  The prediction of stellar ($\gamma$,$\alpha$) reaction rates for heavy nuclei
is based on the calculation of ($\alpha$,$\gamma$) cross sections at
sub-Coulomb energies. These rates are essential for modeling the
nucleosynthesis of so-called $p$-nuclei. The standard calculations in the
statistical model show a dramatic sensitivity to the chosen $\alpha$-nucleus
potential. The present study explains the reason for this dramatic sensitivity
which results from the tail of the imaginary $\alpha$-nucleus potential in the
underlying optical model calculation of the total reaction cross section. As an
alternative to the optical model, a simple barrier transmission model is
suggested. It is shown that this simple model in combination with a well-chosen
$\alpha$-nucleus potential is able to predict total $\alpha$-induced reaction
cross sections for a wide range of heavy target nuclei above $A \gtrsim 150$
with uncertainties below a factor of two. The new predictions from the simple
model do not require any adjustment of parameters to experimental reaction
cross sections whereas in previous statistical model calculations all
predictions remained very uncertain because the parameters of the
$\alpha$-nucleus potential had to be adjusted to experimental data. The new
model allows to predict the reaction rate of the astrophysically important
$^{176}$W($\alpha$,$\gamma$)$^{180}$Os reaction with reduced uncertainties,
leading to a significantly lower reaction rate at low temperatures. The new
approach could also be validated for a broad range of target nuclei from $A
\approx 60$ up to $A \gtrsim 200$.
