Measurement of the scintillation and ionization response of liquid xenon at MeV energies in the EXO-200 experiment

Liquid xenon (LXe) is employed in a number of current and future detectors for rare event searches. We use the EXO-200 experimental data to measure the absolute scintillation and ionization yields generated by $\gamma$ interactions from $^{228}$Th (2615 keV), $^{226}$Ra (1764 keV) and $^{60}$Co (1332 keV and 1173 keV) calibration sources, over a range of electric fields. The measured $W$-value, defined as the energy required to produce either an electron-ion pair or a photon in the LXe is $11.5~\pm~0.5$~(syst.)~$\pm~0.1$~(stat.) eV. These data are also used to measure the recombination fluctuations in the number of electrons and photons produced by the calibration sources at the MeV-scale, which deviate from extrapolations of lower-energy data. Additionally, a semi-empirical model for the energy resolution of the detector is developed, which is used to constrain the recombination efficiency, i.e., the fraction of recombined electrons that result in the emission of a detectable photon. Detailed measurements of the absolute charge and light yields for MeV-scale electron recoils are important for predicting the performance of future neutrinoless double beta decay detectors.