  The feasibility of an ultra-low energy nuclear-recoil measurement in liquid
xenon using neutron capture is investigated for a small (sub-kilogram) liquid
xenon detector that is optimized for a high scintillation gain, and a pulsed
neutron source. The measurement uses the recoil energies imparted to xenon
nuclei during the de-excitation process following neutron capture, where
promptly emitted $\gamma$ cascades can provide the nuclei with up to $0.3$
keV$_\text{nr}$ of recoil energy due to conservation of momentum. A successful
calibration of scintillation photon and ionization electron yields below this
energy will contribute to a greater sensitivity for liquid xenon experiments in
searches for light WIMPs.
