  Statistical model calculations have to be used for the determination of
reaction rates in large-scale reaction networks for heavy-element
nucleosynthesis. A basic ingredient of such a calculation is the a-nucleus
optical model potential. Several different parameter sets are available in
literature, but their predictions of a-induced reaction rates vary widely,
sometimes even exceeding one order of magnitude.
  This paper presents the result of a-induced reaction cross-section
measurements on gold which could be carried out for the first time very close
to the astrophysically relevant energy region. The new experimental data are
used to test statistical model predictions and to constrain the a-nucleus
optical model potential.
  For the measurements the activation technique was used. The cross section of
the (a,n) and (a,2n) reactions was determined from g-ray counting, while that
of the radiative capture was determined via X-ray counting.
  The cross section of the reactions was measured below E$_a=20.0$~MeV. In the
case of the $^{197}$Au(a,2n)$^{199}$Tl reaction down to 17.5~MeV with 0.5-MeV
steps, reaching closer to the reaction threshold than ever before. The cross
section of $^{197}$Au(a,n)$^{200}$Tl and $^{197}$Au(a,g)$^{201}$Tl was measured
down to E$_a=13.6$ and 14.0~MeV, respectively, with 0.5-MeV steps above the
(a,2n) reaction threshold and with 1.0-MeV steps below that.
  The new dataset is in agreement with the available values from the
literature, but is more precise and extends towards lower energies. Two orders
of magnitude lower cross sections were successfully measured than in previous
experiments which used g-ray counting only, thus providing experimental data at
lower energies than ever before. The new precision dataset allows us to find
the best-fit a-nucleus optical model potential and to predict cross sections in
the Gamow window with smaller uncertainties.
