The $A_T$ emission of KCl:Tl interpreted as a double $A_T+A_X$ emission

The experimental evidence of an anomalous behavior in the decay times of Tl$^+$-like impurity centers in alkali-halide crystals has generated a revival of interest with respect to these materials. We discuss here about the possibility that the $A_T$ emission of KCl:Tl can be considered as a double emission, namely as a superposition of the $A_T$ and $A_X$ emission bands. The plausibility of this hypothesis is discussed in the light of the available, old and recent, experimental features. A quantitative test of this assumption is performed in the framework of a model which demonstrates to be suitable for interpreting other similar cases.