Bound surface states and the nuclear spin relaxation of $^{199}$Hg

The possible use of optically pumped $^{199}$Hg nuclear spin magnetometry for fundamental physics studies, particularly in the search for electric dipole moments, remains of great interest. Understanding surface-induced relaxation is necessary for the development of both large- and small-volume cells that have a long and stable nuclear spin lifetime. Such cells are critical to several ongoing experiments, including the measurement of the neutron electric dipole moment, zero or otherwise. $^{199}$Hg, due to its large mass, has a multitude of bound surface states that affect the interaction time with the surface and are an important factor in the interpretation of previously acquired data. It is shown that the inclusion of these states brings consistency to the derived surface interaction properties.