The Kuo–Brown effective interaction: From 18O to the Sn isotopes

After briefly reviewing the pioneering work on effective interactions by Gerry Brown and his group, and the developments which followed, we apply present-day effective interactions to large-scale shell-model calculations on the entire range of Sn isotopes from 102Sn to 132Sn. We have made explorative calculations starting from three different nucleon–nucleon potentials (Argonne V18, CD-Bonn, and N3LO) and evaluated the higher-order contributions to the effective interaction from both G  -matrix and VlowkVlowk interactions. Further, we have checked the convergence of intermediate-state excitations up to 10ħω10ħω harmonic oscillator energy. Final extensive calculations were made of binding energies, excitation energies and B(E2) transition rates using an effective interaction based on a G  -matrix evaluated from the chiral N3LO potential and including intermediate excitations up to 10ħω10ħω harmonic oscillator energy. The energy spectra are well reproduced throughout the region while overbinding of the ground states emerges as valence nucleons are added. The B(E2) rates agree well for the heavy isotopes, while they seem too low for the lighter ones.