DOSIMETRY OF A BETATRON ELECTRON BEAM IN ALKALI-HALIDE SALT CRYSTALS

V. N. RUDENKO

Introduction

In studying radiation damage in a solid produced by high-energy electrons, in determining the light yield of scintillators, and in selecting materials for radiation shielding, it is necessary to know the depth of penetration of electrons into a substance, the energy losses of electrons while passing through a braking material, the nature of electron scattering, and the influence of electron scattering on the depth of their penetration into a substance and on energy losses.

The aim of our work was to study the passage of electrons of energy \(5 \div 12\) MeV, extracted from a betatron, through crystals of alkali-halide salts; the distribution of the absorbed energy of the betatron electron beam in the crystals; determination of the ratio of the incident and absorbed energy of the electron beam in the crystals; the dependence of the electron penetration depth on the chemical composition of the crystals; investigation of the nature of electron scattering in the crystals; and establishment of the relation between the electron penetration depth and the intensity of scattering in crystals of different chemical composition.

The theory of energy losses by electrons during passage through matter was developed by Bohr, Bloch, Bethe, Heitler, and other investigators [1, 2, 4, 9] comparatively long ago. Experimental studies of electron energy losses in thin foils [7, 10, 8] showed good agreement between the experimental data and theory. The question of electron scattering during passage through matter has also been considered by a number of investigators as part of the general problem of the scattering of charged particles in matter [3, 9, 13].

Dosimetric studies of the passage of high-energy electrons (\(1 \div 30\) MeV) through matter were carried out by Laughlin, Breitling, and others [11, 12]. Laughlin and co-workers [12] investigated the dose distribution in a water phantom when it was irradiated by a betatron electron beam for different electron energies in the beam and different beam diameters. Breitling [10] investigated the distribution of energy losses of a betatron electron beam in samples of different chemical composition, mainly in metals.

Backscattering of high-energy electrons has also been the subject of investigation by a number of authors [13—16]. Wright and Trump [14] pro-

performed the most complete experimental study of backscattered electrons with energies of \(1 \div 3\) MeV.

In our studies, devoted to investigation of the dose distribution in alkali-halide salt crystals under irradiation with the electron beam of a betatron, the main attention was given to determining the penetration depth of electrons into crystals of different chemical composition, the influence of electron scattering on the depth of their penetration into crystals, and the relationship between the energy incident on the crystal surface and the absorbed energy of the electron beam.

Theoretical discussion

The principal types of energy losses by electrons passing through matter are losses to ionization and excitation of atoms of the medium, and to bremsstrahlung.

At electron energies of \(5 \div 15\) MeV in crystals of alkali-halide salts, ionization losses predominate. The calculation of ionization losses was carried out using the Bethe—Bloch formula [1] for the mean energy losses by electrons:

\[ \left(\frac{dT}{dx}\right)_{\text{ion}} = \frac{2\pi e^{4}NZ}{m_{0}v^{2}} \left[ \ln \frac{m_{0}v^{2}T}{2I^{2}(1-\beta^{2})} - \ln 2(2\sqrt{1-\beta^{2}}-1+\beta^{2}) + 1-\beta^{2} + \frac{1}{8}\left(1-\sqrt{1-\beta^{2}}\right)^{2} \right], \tag{1} \]

where \(N\) is the number of atoms in \(1\ \text{cm}^{3}\), \(Z\) is the nuclear charge, and \(I\) is the mean ionization potential of the atom.

It is of interest to consider the specific energy losses by electrons, i.e., losses per \(\text{g}/\text{cm}^{2}\). For this purpose both parts of equation (1) must be divided by \(\rho\), the density of the stopping substance. Since \(NZ\rho\) is equal to the number of electrons per \(1\) g of stopping substance, which decreases with increasing \(Z\), while \(I\) varies according to the approximate law \(I = 11.5 Z\) eV, the ionization losses decrease with increasing \(Z\).

In our case, the calculation of ionization losses was carried out separately for each element, and then summation was performed according to the weight fractions of the element in the salt crystals. The ionization potential was chosen by interpolation from known experimental values [6]. The polarization correction for ionization losses was calculated on the basis of the data of Halpern and Hall [17] and Sternheimer [4].

Fig. 1. Dependence of the mean range of electrons in crystals on energy.

At electron energies greater than \(1\) MeV it is necessary to take into account the energy losses by electrons to bremsstrahlung. Radiative losses increase in proportion to \(Z\) and therefore are of substantial importance for salts containing chemical elements of high atomic number in their composition (KBr, NaJ, KJ).

On the basis of the mean ionization losses, the polarization correction, and the mean losses to bremsstrahlung, electron ranges were calculated for a number of crystals of alkali-halide salts. Such a calculation is not entirely exact; however, it makes it possible to estimate the relative magnitude of the electron ranges in crystals of different chemical composition.

Figure 1 gives the calculated electron ranges in crystals of the salts NaCl, NaBr, KCl, and KBr. In the energy interval \(5 \div 10\) MeV, the electron ranges in these crystals differ only slightly (by no more than 2%). This is explained by the fact that, with increasing \(Z\) and increasing radiative losses, the losses to ionization and excitation of the atoms of the medium decrease.

Experimental Method

The source of high-energy electrons was a 15 MeV betatron (Fig. 2). The electrons were extracted from the betatron electrostatically through an exit window closed with aluminum foil \(0.05\) mm thick. The intensity of the electron beam was monitored with a transmission ionization chamber. The electron-beam intensity was measured with a calorimeter and a Faraday cylinder.

The study of the energy losses of the electron beam in crystals of alkali-halide salts was carried out with miniature ionization chambers of volume \(0.2\)—\(0.4\ \mathrm{cm}^3\) (Fig. 3). The chamber walls were made of crystals of the salts under investigation. The front, rear, and side walls of the chambers could be built up from \(0.1\) mm to the required thickness. The ionization in the chamber corresponds to the absorbed radiation energy at the given point of the crystal.

Fig. 2. Arrangement of the apparatus: 1—betatron, 2—collimator, 3—transmission ionization chamber, 4—miniature ionization chamber.

Fig. 3. General view of miniature ionization chambers.

Changing the thickness of the front wall of the chamber corresponded to shifting the air volume of the chamber along the depth of the irradiated specimen, which made it possible to measure the distribution of ionization with depth in the crystal of the salt being studied.

Changing the thickness of the rear wall of the chamber made it possible to study the effect of backscattering of electrons on the dose magnitude and to investigate the dependence of the backscattering intensity on the thickness of the reflector.

The dose distribution in the plane of the crystal perpendicular to the direction of the electron beam was measured by building up the side wall.

the chamber wall, which corresponded to displacement of the air volume of the chamber in the plane of the crystal.

Control measurements were made with a variable-volume chamber of \(0.1 \div 0.9\ \text{cm}^3\)—an extrapolation chamber. The walls of the extrapolation chamber were also made from crystals of the salts under investigation.

Experimental data

a. Dose distribution over the depth of the crystals

The distribution of the absorbed energy of the electron beam over the depth of the irradiated samples is presented in Figs. 4, 5, 6, 7.

Figures 4 and 5 show the dependences of the dose distribution over the depth of KCl, KBr, KJ, NaCl, NaBr, and NaJ crystals at an electron energy in the beam of \(7\ \text{MeV}\). At some distance from the surface into which the electron beam enters, the presence of a dose maximum is characteristic. The value of the maximum increases with increasing atomic number of the chemical elements making up the salt, while the penetration depth of the electrons decreases. After the maximum there is a rapid falloff of the dose, and the steepness of the slope of the rear front of the distribution curve is greater for the heavier salt.

Fig. 4. Dose distribution over the depth of KCl, KBr, KJ crystals.

Fig. 5. Dose distribution over the depth of NaCl, NaBr, NaJ crystals.

Figure 6 gives the dependences of the dose distribution over the depth of an NaCl crystal for different energies of the bombarding electrons. As the electron energy increases, the dose maximum shifts slightly in depth, and the slope of the rear front of the dose-distribution curve over depth decreases.

For comparison of the penetration depth of electrons in salts of different chemical composition, Fig. 7 gives curves of the dose distribution in crystals of the salts NaCl and NaBr, where the absorber thickness in \(\text{g}/\text{cm}^2\) is plotted along the abscissa axis.

If the most nearly rectilinear section of the rear front of the dose-distribution curve over depth is extended by a straight line to its intersection with the abscissa axis, then the “extrapolated range” of the electrons thus obtained—\(R\)—is a characteristic of the penetration of electrons into the irradiated sample. Figure 8 presents the dependences of the extrapolated range in various crystals on the electron energy—

electrons in the beam. The magnitude of the extrapolated range (in g/cm²) decreases with increasing atomic number of the chemical elements making up the salt.

Fig. 6. Dose distribution with depth in an NaCl crystal for different energies of the bombarding electrons.

Fig. 7. Dose distribution in NaCl and NaBr crystals. The thickness of the crystal in g/cm² is plotted along the abscissa.

Fig. 8. Dependence of the magnitude of the extrapolated electron range in crystals on their energy.

Fig. 9. Dose distribution with depth in KJ and NaCl crystals, taking backscattering into account. The distance between the dashed and solid curves determines the contribution of backscattered electrons to the dose.

b. Backscattering of electrons

Electrons, being scattered in the backward direction, create an additional dose, the magnitude of which depends on the chemical composition of the crystals.

Figure 9 presents the dose distribution with depth in NaCl and KJ crystals, where the dashed dependence was measured with a chamber whose rear wall was covered with aluminum foil 0.05 mm thick, while the solid dependence was measured using a chamber whose rear wall was covered with a crystal. The thickness of this crystal was chosen such that saturation of the backscattered electrons occurred. Backscattered electrons create an additional dose throughout the entire depth of the irradiated sample.

The dependence of the intensity of electron backscattering (the contribution to the total dose by backscattered electrons) on the thickness of the rear

wall–reflector is shown in Fig. 10. As can be seen from Fig. 10, the intensity of backscattering increases with increasing effective atomic number of the atoms of the crystal.

With increasing energy of the bombarding electrons, backscattering decreases. This is due to the fact that, in a collision with a nucleus of charge \(Z\), an electron is scattered through an angle \(\Theta\), which is proportional to \(Z^2\) and inversely proportional to the electron energy.

Fig. 10. Dependence of the intensity of backscattering on the thickness of the reflector. (Contribution to the dose from backscattered electrons as a function of the thickness of the rear wall.)

Fig. 11. Dependence of the intensity of electron backscattering on the chemical composition of the crystals and the electron energy. Along the abscissa is plotted the electron energy; along the ordinate, the percentage increase in the dose at the front surface of the irradiated crystals due to backscattered electrons.

Figure 11 gives the dependences of the increase in dose at the front surface of the irradiated crystals (in % of the total dose) on the energy of the bombarding electrons. A substantial increase in the intensity of backscattering with increasing effective atomic number of the atoms of the salt is noticeable, as well as a slight decrease in backscattering with increasing electron energy.

c. Lateral scattering of electrons

Lateral scattering of electrons, like backscattering, characterizes the influence of electron scattering on the depth of their penetration into the irradiated material and the leakage of energy of the electron beam from the irradiated specimen. As a result of electron scattering through the side wall of the crystal, the dose decreases from the center of the specimen to its edge. Figure 12 shows the dose distribution at various distances from the surface of an NaCl crystal at an electron energy of 7 MeV.

Lateral scattering of electrons leads to the dose magnitude over the depth of the crystal depending on its transverse dimensions. Figure 13 shows the dose distribution over the depth of an NaCl crystal for transverse dimensions of \(10 \times 10\ \mathrm{mm}^2\) and \(20 \times 20\ \mathrm{mm}^2\). The magnitude of the depth dose is smaller for the smaller dimensions of the irradiated specimen, although the extrapolated range of the electrons changes little. The slight dependence of the extrapolated electron range in the crystal on its transverse dimensions is explained by the fact that the greatest penetration depth is possessed by electrons undergoing small scatterings, i.e., those which change their initial direction only slightly.

For certain transverse dimensions of the sample, depending on its chemical composition and the energy of the electrons, “saturation” of the depth dose occurs, and a further increase in its transverse dimensions does not affect the magnitude of the dose with depth.

Fig. 12. Dose distribution at various distances from the front surface of a NaCl crystal.

Fig. 13. Dependence of the depth dose on the transverse dimensions of the sample.

Discussion of Results

Let us compare the penetration depth of electrons in crystals of different chemical composition. Since the betatron is a source of monoenergetic high-energy electrons, the dose distribution with depth in the crystals characterizes the energy losses of a monoenergetic electron beam in a solid.

The penetration depth of electrons into crystals of different chemical composition is characterized by the extrapolated range. Figure 8 presents the value of the extrapolated range (in g/cm²) in crystals of different chemical composition as a function of the energy of the bombarding electrons.

With increasing electron energy in the beam, the extrapolated range increases almost linearly. The slight nonlinearity is due to the increase in radiative energy losses of electrons with increasing energy.

When comparing the experimental data on the penetration depth of electrons into crystals with the calculated electron range in crystals (Fig. 1), a substantial difference is noticeable; moreover, this difference increases with increasing atomic number of the chemical elements making up the crystal. If the electron range in crystals increases (1–3%) with increasing atomic number of the elements in the compound, then the electron penetration depth decreases. Such a discrepancy between the calculated electron range in crystals and the actual penetration depth occurs as a result of the influence of multiple scattering of electrons on their penetration depth. Under the influence of multiple scattering, the actual path length of an electron in a substance increases, and this increase is greater the higher the atomic number of the atoms of the stopping substance.

The intensity of electron scattering in alkali-halide salt crystals is characterized by the backscattering and lateral scattering of electrons (Figs. 9–13).

The contribution to the total magnitude of the depth dose from backscattered electrons increases as the atomic number of the atoms of the stopping substance increases, whereas the electron penetration depth decreases. Thus, the increase in dose with depth in crystals caused by backscattered electrons characterizes the intensity of electron scattering in crystals of different chemical composition.

Backscattering and lateral scattering of electrons lead to losses of energy from the electron beam irradiating the sample. The magnitude of these losses in each specific case can be determined from experimental data on the backscattering and lateral scattering of electrons and from the dependences of dose distribution over the depth of the crystals.

Conclusion

Energy losses of an electron beam in alkali-halide salt crystals have been investigated. The penetration depth in crystals of different chemical composition has been determined, and the distribution of electron-beam energy over the depth and in the plane of the crystals has been measured. It is shown that the degree of penetration of electrons into the irradiated sample is determined not only by the mean energy losses per unit path length, but also by the intensity of scattering; moreover, as the atomic number of the atoms of the stopping substance increases, scattering has an ever greater effect on the distribution of the electron beam in the irradiated sample. Specific data have been obtained on the distribution of the absorbed radiation energy of an electron beam in crystals of different chemical composition, taking into account backscattered electrons. It was found that backscattered electrons make a substantial contribution to the depth dose—up to 27% for KJ, 16% for KBr, and 8% for NaCl.

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