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

Abstract

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-J\"ulich potential in comparison to the phenomenological Reid soft-core interaction. The Bonn-J\"ulich $N\ensuremath{-}N$ 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 $2\ensuremath{\hbar}\ensuremath{\omega}$ 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-J\"ulich $N\ensuremath{-}N$ potential.NUCLEAR STRUCTURE $^{18}\mathrm{O}$, $^{18}\mathrm{F}$; dependence of effective interaction on $N\ensuremath{-}N$ tensor force. Convergence of intermediate state summation in core polarization.