A Continuum Theory for Scintillating Crystals

TL;DR

This paper develops a continuum microstructure-based model for scintillating crystals, deriving evolution equations for excitation carriers coupled with heat and electrostatic effects, enabling explicit decay time estimates and unifying existing phenomenological models.

Contribution

It introduces a novel continuum microstructure model for scintillators, deriving coupled PDEs that describe their non-proportional response and recover popular models as special cases.

Findings

Explicit decay time estimate for scintillators

Recovery of Kinetic and Diffusive models from the new framework

Application to NaI:Tl data showing energy dependence

Abstract

We obtain, by starting from the balance laws of a continuum endowed with a vectorial microstructure and with a suitable thermodynamics, the evolution equation for the excitation carriers in scintillating crystals. These equations, coupled with the heat and electrostatic equations, describe the non-proportional response of a scintillator to incoming ionizing radiations in terms of a Reaction and Diffusion-Drift system. The system of partial differential equations we arrive at allows for an explicit estimate of the decay time, a result which is obtained here for the first time for scintillators. Moreover we show how the two most popular phenomenological models in use, namely the Kinetic and Diffusive models, can be recovered, amongst many others, as a special case of our model. An example with the available data for NaI:Tl is finally given and discussed to show the dependence of these models on the energy of ionizing radiations.