  In two previous papers a semi-analytical model was presented for the
hierarchical clustering of halos via gravitational instability from peaks in a
random Gaussian field of density fluctuations. This model is better founded
than the extended Press-Schechter model, which is known to agree with numerical
simulations and to make similar predictions. The specific merger rate, however,
shows a significant departure at intermediate captured masses. The origin of
this was suspected as being the rather crude approximation used for the density
of nested peaks. Here, we seek to verify this suspicion by implementing a more
accurate expression for the latter quantity which accounts for the correlation
among peaks. We confirm that the inclusion of the peak-peak correlation
improves the specific merger rate, while the good behavior of the remaining
quantities is preserved.
