Ultra-low-background experiments address some of the most important open questions in particle physics, cosmology and astrophysics: the nature of dark matter, whether the neutrino is its own antiparticle, and does the proton decay. These rare event searches require well-understood and minimized backgrounds. Simulations are used to understand backgrounds caused by naturally occurring radioactivity in the rock and in every piece of shielding and detector material used in these experiments. Most important are processes like spontaneous fission and ({alpha},n) reactions in material close to the detectors that can produce neutrons. A comparison study between two dedicated software packages is detailed. The cross section libraries, neutron yields, and spectra from the Mei-Zhang-Hime and the SOURCES-4A codes are presented. The resultant yields and spectra are used as inputs to direct dark matter detector toy models in GEANT4, to study the impact of their differences on background estimates and fits. Although differences in neutron yield calculations up to 50% were seen, there was no systematic difference between the Mei-Hime-Zhang and SOURCES-4A results. Neutron propagation simulations smooth differences in spectral shape and yield, and both tools were found to meet the broad requirements of the low-background community.
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