Total number density of Raman-active two level systems in fluorite mixed crystals and the law of mass action

The low frequency, low temperature Raman spectra of fluorite crystal hosts doped with large amounts of LaF3 show a broad distribution of two level systems (TLS) displaying A(1g) symmetry. When the total number of Raman active TLS per unit volume is determined as a function of LaF3 concentration unusual dependencies are found. The results are consistent with a model where the TLS number density is controlled by the law of mass action with the "effective" temperature determined by the frozen-in lattice disorder.