Brueckner Theory in an Oscillator Basis. I. The Method of Reference Bethe-Goldstone Equations and Comparison of the Yale, Reid (Hard-Core), and Hamada-Johnston Interactions
- 20 October 1968
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 174 (4), 1264-1290
- https://doi.org/10.1103/physrev.174.1264
Abstract
Arguments are given for preferring discrete localized excited single-particle states to plane waves in Brueckner theory for finite nuclei. Short-range internuclear repulsion requires transforming pair states to relative and c.m. coordinates, in which only constant and harmonic potentials separate. This series of papers develops a form of Brueckner theory in which single-particle states are expanded in harmonic-oscillator functions. This paper is limited to the single-oscillator-configuration (SOC) approximation. The reaction matrix is obtained in two steps: A reference matrix, involving the potential and Eden and Emery's rather good approximate Pauli operator, is obtained by solving radial Bethe-Goldstone equations. The off-diagonal elements of the tensor interaction are treated exactly in coupled equations. Second, essentially the exact SOC matrix is calculated; by making the Pauli and spectral corrections on the reference two-body rather than the relative matrix elements the exact SOC Pauli operator can be used, and energies of low-lying excited states can be varied (e.g., to satisfy self-consistency conditions). The Pauli corrections are much smaller than when the Pauli effect is omitted entirely in the reference matrix. By proper choice of , the spectral corrections also may be reduced. Three interactions with hard cores are compared under the same conditions. The gap between occupied and excited states is greater than the normal oscillator spacing . Occupied-state energies and pair-creation matrix elements of are made nearly self-consistent. The three interactions are practically equivalent, as demonstrated in a calculation of the energetics of . The most advantageous choice of excited-state spectrum remains the outstanding uncertainty, probably requiring careful evaluation of the Bethe three-body cluster for finite nuclei.
Keywords
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