  We study the single-particle density of states of one-dimensional and
two-dimensional quantum disordered systems with long-range interactions. We
consider a $1/\sqrt{r}$ interaction in one dimension and a Coulomb interaction
in two dimensions, which produce linear gaps in the density of states in both
cases. We focus on the strong localization regime where the localization length
is small but non-zero. We use an exact diagonalization technique for small
system sizes and a perturbation approach for larger sizes. We find that, with
both methods, the inclusion of a finite hopping contribution does not change
the linear character of the gap, but reduces its slope, widening the gap.
