  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 $W$-value
that defines the recombination-independent energy scale is measured to be
$11.5~\pm~0.5$~(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.
