  Future direct searches for low-mass dark matter particles with germanium
detectors, such as SuperCDMS SNOLAB, are expected to be limited by backgrounds
from radioactive isotopes activated by cosmogenic radiation inside the
germanium. There are limited experimental data available to constrain
production rates and a large spread of theoretical predictions. We examine the
calculation of expected production rates, and analyze data from the second run
of the CDMS low ionization threshold experiment (CDMSlite) to estimate the
rates for several isotopes. We model the measured CDMSlite spectrum and fit for
contributions from tritium and other isotopes. Using the knowledge of the
detector history, these results are converted to cosmogenic production rates at
sea level. The production rates in atoms/(kg$\cdot$day) are 74$\pm$9 for $^3$H,
1.5$\pm$0.7 for $^{55}$Fe, 17$\pm$5 for $^{65}$Zn, and 30$\pm$18 for $^{68}$Ge.
