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.
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