In perturbative QCD, we study a set of pomeron fan diagrams propagating from a projectile to <nobr>$A$</nobr> nucleons in the nucleus target for finite <nobr>$A$</nobr> and investigate its behavior at large <nobr>$A$</nobr> and convergence as <nobr>$A\to\infty$</nobr>. We find convergence for only very small values of the coupling constant <nobr>$\alpha_\mathrm{s}$</nobr>, much smaller than the commonly assumed values. We compare the results with the solution of the Balitski–Kovchegov equation.