  The production of radioactive isotopes by interactions of cosmic-ray
particles with sodium iodide (NaI) crystals can produce radioactive backgrounds
in detectors used to search for rare events. Through controlled irradiation of
NaI crystals with a neutron beam that matches the cosmic-ray neutron spectrum,
followed by direct counting and fitting the resulting spectrum across a broad
range of energies, we determined the integrated production rate of several
long-lived radioisotopes. The measurements were then extrapolated to determine
the sea-level cosmogenic neutron activation rate, including the first
experimental determination of the tritium production rate: $(80 \pm 21)$
atoms/kg/day. These results will help constrain background estimates and
determine the maximum time that NaI-based detectors can remain unshielded above
ground before cosmogenic backgrounds impact the sensitivity of next-generation
experiments.
