  The convergence of the perturbation expansion for the effective interaction
to be used in shell-model calculations is investigated as 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.
