Contributions from high-momentum intermediate states to effective nucleon-nucleon interactions

We reexamine the intermediate state convergence problem for the core polarization diagram ($G_{3\mathrm{p}1\mathrm{h}}$) in the expansion of an effective shell-model interaction using a modern meson exchange Bonn-Jülich potential in comparison to the phenomenological Reid soft-core interaction. The Bonn-Jülich $N-N$ potential contains a much weaker tensor force as compared with the Reid soft-core interaction. As a consequence its repulsive contributions to $G_{3\mathrm{p}1\mathrm{h}}$ from high momentum intermediate particle states are much reduced and $G_{3\mathrm{p}1\mathrm{h}}$ can be calculated in a good approximation with $2\hslash \omega$ particle-hole excitations alone. This opens up the possibility of calculating higher order processes in a reliable and expendient way. We have further determined the spectra of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ using the folded diagram perturbation theory to determine the effective interaction. The energy levels are best reproduced by the Bonn-Jülich $N-N$ potential.