Spatial anisotropy of the exciton level in CaF₂ at 11.1 eV and its relation to the weak optical anisotropy at 157 nm

The energy level of the exciton around the $\Gamma$ point in CaF$_2$ at about 11.1 eV was investigated by reflection measurements on oriented surfaces using dispersed synchrotron radiation. A small but clear energy shift of the exciton resonance structure was observed which depends on the crystal orientation with respect to the incoming beam. By interpreting the results in terms of the complex dielectric function it becomes possible to determin the respective exciton levels and lifetimes. For crystal samples oriented in the (111) direction, the exciton has an excitation energy 0.02 eV above the energy of samples oriented in the (100) direction. The results obtained suggest that the exciton-energy shift is related to the spatial anisotropy recently measured in CaF$_2$ at 157 nm.