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

Scintillation efficiency measurement of Na recoils in NaI(Tl) below the DAMA/LIBRA energy threshold