Towards a Continuum Theory for Scintillators.

A scintillator is a material that exhibits scintillation, the property of luminescence when excited by ionizing radiation. Luminescent materials, when struck by an incoming particle, absorb its energy and scintillate, i.e., re-emit the absorbed energy in the form of light. Scintillators can be organic and inorganic: we deal only with inorganic scintillators, i.e. furnace-growth crystals. For the relevant applications, the crystals are growth and cut in massive specimen, namely of the order of centimeters and there is a need of a description of the behavior of the massive crystal starting from the microscopic description. In this paper we shall begin to give a basic description of scintillation by using a continuum mechanics approach and by means the introduction of balance laws and energy dissipation inequalities for continua with microstructure, as it was done for the Ginzburg-Landau and Cahn-Hillard equations. We limit our analysis to one-dimensional, non-deformable and "isotropic" crystals, and we are able to recover and generalize, within the framework of the theory of continua with microstructure the equations of the so-called "kinetic approach".