  Inorganic scintillating crystals can be modelled as continua with
microstructure. For rigid and isothermal crystals the evolution of charge
carriers becomes in this way described by a reaction-diffusion-drift equation
coupled with the Poisson equation of electrostatic. Here we give a survey of
the available existence and asymptotic decays results for the resulting
boundary value problem, the latter being a direct estimate of the scintillation
decay time. We also show how to recover various approximated models which
encompass also the two most used phenomenological models for scintillators,
namely the Kinetic and Diffusive ones. Also for these cases we show, whenever
it is possible, which existence and asymptotic decays estimate results are
known to date.
