Neutron production induced by ($alpha$,n) reactions is important in various scenarios. One of the most relevant ones is related to underground dark matter experiments, where the neutrons produced by the $alpha$-decay from radioactive contaminants in the detector materials can generate an irreducible background, limiting the sensitivity of the experiment. A precise estimate of the background due to these neutrons is crucial for the experiments currently taking data and for the design of the next generation detectors. In this work, we prove that Geant4 can be used to calculate neutron yields and energy spectra induced by $alpha$-decay. These neutrons are produced according to the information compiled in data libraries originally written in the ENDF-6 format. In this article we also review the different databases available, showing the differences and similarities among them. Finally, we compare several Geant4 neutron production yields and spectra with experimental data and other codes.
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