Test of shell-model interactions for nuclear structure calculations.
The binding energy and excitation spectra of 6Li are calculated in a no-core shell-model space giving encouraging results. The results of this calculation are then treated as a theoretical experiment, against which different effective-interaction approximations are compared. In this way insight into the perturbation expansion for the effective interaction is obtained.
Comparison of the effective interaction to various orders in different mass regions
The convergence of the perturbation expansion for the effective interaction to be used in shell-model calculations is investigated as a function of the mass number A, from A = 4 to A = 208. As the mass number increases, there are more intermediate states to sum over in each higher-order diagram which contributes to the effective interaction. Together with the fact that the energy denominators in each diagram are smaller for larger mass numbers, these two effects could largely enhance higher-order contributions to the effective interaction, thereby deteriorating the order-by-order convergence of the effective interaction. This effect is counterbalanced by the short range of the nucleon - nucleon interaction, which implies that its matrix elements are weaker for valence single-particle states in `large' nuclei with large mass number as compared to those in light nuclei. These effects are examined by comparing various mean values of the matrix elements. It turns out that the contributions from higher-order terms remain fairly stable as the mass number increases from A = 4 to A = 208. The implications for nuclear structure calculations are discussed.
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-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.