The kinetics of the thermoluminescence (TL) is analysed using the conventional model of recombination and trapping in the case of initially filled traps in insulating material. A new parameter called fractional recombination probability is introduced. This parameter shows whether the physical process (either recombination or retrapping) is dominant in the TL at given temperature T. The shape of the TL curve and its peak position Tm, the trap occupancy μ, the symmetry factor of the TL curve μg, the fractional recombination probability γ, the free electron concentration, and the free electron lifetime are calculated as a function of temperature and trap parameters. The results show that γ depends, in general, on the temperature and the trap parameters and thereby characterizes various kinetics of the TL. The method based on the temperature dependence of the TL intensity I in the form In [I/(γμ)] = f(1/T) is suggested for the determination of the fractional recombination probability. The calculated dependence of μ(Tm), μg, and bg on γ(Tm) are strongly not univocal (bg is the effective kinetics order of the TL). Because the parameters μg and bg do not have, in general, simple connection with the physical TL process, they do not seem to be useful for the characterization of the TL kinetics.

All bialgebra structures for centrally extended Galilei algebra are classified. The corresponding Lie-Poisson structures on centrally extended Galilei group are found.

The thermoluminescence (TL) in insulating crystals with various initial trap occupancy (m̈0) is analysed. The conventional model of n‐t ype compensated material having one class of active (shallow) electron traps, one class of thermally disconnected (deep) electron traps, and one class of recombination centres is used for the analysis. A formula for calculating the kinetics order (b) is derived. For the analysis of the TL kinetics the parameter called fractional recombinational probability (γ) is used, too. Various TL characteristics including m̈0, γ, b, τ, and I are numerically calculated as functions of the trap parameters, temperature, and the initial trap occupancy (τ denotes the free electron lifetime and I the TL intensity). The results show that the shape of the TL curve and other TL characteristics are dependent on the initial trap occupancy. The TL curves calculated for different values of the trap parameters and the initial trap occupancies corresponding to different retrapping probability, can have similar shape. The shape of the TL curve can not, therefore, be a useful tool for the study of the recombination model of insulating crystals.

The description of the thermoluminescence (TL) kinetics with the kinetics order formalism is analysed for the case of initially filled traps in an insulating crystal. The results show that the kinetics order value b can be estimated with the relation b = lg R/lg μ, where R is the recombination kinetics parameter, and μ is the occupancy of the active traps. The calculated b is, in general, dependent on the trap parameters and the temperature. The result suggest that b has the meaning of a “shape parameter” of the TL curve which is not, in general, in simple relationship with the fractional recombination probability γ.