary-Sauer-Wong effect is clearly maintained. Namely there are strong cancellations between the contributions from the low and high energy p states. This makes the net effect from the core polarization diagrams significantly weaker than from G3p1h calculated with 2ω excitations alone. We also study some intermediate choices for the propagator of p, where the free particle propagator is used only for high energy valence states. The Brueckner reaction matrix elements in a mixed representation where one particle is in a harmonic oscillator state and the other in a plane wave state are needed in our calculations. By using the vector transformation brackets of Wong and Clement and of Balian and Brezin and the Tsai-Kuo treatment of the Pauli exclusion operator, we have developed a technique for accurately calculating these matrix elements.

NUCLEAR STRUCTURE Contributions to effective interaction for A=18 nuclei calculated from converged values of lowest order core polarization diagrams as function of intermediate state propagator using new momentum space techniques.

  • Received 7 August 1978

DOI:https://doi.org/10.1103/PhysRevC.19.1063

©1979 American Physical Society

Authors & Affiliations

C. L. Kung and T. T. S. Kuo

  • Physics Department, State University of New York at Stony Brook, Stony Brook, New York 11794

K. F. Ratcliff

  • Physics Department, State University of New York at Albany, Albany, New York 12222

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Vol. 19, Iss. 3 — March 1979

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