  We present a reliable double-folding (DF) model for $^{4}$He-nucleus
scattering, using the Melbourne $g$-matrix nucleon-nucleon interaction that
explains nucleon-nucleus scattering with no adjustable parameter. In the DF
model, only the target density is taken as the local density in the Melbourne
$g$-matrix. For $^{4}$He elastic scattering from $^{58}$Ni and $^{208}$Pb
targets in a wide range of incident energies from 20~MeV/nucleon to
200~MeV/nucleon, the DF model with the target-density approximation (TDA)
yields much better agreement with the experimental data than the usual DF model
with the frozen-density approximation in which the sum of projectile and target
densities is taken as the local density. We also discuss the relation between
the DF model with the TDA and the conventional folding model in which the
nucleon-nucleus potential is folded with the $^{4}$He density.
