The unusual temperature dependence of the Eu$^{2+}$ fluorescence lifetime in CaF$_2$ crystals

Fluorescence lifetimes of Eu$^{2+}$ doped in CaF$_2$ are measured at various temperatures between 4K and 450K. The lifetime increases with between 100K and 300K, in contrast to the usual lifetime-temperature dependence. At higher or lower temperatures the lifetime decreases with increasing temperature. The phenomenon is explained by simulation of the energy levels and lifetimes of low-lying $4f^65d$ states involved in the fluorescence.