Heavily obscured active galactic nuclei (AGNs) play an important role in contributing to the cosmic X-ray background (CXRB). However, the AGNs found in deep X-ray surveys are often too weak to allow direct measurement of the column density of obscuring matter. One method adopted in recent years to identify heavily obscured, Compton-thick AGNs under such circumstances is to use the observed mid-infrared to X-ray luminosity ratio as a proxy for the column density. This is based on the supposition that the amount of energy lost by the illuminating X-ray continuum to the obscuring matter and reprocessed into infrared emission is directly related to the column density and that the proxy is not sensitive to other physical parameters of the system (aside from contamination by dust emission from, for example, star-forming regions). Using Monte Carlo simulations, we find that the energy losses experienced by the illuminating X-ray continuum in the obscuring matter are far more sensitive to the shape of the X-ray continuum and to the covering factor of the X-ray reprocessor than they are to the column density of the material. Specifically we find that it is possible for the infrared to X-ray luminosity ratio for a Compton-thin source to be just as large as that for a Compton-thick source even without any contamination from dust. Since the intrinsic X-ray continuum and covering factor of the reprocessor are poorly constrained from deep X-ray survey data, we conclude that the mid-infrared to X-ray luminosity ratio is not a reliable proxy for the column density of obscuring matter in AGNs even when there is no other contribution to the mid-infrared luminosity aside from X-ray reprocessing. This conclusion is independent of the geometry of the obscuring matter.
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