INVESTIGATION OF THE ABSORPTION OF HIGH-ENERGY GAMMA QUANTA

Until recently, experimental verification of the laws of absorption of $\gamma$-rays was limited to the region of comparatively low energies.

The greatest energy of $\gamma$-rays obtained in various radioactive transformations is 17 MeV (the reaction $\mathrm{Li}^7(p,\gamma)\mathrm{Be}^8$). The appearance of electron accelerators (betatron and synchrotron), which produce, upon the abrupt braking of accelerated electrons, a directed beam of $\gamma$-quanta, extends the accessible energy range to hundreds of MeV.

Investigation with the aid of accelerators, however, is made very difficult by the fact that the spectrum of the radiation is in this case continuous.

In Adams’ work the region of absorption of $\gamma$-quanta obtained from a 22 MeV betatron is studied in the energy interval between 1 and 20 MeV.

Table I

The method of measurement is based on the use of the reaction $(\gamma,n)^*$, as a result of which a radioactive isotope of the detector element is formed. In front of the detector under study there is placed a control plate of the same material and of the same dimensions as the detector. The ratio of the activities induced in the detector and in the control plate after irradiation serves as an indicator of the absorption of $\gamma$-rays in the absorber. The absorption coefficient $(\tau)$ is determined from the formula $\dfrac{I}{I_0}=e^{-\tau x}$, where $x$ is the thickness of the absorber, and $I_0$ and $I$ are the intensities of the beam before and after absorption, propor—

* See Uspekhi Fizicheskikh Nauk, XXXVII, 256 (1949).

Table II

[[unclear: beginning of word]] of the induced activity in the detector and in the control plate. The width of the energy interval for which absorption was determined is bounded below by the threshold of the nuclear photoeffect of the detector material. The upper limit is the maximum energy of the spectrum, i.e., the energy to which the electrons are accelerated in the accelerator.

Table I gives the reactions, their threshold energy, and the width of the spectral interval used.

The beam intensity at a distance of 1 m from the target, measured with a thick-walled ionization chamber, was about 100 roentgens per minute.

Aluminum, iron, copper, and lead were used as absorbers. Measurements were made for various absorber thicknesses (up to twelve), confirming the exponential law of absorption.

Table II gives the measured absorption coefficients, their theoretical values, and the difference between the theoretical and experimental values.

As is seen from the table, for absorption in aluminum and iron the experimental results obtained are in excellent agreement with the theoretical ones.

For copper and lead there is a considerable discrepancy between the theoretical and experimental data, exceeding the magnitude of the error severalfold. The reduced, in comparison with the theoretical, absorption coefficient for copper is explained by the author by the influence of the $(\gamma, n)$ reaction. The decrease in the absorption coefficient in the case of lead may be ascribed to the inapplicability of the Born approximation to the calculation of pair production in lead

\[ \left(\frac{Ze}{\hbar} = 0.6\right). \]

A detailed work by Puusson² is devoted to the study of the absorption of $\gamma$-rays with energy

about 90 MeV, carried out on a 100 MeV betatron*). As a detector there was used a spectrometer registering coincidences from pairs created by gamma rays. The number of pairs registered in a given narrow energy interval is proportional to the total number of gamma quanta in this interval. However—

Fig. 1. Schematic of the setup: 1 — ionization chamber; 2 — lead shield; 3 — absorber; 4 — collimator; 5 — target; 6 — counters.

Fig. 2. General view of the setup.

the decrease in intensity in the middle part of the gamma spectrum caused by the introduction of the absorber directly characterizes the coefficient

* For a description of this betatron see UFN, XXX, 11 (1946).

absorption in the given interval, since, while scattering in the absorber, γ-quanta of higher energy also enter the counter. However, if one chooses an interval located sufficiently close to the upper edge of the spectrum, then, obviously, the indicated distortion can be neglected.

Table III

In the work, absorption coefficients were found separately for the process of pair production and for the Compton effect.

For this the relation

\[ \frac{\sigma'}{\sigma''}= \frac{\sigma'_p(1+\alpha')}{\sigma''_p(1+\alpha'')}, \tag{2} \]

was used, where \(\sigma'\) and \(\sigma''\) are the total effective absorption cross sections in materials I and II, \(\sigma'_p\) and \(\sigma''_p\) are, respectively, the effective cross sections for pair production, and \(\alpha'\) and \(\alpha''\) are the ratios of the Compton-scattering cross section to the pair-production cross section.

If material II is taken with a high atomic number \(Z\), then at \(E \sim 90\) MeV the value of \(\alpha''\) may be neglected, and from (2) the value of \(\alpha'\) is obtained with good accuracy.

Table IV

Value of \(\alpha\) at \(E = 88\) MeV

The mean value of the energy for which the cross sections were determined was \(88 \pm 1\) MeV. The arrangement of the apparatus is shown in Fig. 1. A beam from the beryllium target passes through a slit in a lead screen and then through the absorber, collimator, and spectrum analyzer. In front of the lead screen there is an ionization chamber that controls the intensity of the betatron. In the collimator, a constant magnetic field removes charged particles from the γ-ray beam.

The main part of the spectrum analyzer is a constant magnet 60 cm in diameter. A target is placed at its edge, in which pairs are produced.

On both sides of the target Geiger–Müller counters are placed, connected in coincidence.

The general view of the apparatus is shown in Fig. 2. Particular attention in the work was paid to collimation of the beam.

The measurements were greatly complicated by the presence of scattered radiation with an energy of about 10 MeV, apparently caused by electrons that had passed through the betatron target.

As a result of the measurements, total cross sections for the absorption of $\gamma$-rays with an energy of 88 MeV were obtained for six elements—Be, Al, Cu, Sn, Pb, and U. Table III compares the values obtained for the total cross sections with the calculated theoretical cross sections.

The deviation of the experimental results from the theoretical ones in all cases, with the exception of Be, is approximately proportional to the square of the atomic number $Z^2$ (within the range of $Z$ values given in the table), which the author explains by the inadequacy of the Born approximation. The discrepancy for Be may be explained by the use of the Fermi–Thomas model in the calculation.

The paper then gives the results of measurements of the ratio of the pair-production cross sections in various materials.

Table IV gives the values found for the quantity $\alpha$ (cm$^2$). These values agree within 15% with the Klein–Nishina formula at an energy of 88 MeV.

P. K.

References

1. G. D. Adams, Physical Review 74, 1707 (1948).
2. J. L. Lauson, Physical Review 75, 433 (1949).