KrF lasers with an emission wavelength of 248 nm offer many applications in medicine: e.g., photoablation of the substantia propria (or stroma of cornea), and high precision tissue ablation.[@medicine; @application] This comes in addition to the common application in photolithography of the semiconductor industry.

Here we will consider cadmium fluoride ($CdF_{2}$) which is characterized by a large gap energy (of the order of 9 eV)[@kalugin] and, hence, a high transparency in a wide energy range, while the more famous calcium fluoride ($CaF_{2}$) has a direct band gap at $\Gamma$ of $12.1$ eV and an indirect band gap estimated around $11.8$ eV.[@rubloff] $CdF_{2}$ has been chosen as a representative candidate for a material class which seems to exhibit similar behavior, as well as numerical problems (e.g., $BaF_{2}$[@unpub]). In particular, its overall very small values of the dielectric function, the extended high-energy tail, and the full ionicity (i.e., the weak band dispersions) may pose critical theoretical and numerical problems.

By doping, usually with trivalent metal impurities and a certain thermochemical treatment, $CdF_{2}$ can be also produced in the semiconducting state.[@hayes] Many dopants, as Sc and Y, generate only a shallow donor state, but In or Ga related defects exhibit a bistable behavior. 