  The production of $^{3}$H, $^{7}$Be, and $^{22}$Na by interactions of
cosmic-ray particles with silicon can produce radioactive backgrounds in
detectors used to search for rare events. Through controlled irradiation of
silicon CCDs and wafers with a neutron beam that mimics the cosmic-ray neutron
spectrum, followed by direct counting, we determined that the production rate
from cosmic-ray neutrons at sea level is ($112 \pm 24$) atoms/(kg day) for
$^{3}$H, ($8.1 \pm 1.9 $) atoms/(kg day) for $^{7}$Be, and ($43.0 \pm 7.1 $)
atoms/(kg day) for $^{22}$Na. Complementing these results with the current best
estimates of activation cross sections for cosmic-ray particles other than
neutrons, we obtain a total sea-level cosmic-ray production rate of ($124 \pm
24$) atoms/(kg day) for $^{3}$H, ($9.4 \pm 2.0 $) atoms/(kg day) for $^{7}$Be,
and ($49.6 \pm 7.3 $) atoms/(kg day) for $^{22}$Na. These measurements will
help constrain background estimates and determine the maximum time that
silicon-based detectors can remain unshielded during detector fabrication
before cosmogenic backgrounds impact the sensitivity of next-generation
rare-event searches.
