Background: alpha-nucleus potentials play an essential role for the calculation of alpha-induced reaction cross sections at low energies in the statistical model... Purpose: The present work studies the total reaction cross section sigma_reac of alpha-induced reactions at low energies which can be determined from the elastic scattering angular distribution or from the sum over the cross sections of all open non-elastic channels. Method: Elastic and inelastic 64Zn(a,a)64Zn angular distributions were measured at two energies around the Coulomb barrier at 12.1 MeV and 16.1 MeV. Reaction cross sections of the (a,g), (a,n), and (a,p) reactions were measured at the same energies using the activation technique. The contributions of missing non-elastic channels were estimated from statistical model calculations. Results: The total reaction cross sections from elastic scattering and from the sum of the cross sections over all open non-elastic channels agree well within the uncertainties. This finding confirms the consistency of the experimental data. At the higher energy of 16.1 MeV, the predicted significant contribution of compound-inelastic scattering to the total reaction cross section is confirmed experimentally. As a by-product it is found that most recent global alpha-nucleus potentials are able to describe the reaction cross sections for 64Zn around the Coulomb barrier. Conclusions: Total reaction cross sections of alpha-induced reactions can be well determined from elastic scattering angular distributions. The present study proves experimentally that the total cross section from elastic scattering is identical to the sum of non-elastic reaction cross sections. Thus, the statistical model can reliably be used to distribute the total reaction cross section among the different open channels.
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