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

摘要: Arguments are given for preferring discrete localized excited single-particle states to plane waves in Brueckner theory finite nuclei. Short-range internuclear repulsion requires transforming pair relative and c.m. coordinates, which only constant harmonic potentials separate. This series of papers develops a form expanded harmonic-oscillator functions. paper is limited the single-oscillator-configuration (SOC) approximation. The reaction matrix obtained two steps: A reference matrix, involving potential ${V}^{R}({r}_{1})=\ensuremath{-}C+\frac{1}{2}m{\ensuremath{\omega}}^{2}{{r}_{1}}^{2}$ Eden Emery's rather good approximate Pauli operator, by solving radial Bethe-Goldstone equations. off-diagonal elements tensor interaction treated exactly coupled Second, essentially exact SOC calculated; making spectral corrections on two-body than operator can be used, energies low-lying varied (e.g., satisfy self-consistency conditions). much smaller when effect omitted entirely matrix. By proper choice $C$, also may reduced. Three interactions with hard cores compared under same conditions. gap between occupied greater $\frac{3}{2}$ normal oscillator spacing $\ensuremath{\hbar}\ensuremath{\omega}$. Occupied-state pair-creation ${V}^{R}$ made nearly self-consistent. three practically equivalent, as demonstrated calculation energetics $^{16}\mathrm{O}$. most advantageous excited-state spectrum remains outstanding uncertainty, probably requiring careful evaluation Bethe three-body cluster