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The convergence of the perturbation expansion for the effective interactionto be used in shell-model calculations is investigated as function of the massnumber $A$, from $A=4$ to $A=208$. As the mass number increases, there are moreintermediate states to sum over in each higher-order diagram which contributesto the effective interaction. Together with the fact that the energydenominators in each diagram are smaller for larger mass numbers, these twoeffects could largely enhance higher-order contributions to the effectiveinteraction, thereby deteriorating the order-by-order convergence of theeffective interaction. This effect is counterbalanced by the short range of thenucleon-nucleon interaction, which implies that its matrix elements are weakerfor valence single-particle states in ``large'' nuclei with large mass numberas compared to those in light nuclei. These effects are examined by comparingvarious mean values of the matrix elements. It turns out that the contributionsfrom higher-order terms remain fairly stable as the mass number increases from$A=4$ to $A=208$. The implications for nuclear structure calculations arediscussed.Comment: Revtex, 20 pages, 1 figure not include

Comparison of the effective interaction to various orders in different mass regions