Microscopic calculations of the spectra of light nuclei

We perform large-space shell-model calculations for the low-lying energy spectra of a few light nuceli${,}^4$He, ${}_{}{}^5{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, in a no-core model space with a realistic effective two-body interaction (Brueckner G matrix). Our G matrices are calculated for the Reid-soft-core potential in a harmonic-oscillator basis. Single-particle ‘‘-U’’ insertions are replaced by two-particle ‘‘-U’’ insertions and are included in the G-matrix calculations, which sum them to all orders. With the starting energy of the G matrix chosen to give approximately the experimental binding energy, we obtain nuclear energy spectra which are in reasonable agreement with experiment. We also investigate the dependence of our results on the size of the model space and on the harmonic-oscillator basis parameter (ħΩ).