Abstract
The convergence of the expansion for the effective interaction is studied considering as examples the shell model for the nuclei 18O and 18F. In this work the effective interaction is computed through third order in the Brueckner G matrix using both a harmonic-oscillator (HO) basis and a Brueckner-Hartree-Fock (BHF) basis. We report significant differences in the convergence behavior of the effective interaction in these two cases. Our results indicate that the choice of the BHF single-particle potential seems to facilitate the convergence of the effective interaction in low orders of the expansion, whereas the HO results exhibit a non-convergent behavior. The implications for the HO approach are discussed. All calculations have been performed considering a modern version of the Bonn one-boson-exchange potential for the nucleon-nucleon interaction.
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