Nonlinear coupling between the mean polarizability $\bar\gamma$ of molecules and the local-field anisotropy in a liquid crystal and change of the "$\bar\gamma=\operatorname{const}$" paradigm

The nonlinear relation between the mean effective polarizability $\bar\gamma$ of molecules and the local-field anisotropy in uniaxial liquid crystals is demonstrated. Stringent constraints on $\bar\gamma$ from below, indicative of the dependence of $\bar\gamma$ on the liquid-crystal state and the change of the "$\bar\gamma=\operatorname{const}$" paradigm, are established. The theoretical results are confirmed by experiments with nematic liquid crystals having high and low birefringences.