  We have performed measurements of sodium nuclear recoils in NaI:Tl crystals,
following scattering by neutrons produced in a $^{7}$Li(p,n)$^{7}$Be reaction.
Understanding the light output from such recoils, which is reduced relative to
electrons of equivalent energy by the quenching factor, is critical to
interpret dark matter experiments that search for nuclear scattering
interactions. We have developed a spectrum-fitting methodology to extract the
quenching factor from our measurements, and report quenching factors for
nuclear recoil energies between 36 and 401 keV. Our results agree with other
recent quenching factor measurements that use quasi-monoenergetic neutron
sources. The new method will be applied in the future to the NaI:Tl crystals
used in the SABRE experiment.
