Mitigation of Backgrounds from Cosmogenic $^{137}$Xe in Xenon Gas Experiments using $^{3}$He Neutron Capture

\Xe{136} is used as the target medium for many experiments searching for \bbnonu. Despite underground operation, cosmic muons that reach the laboratory can produce spallation neutrons causing activation of detector materials. A potential background that is difficult to veto using muon tagging comes in the form of \Xe{137} created by the capture of neutrons on \Xe{136}. This isotope decays via beta decay with a half-life of 3.8 minutes and a \Qb\ of $\sim$4.16 MeV. This work proposes and explores the concept of adding a small percentage of \He{3} to xenon as a means to capture thermal neutrons and reduce the number of activations in the detector volume. When using this technique we find the contamination from \Xe{137} activation can be reduced to negligible levels in tonne and multi-tonne scale high pressure gas xenon neutrinoless double beta decay experiments running at any depth in an underground laboratory.