A brief overview of existence results and decay time estimates for a mathematical modeling of scintillating crystals

TL;DR

This paper surveys mathematical results on the existence and decay time estimates for reaction-diffusion models of scintillating crystals, including derivations of simplified models used in scintillator physics.

Contribution

It provides a comprehensive overview of existence and decay estimates for complex and simplified models of scintillating crystals, connecting rigorous analysis with phenomenological models.

Findings

Existence results for the reaction-diffusion-Poisson system

Decay time estimates for the boundary value problem

Recovery of kinetic and diffusive models from the full system

Abstract

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.