STUDY OF BREMSSTRAHLUNG ABSORPTION IN ALKALI HALIDE CRYSTALS UNDER VARIOUS IRRADIATION CONDITIONS

A. A. VOROB'EV, V. A. VOROB'EV, E. K. ZAVADOVSKAYA, G. P. SOKOLOV

Under the action of radiation, materials change their physicomechanical properties [1], and one of the characteristics of the radiation field associated with changes in the properties of the irradiated substance is the absorbed energy [2, 3, 4, 5]. In radiation physics and technology, in addition to the integral value of the absorbed energy, it is important to know its distribution over the volume of the absorber under various irradiation conditions [7].

We considered the distribution of absorbed energy over the volume of an absorber made of alkali halide compounds under irradiation by bremsstrahlung with maximum energies of 6, 10, and 30 MeV. All results were obtained by the method of statistical trials [6] and checked experimentally [10] using X-ray films, ionization chambers, and a calorimeter.

The geometry of the problem being solved is as follows. A flux of bremsstrahlung is incident perpendicularly on the end face of an absorber of cylindrical shape. The diameter of the irradiation field varies from 0.5 cm to \(D_{\mathrm{cr}}\), the diameter of the absorber. The absorber was taken in the form of cylinders with diameters from 1.5 cm to 10 cm. The distribution of absorbed energy was determined over the depth of the absorber and over the radius. The relative root-mean-square error of the calculation results does not exceed 10–12%. As the initial bremsstrahlung spectrum, the spectrum calculated by Schiff’s formula for a tungsten target was adopted.

In the calculation, the following elementary processes of interaction of electromagnetic radiation with matter were taken into account: photoelectric absorption, Compton scattering, pair production; among secondary processes, annihilation of the electron and positron was taken into account.

In the general case, the absorbed energy is determined by the expression:

\[ E_{\mathrm{p}}\left(\vec r\right)=\int_{0}^{E_m} N\left(E,\vec r\right)E\cdot \mu_a(E)\,dE, \tag{1} \]

where \(E\) is the quantum energy, \(N\) is the spectrum of quanta at the point \(\vec r\), and \(\mu\) is the energy absorption coefficient.

Strictly speaking, calculation by formula (1) gives the energy transferred by quanta to secondary electrons and with the accuracy with which it is possible

neglect the transfer of energy by secondary electrons, this calculation will correspond to the absorbed energy.

To take into account the transfer of energy by secondary electrons, we proposed and investigated the following model. We assume that a secondary electron is emitted in the direction of the quantum that produced it. In this case the electron energy is absorbed along the direction of its flight according to experimentally recorded transition curves.

We carried out a test calculation of the distribution of absorbed energy over the volume of sodium chloride samples with a thickness of \(40 \ \text{g}/\text{cm}^2\) and diameters of \(1.5\), \(5\), and \(10 \ \text{cm}\), taking into account energy transfer by secondary electrons according to the model described above.

The calculations according to the model described and the results of the calculation by formula (1), within the accuracy of the calculation at depths greater than the position of the maximum, coincide.

A substantial difference in the results is observed at absorber depths smaller than the thickness of the layer in which the conditions of electronic equilibrium are fulfilled. It follows from this that, when calculating the distribution of absorbed bremsstrahlung energy in samples whose thickness is less than the range of the secondary electrons, it is necessary to take into account energy transfer by secondary electrons.

The distribution of absorbed energy over the depth of the absorber for single crystals of alkali-halide compounds is presented in Figs. 1—I, III. Along the abscissa axis is plotted the depth in the crystal in \(\text{g}/\text{cm}^2\); along the ordinate axis, the absorbed energy in units of \(\text{MeV}_{\text{abs}}/\text{MeV}_{\text{inc}}\cdot(\text{g}/\text{cm}^2)\). The obtained distributions of absorbed energy over depth are in good agreement with the experimental results [8, 9].

We also investigated the dependence of the integral value of the energy absorbed in the sample and its distribution over the volume on the dimensions of the body and the beam diameter.

The distributions of absorbed energy over the radius of the crystal have the form of decreasing curves approaching saturation. Irradiating samples with a flux of electromagnetic radiation whose cross section is equal to the area of the absorber end face on which the absorbed energy is considered as a function of the sample radius leads to a more uniform radial distribution.

The influence of the size of the irradiation field on the magnitude of the absorbed bremsstrahlung energy in alkali-halide crystals is presented in Figs. 1—III, where the abscissa axis gives the diameter of the irradiation field in \(\text{cm}\), and the ordinate axis gives the absorbed energy in \(\text{MeV}\) per \(1 \ \text{MeV}\) of incident energy.

From these results it is seen that the magnitude of the energy absorbed in the sample depends linearly on the diameter of the irradiation field. The dependence of the absorbed energy on the diameter of the samples under complete irradiation, however, exhibits saturation (Fig. 2—I).

Both of the latter dependences are determined by the magnitude of energy leakage from the sample volume. The dependence of the leakage, defined as the removal of energy through the side surfaces of the sample, on the diameter of the sample and of the irradiation field is presented in Fig. 2—II.

For unchanged combinations of irradiation field and absorber diameter, the leakages decrease on going to an absorber with a higher atomic number and on going to lower maximum bremsstrahlung energies. This is due to the fact that at larger atomic numbers of the absorber and lower bremsstrahlung energies, the mean free path of the quanta is shortened, which leads to greater absorption of the scattered radiation.

Fig. 1. Distribution of absorbed energy over the volume of samples of alkali-halide crystals under irradiation by bremsstrahlung of different energy.

I

Vertical axis: Absorbed energy, \(\left[\dfrac{\mathrm{MeV}}{\mathrm{MeV}\cdot \mathrm{cm}^{2}/\mathrm{g}}\right]\)

Horizontal axis: Crystal depth \([\,\mathrm{g}/\mathrm{cm}^{2}\,]\)

a) KCl
1 — \(E_{\max}=6\) MeV
2 — \(E_{\max}=10\) MeV
3 — \(E_{\max}=30\) MeV

b) KBr
\(D_{\mathrm{irr}}=10\) cm
Additional: \(D_{\mathrm{irr}}\)
\(H=60\ \mathrm{g}/\mathrm{cm}^{2}\)

c) KI

II

Vertical axis: Absorbed energy, \(\left[\dfrac{\mathrm{MeV}}{\mathrm{MeV}\cdot \mathrm{cm}^{2}/\mathrm{g}}\right]\)

Horizontal axis: Absorber depth \([\,\mathrm{g}/\mathrm{cm}^{2}\,]\)

a)
1 — KI
2 — KBr
3 — KCl
\(E_{\max}=6\) MeV
Additional: \(D_{\mathrm{irr}}=10\) cm

b)
1 — KI
2 — KBr
3 — KCl
\(E_{\max}=10\) MeV
Additional: \(D_{\mathrm{irr}}=10\) cm

c)
1 — KI
2 — KBr
3 — KCl
\(E_{\max}=30\) MeV

III

Vertical axis: Absorbed energy, \(\left[\dfrac{\mathrm{MeV}}{\mathrm{MeV}\cdot \mathrm{cm}^{2}/\mathrm{g}}\right]\)

a)
Horizontal axis: Absorber depth \([\,\mathrm{g}/\mathrm{cm}^{2}\,]\)

KCl
\(E_{\max}=30\) MeV
\(D_{\mathrm{irr}}=10\) cm
1 — Additional: 2 cm
2 — Additional: 4 cm
3 — Additional: 6 cm
4 — Additional: 8 cm
5 — Additional: 10 cm

b)
Vertical axis: Absorbed energy relative to the axis

Horizontal axis: Distance from the crystal axis [cm]

1 — depth \(10\ \mathrm{g}/\mathrm{cm}^{2}\)
2 — 20
3 — 30
4 — 40

c)
Vertical axis: Absorbed energy, \(\left[\dfrac{\mathrm{MeV}}{\mathrm{MeV}\cdot \mathrm{cm}^{2}/\mathrm{g}}\right]\)

Horizontal axis: Diameter of the irradiation field [cm]

\(E_{\max}=30\) MeV; 1 — NaCl; 2 — LiF; \(H=40\ \mathrm{g}/\mathrm{cm}^{2}\); \(D_{\mathrm{irr}}=10\) cm; 2a — \(D_{\mathrm{irr}}=10\) cm; 2b — \(D_{\mathrm{irr}}=4\) cm; 2c — \(D_{\mathrm{irr}}=2\) cm; 3 — KCl; 4 — KBr; 5 — KI; \(D_{\mathrm{irr}}=6\) cm

IV

Vertical axis: Absorbed energy, \(\left[\dfrac{\mathrm{MeV}}{\mathrm{MeV}\cdot \mathrm{cm}^{2}/\mathrm{g}}\right]\)

Horizontal axis: Absorber depth \([\,\mathrm{g}/\mathrm{cm}^{2}\,]\)

Columns:
\(E_{\max}=6\) MeV; \(E_{\max}=10\) MeV; \(E_{\max}=30\) MeV

Rows:
KCl
KBr
KI

Fig. 2. Dependence of the energy absorbed in the sample and its leakage on the dimensions of the samples and the cross section of the incident radiation flux

The magnitude of the energy leakage of the electromagnetic-radiation flux through the side walls of cylindrical samples is determined mainly by the ratio of the area of the irradiation field to the cross-sectional area of the sample and decreases as the cross section of the sample increases in the case where the diameter of the irradiation field and that of the absorber are equal. In this case, the error in determining the energy absorbed in the sample may reach 25% due solely to lateral leakage, especially for materials with small effective atomic numbers and density. For ratios of the diameters of the absorber and the irradiation field of 3:2 and larger, the leak—

energy losses through the lateral surfaces of the samples do not exceed 5% of the absorbed energy and may be neglected.

The results obtained for the volume distribution of absorbed energy make it possible:

a) to determine the amount of absorbed energy in any element of the sample volume from the experimentally measured amount of bremsstrahlung energy incident on the sample during an irradiation session;

b) to select, from the volume of the sample, a layer of material having the greatest uniformity in the radial distribution of absorbed energy;

c) when irradiating tissues in medical radiology, to estimate, in the part of the tissue shielded by a screen, the magnitude of the absorbed energy caused by leakage of energy under the screen from the irradiated part.

In carrying out many irradiation studies, in order to obtain the same radiation effect it is necessary to achieve uniformity in the distribution of absorbed energy throughout the sample volume. This can be achieved by using two-sided irradiation of the samples. The results obtained make it possible to estimate the uniformity of the distribution of absorbed energy with depth in the absorber under two-sided irradiation. It follows from Figs. I—IV that, by selecting the bremsstrahlung energy, it is possible under two-sided irradiation to achieve a uniformity of the depth distribution of absorbed energy no worse than 10%, which is acceptable in many problems.

REFERENCES

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3. Measurement of Absorbed Dose in Neutron Fields and in Mixed Fields “Gamma Radiation—Neutrons.” Atomizdat, Moscow, 1964.

4. A. Kh. Breger. Isotopes in the USSR, No. 2, 11 (1966).

5. V. L. Karpov. Proceedings of the All-Union Conference (Riga, April 1962), p. 42, Moscow, 1962.

6. U. Fano, L. Spencer, M. Berger. Transport of Gamma Radiation. Moscow, 1963.

7. V. A. Vorob’ev. “Radiation Physics of Nonmetallic Crystals.” Proceedings of a conference, Kiev, Naukova Dumka Publishing House, 1967, p. 327.

8. V. A. Vorob’ev. Dissertation, Tomsk, TPI, 1965.

9. G. P. Sokolov. Dissertation, TPI, Tomsk, 1968.