[en] The convergence of the expansion for the effective interaction is studied considering as example 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. The significant differences in the convergence behavior of the effective interaction in these two cases are reported. The results indicate that the choice of the BHF single-particle potential facilitates 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. 23 refs., 4 figs., 2 tabs