  Measuring the scintillation and ionization yields of liquid xenon in response
to ultra-low energy nuclear recoil events is necessary to increase the
sensitivity of liquid xenon experiments to light dark matter. Neutron capture
on xenon can be used to produce nuclear recoil events with energies below $0.3$
keV$_\text{NR}$ via the asymmetric emission of $\gamma$ rays during nuclear
de-excitation. The feasibility of an ultra-low energy nuclear recoil
measurement using neutron capture was investigated for the Michigan Xenon (MiX)
detector, a small dual-phase xenon time projection chamber that is optimized
for a high scintillation gain. Simulations of the MiX detector, a partial
neutron moderator, and a pulsed neutron generator indicate that a population of
neutron capture events can be isolated from neutron scattering events. Further,
the rate of neutron captures in the MiX detector was optimized by varying the
thickness of the partial neutron moderator, neutron pulse width, and neutron
pulse frequency.
