Determination of the scintillation and ionization yield of nuclear recoils in liquid Xe from XENON10 neutron calibration data

Neutron calibration data from the XENON10 experiment is used as a sensitive probe of the Xe scintillation yield ($\mathcal{L}_{eff}$) and ionization yield, for nuclear recoils on liquid Xe. Previous data for the ionization yield $-$ the number of ionization electrons extracted per keV recoil energy (keVr) $-$ do not extend below 25 keVr, while our method is robust to $<3$ keVr. Previous data for the scintillation yield vary by $\times1.5$ at 10 keVr, with limited data at lower energies. We show the most likely $\mathcal{L}_{eff}$ curve consistent with the XENON10 neutron calibration data, along with statistical and systematic limits on it's variation.