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

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 $\omega$. Ground state properties of deformed rare earth nuclei ($Z=64\mathrm{}-76,N=90\mathrm{}-102$) and spherical semimagic nuclei ($\mathrm{Sn},\mathrm{Pb},N=82,N=126\mathrm{}$) 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 ${\epsilon }_{\mathrm{spherical}}$, ${\beta }_2$, ${\beta }_4$, ${\Delta }_p$, ${\Delta }_n$, and $E_{\mathrm{po}}$ (prolate-oblate energy difference) on $N$ and $Z$ is reproduced. However, the magnitudes of ${\beta }_2$, ${\Delta }_n$, and $E_{\mathrm{po}}$ are too small. This may be largely due to the lack of isospin dependence of the oscillator basis states. ${\beta }_2$ 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.