On the Choice of Optimal Dimensions of Scintillation Crystals in Betatron Flaw Detection

V. A. VOROB'EV, A. V. POKROVSKII, G. P. SOKOLOV

In the dosimetry of bremsstrahlung radiation, scintillators based on alkali-halide salts of sodium iodide and cesium iodide are widely used [1, 2, 3]. The sensitivity in measuring bremsstrahlung radiation by the scintillation method increases with increasing crystal size [4]. Increasing the dimensions of the crystals leads to an increase in the efficiency of registration of electromagnetic radiation and, correspondingly, to an increase in the luminous flux. But, on the other hand, as the dimensions of the crystal grow, owing to absorption of light in the scintillator itself, the light output from the face of the crystal turned toward the photomultiplier decreases. The simultaneous occurrence of the processes of increasing crystal luminescence with increasing height and increasing light absorption determines the existence of optimal crystal dimensions for each energy range of electromagnetic radiation and crystal composition. For bremsstrahlung radiation with a maximum energy of up to 30 MeV, the literature contains no data on the optimal dimensions of crystals. The present work sets forth the results of theoretical and experimental studies of the light output from NaI (Tl) scintillation crystals when irradiated with bremsstrahlung radiation of 6, 10, and 30 MeV.

According to [5], the integral light output \(I'_{\mathrm{cb}}(H)\) from a crystal with a mirror reflector as a function of the crystal height \(H\) is determined by the expression:

\[ I'_{\mathrm{cb}}(H)=\gamma\int\left[0.208\cdot e^{-1.29\nu z}+0.124\cdot e^{-1.42(2H-z)}+ \right. \tag{1} \]

\[ \left. +0.080\cdot e^{-1.08(2H-z)}\right]dz, \]

where \(\nu\) is the coefficient of absorption of the crystal’s own radiation by the crystal, \(z\) is the distance from the front face of the crystal to the point at which absorption of the quantum occurred, and \(\gamma\) is a constant, weakly dependent on the type of reflector and approximately equal to unity. The total light output from crystals, in which the distribution density of the absorbed energy \(D(z,\varepsilon)\) [7] is determined by the expression

\[ I_{\mathrm{cb}}(H,R)=2\pi \xi \int_H dz \int_R \rho\, d\rho\, D(z,\rho)\, I'_{\mathrm{cb}}(H,R), \tag{2} \]

where \(\xi\) is the conversion efficiency of the scintillator, and \(R\) is the radius of the crystal. Calculation by formula (2) was carried out by us on an M-20 computer by the Monte Carlo method, with a root-mean-square error no worse than 10%, for the values \(\nu=0.146\) [5]; \(\nu=0.035\) [2] and \(0.0035\) [6]. The results of the calculations are presented in the form of curves in Fig. 1. The difference in the values of the coefficients \(\nu\) given in works [2, 5, 6] is evidently explained by differences in the technology of crystal manufacture and by the conditions of the experiments carried out to determine them. To determine the magnitude of the coefficient, we experimentally determined the dependence of the light output on the height of the crystal. In the course of the experiment, a scintillation detector with a NaJ (Tl) crystal 50 mm in diameter and an FEU-16 photomultiplier was placed in a lead container with a collimator diameter of 8 mm. During the experiment the height of the crystal was varied from 30 to 100 mm in steps of 10 mm. The stability of the bremsstrahlung intensity was maintained to within no worse than 2% and was monitored by means of a transmission counter with recording on a self-recording instrument of the type

Fig. 1. Dependence of the light output on the height of the scintillator at different maximum energies of bremsstrahlung radiation.

EPP-0.9. The photomultiplier operated in current mode with a constant integration time of 1 sec. The exposure-dose rate of the bremsstrahlung was set at 1 R/min, which ensured operation of the detector without overloads in the range 0.5–2 μA. Additional studies showed that when the dose rate was varied by a factor of 3–4, proportionality between the dose rate and the output current of the photomultiplier was maintained satisfactorily. To improve the reproducibility of the measurement results, the betatron was switched off during the experiment by removing the injection voltage; thus, in all measurements, the operating mode of the setup was kept constant.

The measurement results are plotted in Fig. 1 as points on the curves obtained by calculation. As can be seen from Fig. 1, agreement between the calculated and experimental data was obtained for a value of $\nu = 0.035—0.04$, which is consistent with the data of [2]. Analyzing the course of the curves, we see that the dimensions of scintillators for bremsstrahlung of 6–30 MeV should be chosen from the condition of maximum efficiency. In [7] it was shown that, for a ratio of the irradiation field to the crystal size of 2:3, for crystals with a diameter greater than 30 mm the radial dimensions of the crystal do not have a significant effect on the distribution of the absorbed energy in it; therefore, based on registration efficiency, the crystal diameter must be taken to exceed the diameter of the radiation flux incident on it by 20–30 mm.

For measuring bremsstrahlung one may restrict oneself to NaJ (Tl) crystals with a height of no more than 60–80 mm, since a further increase does not lead to any noticeable rise in registration efficiency.

REFERENCES

1. A. A. Vorob’ev, V. A. Vorob’ev, V. I. Gorbunov, G. V. Titov, Betatron Flaw Detection of Materials and Products. Moscow, Atomizdat, 1965.
2. V. I. Gorbunov, V. K. Kuleshov. Izvestiya TPI, 138, 1965.
3. A. V. Pokrovskii. Dissertation, Tomsk, TPI, 1967.
4. V. I. Gorbunov et al. Izvestiya TPI, 1938, 1965.
5. A. M. Ratter et al. PTE 2 (1961) 53.
6. E. I. Stolyarova. Applied Spectrometry of Ionizing Radiations, Moscow, Atomizdat, 1964.
7. G. P. Sokolov. Dissertation, Tomsk, TPI, 1968.