  The dark matter interpretation of the DAMA modulation signal depends on the
NaI(Tl) scintillation efficiency of nuclear recoils. Previous measurements for
Na recoils have large discrepancies, especially in the DAMA/LIBRA modulation
energy region. We report a quenching effect measurement of Na recoils in
NaI(Tl) from 3keV$_{\text{nr}}$ to 52keV$_{\text{nr}}$, covering the whole
DAMA/LIBRA energy region for light WIMP interpretations. By using a low-energy,
pulsed neutron beam, a double time-of-flight technique, and pulse-shape
discrimination methods, we obtained the most accurate measurement of this kind
for NaI(Tl) to date. The results differ significantly from the DAMA reported
values at low energies, but fall between the other previous measurements. We
present the implications of the new quenching results for the dark matter
interpretation of the DAMA modulation signal.
