  In the paper the Pair Approximation (PA) method for studies of the
site-diluted spin-1/2 systems of arbitrary dimensionality with the long-range
ferromagnetic interactions is adopted. The method allows to take into account
arbitrary anisotropy of the interactions in the spin space, so it is not
limited to purely Ising couplings. Within this approach, the Gibbs free energy
is obtained, which allows to derive all the further interesting thermodynamic
properties. In particular, we obtain an equation for the critical temperature
of the second-order phase transitions for the model in question. In the study
we focus our attention on the systems with ferromagnetic interactions decaying
with the distance according to the power law $J(r)\propto r^{-n}$. We discuss
the dependence of the critical temperature on the concentration of magnetic
component and the index $n$ for selected one-, two- and three-dimensional
lattices.We confirm the absence of the critical concentration for a diluted
magnet with infinite interaction range. In the regime of the low concentrations
of magnetic component, we find a non-linear increase of the critical
temperature with the concentration in the form of $T_{c}\propto p^{n/d}$,
depending on the system dimensionality $d$ and the index $n$, whereas $n > d$.
