  We study the basic thermodynamic and electromagnetic properties of the
superconductor described by the negative-$U$ Hubbard model (gap parameter
$\Delta$, critical temperature $T_c$, London penetration depth $\lambda$,
thermodynamic critical field $H_c$ and Ginzburg-Landau correlation length
$\xi_{G-L}$).The calculations are performed for square (SQ, d=2), simple cubic
(SC, d=3) and face-centered cubic (FCC, d=3) lattices. We analyze the results
as a function of electron density $n$ and interaction $U$ using the
Hartree-Fock approximation in the weak-to-intermediate $U$ case combined with
the conclusions from the perturbation theory valid in the strong coupling
limit. From the equality: $\lambda/\xi_{G-L}}=1/\sqrt{2}$ we find the
boundaries between local and nonlocal electronic behaviour of the $U<0$ Hubbard
model in the $U-n$ parameter space. Using the calculated values of $T_c$ and
$\lambda$ we compare the `universal plot' of $T_c/T_c^m$ vs.
$[\lambda(0)/\lambda^m(0)]^2$ ( where: $T_c^m$ denotes maximum $T_c$ as a
function of $n$ and $\lambda^m(0)$ corresponds to $T_c^m$) with the recent
experimental data for various families of nonconventional superconductors and
conclude that the best agreement can be obtained for intermediate values of the
local attraction.
  Keywords: negative-$U$ Hubbard model, London penetration depth, high-$T_c$
superconductivity
