  We provide a global density-dependent $^4$He-nucleon (DD-$\alpha N$)
interaction to construct the $\alpha$-nucleus optical model potential (OMP) in
a wide range of incident energies. The global parametrization for the
DD-$\alpha N$ interaction is obtained based on the proton-$^4$He OMP which
reproduces the elastic scattering cross-section data very well in the incident
energies of 12.04--500 MeV per nucleon. We derive the $\alpha$-nucleus
potential by a folding procedure with the point-nucleon density obtained by a
microscopic mean-field model using the present DD-$\alpha N$ interaction. The
density dependence of the DD-$\alpha N$ interaction is fixed phenomenologically
to reproduce the $\alpha$-nucleus elastic scattering cross-section data by the
$^{16}$O, $^{40}$Ca, $^{58}$Ni, $^{90}$Zr, and $^{208}$Pb targets at $E/A =$
10--342.5 MeV. We also show the total reaction cross sections, which are
helpful in fixing one free parameter, the renormalization factor for the
imaginary part of the $\alpha$-nucleus potential. Lastly, we show some
examples, which clearly demonstrate the validity and power of the present
DD-$\alpha N$ approach.
