Determination of the Absolute Intensity of $\gamma$-Ray Beams

Determination of the energy flux in a beam of $\gamma$-quanta, necessary for finding the cross sections of nuclear reactions, is usually carried out by measuring the ionization in a thick-walled graphite ionization chamber.^1 In this case the intensity of the $\gamma$-ray beam is measured in roentgens, whose conversion into the number of quanta requires a special choice of the chamber geometry and the specification of a number of parameters. In the case of high-energy $\gamma$-rays, apparently more convenient and accurate are methods proposed in work on the study of the absolute energy of the $\gamma$-beam at the 330-MeV synchrotron.^2 The authors proposed two methods for calibrating the beam. The first of them is based on measuring the area under the curve of ionization losses as a function of absorber thickness in $\mathrm{g/cm^2}$ for various elements. The inaccuracy of the area method consists in the difficulty of allowing for small changes of $dE/dt$ with electron energy. Good results are obtained when a light absorber is used. The second method for measuring the absolute intensity of a $\gamma$-beam consists in studying the initial slope of the ionization-loss curves. At the beginning of the transition curve the cascade processes are negligibly small; therefore, by comparing the curves for two elements, one can, using the different dependence on $Z$ of the separate terms of the Compton effect and of the pair-production effect, separate the latter. Then, on the basis of the theoretical value for the pair-production cross section, averaged over the primary spectrum of the $\gamma$-rays, the absolute value of the energy flux is found. Naturally, for the measurement it is better to take elements that differ strongly in $Z$.

The table gives the calibration results obtained by both methods.

The described method is also suitable for lower energies. Thus, in work carried out on the 46-MeV betatron,^3 the authors, using Pb, Cu, Al, and C as absorbers, obtained mutually consistent results for both methods. To check them, the integrated cross section for the reaction \(\mathrm{Cu}^{63}(\gamma,n)\mathrm{Cu}^{62}\) was measured. The activity induced in a copper foil was measured with a calibrated counter. It was found that

\[ \int \sigma_{\gamma n}(E)\,dE = (0.77 \pm 0.15)\,10^{-24}\ \mathrm{cm^2\,MeV}. \]

The value obtained is close to the previously measured values \((1.5\cdot10^{-24}\ \mathrm{cm^2\,MeV},\ 0.6\cdot10^{-24}\ \mathrm{cm^2\,MeV}\) and \(0.7\cdot10^{-24}\ \mathrm{cm^2\,MeV})\), and also agrees with the theoretical cross section, equal to \(0.95\cdot10^{-24}\ \mathrm{cm^2\,MeV}\).

The calorimetric method for measuring the energy flux of \(\gamma\)-rays was used in work carried out on a betatron with a maximum energy in the \(\gamma\)-ray spectrum of \(E_{\gamma m}=22.6\ \mathrm{MeV}\).^6 The calorimeter consisted of an octagonal vessel immersed in an oil bath. In two identical lead cylinders (4.2 cm in diameter and 3.0 cm long) placed in the calorimeter, 3000-ohm thermistors, forming the arms of a Wheatstone bridge, were mounted. One of the cylinders was irradiated with the \(\gamma\)-beam for 5 min. The energy required to reproduce the resistance-change curve of the thermistor obtained under irradiation was supplied from a calibration coil, also placed in the cylinder. The fraction of the \(\gamma\)-beam energy absorbed in the lead cylinder and causing the observed temperature rise was determined by measuring the distribution of ionization along the depth of the lead, performed by means of a plane ionization chamber. The ionization distribution in the transverse direction was found with the aid of x-ray film. The energy flux of \(\gamma\)-rays measured in this way was \(4695 \pm 100\ \mathrm{erg/cm^2\,roentgen}\), calculated for a thimble chamber surrounded by 8 cm of lead.

Absolute intensity in units of \(10^9\ \mathrm{MeV/sec}\) at a distance of 140 cm from the synchrotron target

According to the authors’ opinion, the calorimetric method can provide high accuracy in determining the intensity of \(\gamma\)-ray beams of various energies.

B. R.

CITED LITERATURE

1. M. Lax, Phys. Rev. 72, 61 (1947).
2. Blocker, Kenney and Panofsky, Phys. Rev. 79, 419 (1950).
3. L. Marshall, A. H. Rosenfeld and S. C. Wright, Phys. Rev. 83, 305 (1951).
4. I. S. Laughlin and I. W. Beattie, Rev. Sci. Instr. 22, 572 (1951).