Phosphors for Radiation Detectors. Группа авторов

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      and

      (1.31)

respectively. In these equations, dn₁/dt and dm₁/dt represent a charging (trapping) process, and (η + ζ)nm and Β_m 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

(1.33)

      If we assume temperature T₀ < < E/k and the heating rate of β, the temperature is

(1.34)

      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

(1.35)

If we change a variable of Equation (1.33) by Equation (1.34), the temperature dependence of the electron concentration can be expressed as

(1.36)

and after the integration of Equation (1.35) by temperature T, we can obtain

(1.37)

In this equation, n₁₀ means an electron density at T = T_0, 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

(1.38)

Equation (1.38) represents a first‐order kinetics, and if the order is higher than 1, Equation (1.38) changes to

(1.39)

      where b is an arbitrary order. Generally, if we can assume E ≫̸ kT and T₀ = 0, then

(1.40)

When we combine Equation (1.40) with Equation (1.38),

(1.41)

      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 T_m, we can obtain the relationship

(1.42)

(1.43)

When we combine Equation (1.43) with Equation (1.41), we obtain the relationship

(1.44)

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

(1.46)

where Δ_m = 2kT_m/E. If we combine Equation (1.46) with Equation (1.44), we obtain

      (1.47)

      and

      (1.48)

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