  The results obtained by studying the background of neutrons produced by
cosmic-ray muons in underground experimental facilities intended for rare-event
searches and in surrounding rock are presented. The types of this rock may
include granite, sedimentary rock, gypsum, and rock salt. Neutron production
and transfer were simulated using the Geant4 and SHIELD transport codes. These
codes were tuned via a comparison of the results of calculations with
experimental data: in particular, with data of the Artemovsk research station
of the Institute for Nuclear Research (INR, Moscow, Russia), as well as via an
intercomparison of results of calculations with the Geant4 and SHIELD codes. It
turns out that the atomic-number dependence of the production and yield of
neutrons has an irregular character and does not allow a description in terms
of a universal function of the atomic number. The parameters of this dependence
are different for two groups of nuclei-nuclei consisting of alpha particles and
all of the remaining nuclei. Moreover, there are manifest exceptions from a
power-law dependence, for example, argon. This may entail important
consequences both for the existing underground experimental facilities and for
those under construction. Investigation of cosmic-ray-induced neutron
production in various materials is of paramount importance for the
interpretation of experiments conducted at large depths under the Earth's
surface.
