  We analyzed the response of NaI(Tl) to low energy nuclear recoils in the
experiment that is reported on here. Such detectors have been used recently to
search for evidence of dark matter in the form of weakly interacting massive
particles (WIMPs). Understanding the response of these detectors to low energy
nuclear recoils is crucial in these searches. We have measured nuclear recoils
and associated quenching factors (QF) for sodium recoils in the energy range of
8 keV - 48 keV. The results are characterized by a decrease in QF as the recoil
energy decreases. The measured values are significantly lower than those
reported by DAMA, but are similar to results from recent measurements. We
present the details of our experiment, including the neutron beam calibration,
shielding optimization, and the experimental design and setup. The DAMA/LIBRA
combined modulation signal is used with the new QF values to illustrate the
changes to the dark matter interpretation resulting from this improved
characterization of these NaI(Tl) detectors.
