alt="equation"/>
and
(1.31)
respectively. In these equations, dn1/dt and dm1/dt represent a charging (trapping) process, and (η + ζ)nm and Βm nm1 represent dissipation processes. Let us consider the energy dissipation after stopping the irradiation at temperature T. In this case, if we assume J = 0 in (1.27)–(1.30) at time t = 0, then TL from the electron centers by electron release is
(1.32)
After this time, the time dependence of concentration of electron trapped centers is
If we assume temperature T0 < < E/k and the heating rate of β, the temperature is
The simplest model of luminescence process under this condition is the Randall–Wilkins model. In this classical model, retrapping of electrons is not considered (γ = 0). If we assume (η + ζ) = 0 in Equation (1.30), the TSL intensity can be written as
If we change a variable of Equation (1.33) by Equation (1.34), the temperature dependence of the electron concentration can be expressed as
and after the integration of Equation (1.35) by temperature T, we can obtain
In this equation, n10 means an electron density at T = T0, which equals the concentration of electron trapping centers generated by ionizing radiation exposure. If we combine Equation (1.36) with Equation (1.37), we obtain
Equation (1.38) represents a first‐order kinetics, and if the order is higher than 1, Equation (1.38) changes to
where b is an arbitrary order. Generally, if we can assume E ≫̸ kT and T0 = 0, then
When we combine Equation (1.40) with Equation (1.38),
When we differentiate Equation (1.38) and assume it is equal to 0, it means there is a glow peak in the TSL glow curve. By using the glow peak temperature Tm, we can obtain the relationship
When we combine Equation (1.43) with Equation (1.41), we obtain the relationship
where Δ = 2kT/E. If we combine Equation (1.42) with Equation (1.41), we obtain a maximum TSL intensity of
(1.45)
and the equation of
where Δm = 2kTm/E. If we combine Equation (1.46) with Equation (1.44), we obtain
(1.47)
and
(1.48)
