Ground state properties of medium-heavy nuclei with a realistic interaction

Abstract

The Brueckner $G$ matrix appropriate for medium-heavy nuclei is obtained from the Reid soft-core nucleon-nucleon potential. The $G$ matrix is strongly affected by the Pauli operator $Q$, which is treated exactly (no angle averaging). Within the range of valence space energies $G$ has a weak dependence on the starting energy $\ensuremath{\omega}$. Ground state properties of deformed rare earth nuclei ($Z=64\ensuremath{-}76,N=90\ensuremath{-}102$) and spherical semimagic nuclei ($\mathrm{Sn},\mathrm{Pb},N=82,N=126$) have been calculated in the Hartree-Fock-Bogoliubov approximation with an inert core of 110 nucleons. Deformations and pair gaps are both determined by the $G$ matrix. The systematic experimental dependence of ${\ensuremath{\epsilon}}_{\mathrm{spherical}}$, ${\ensuremath{\beta}}_{2}$, ${\ensuremath{\beta}}_{4}$, ${\ensuremath{\Delta}}_{p}$, ${\ensuremath{\Delta}}_{n}$, and ${E}_{\mathrm{po}}$ (prolate-oblate energy difference) on $N$ and $Z$ is reproduced. However, the magnitudes of ${\ensuremath{\beta}}_{2}$, ${\ensuremath{\Delta}}_{n}$, and ${E}_{\mathrm{po}}$ are too small. This may be largely due to the lack of isospin dependence of the oscillator basis states. ${\ensuremath{\beta}}_{2}$ and ${E}_{\mathrm{po}}$ could receive additional significant contributions from core polarization of the 110 particle core which is neglected here. The Hartree-Fock-Bogoliubov ground states obtained with this realistic interaction provide a reasonable foundation for high spin calculations.NUCLEAR STRUCTURE Brueckner reaction matrix; Hartree-Fock-Bogoliubov theory; ground state properties of medium-heavy nuclei.