Generation of Protons by High-Energy γ-Rays

Until the present time, the bulk of experimental work on the study of the \((\gamma, p)\)-reaction has concerned the region of γ-ray energies of the order of 20–30 MeV. Since, with further increase of the γ-ray wavelength, it becomes smaller than the dimensions of the nucleus, one should expect a change in the mechanism of their interaction with nuclei. Consequently, the study of this interaction should shed additional light on the nature of the binding of nucleons in the nucleus. In this connection, work \(^{1}\) is of interest, in which an investigation was made of the angular and energy distribution of protons ejected from nuclei of various substances by the bremsstrahlung spectrum of γ-rays with a maximum energy of 320 MeV. Measurements of the range and angular distribution of the protons were made with the aid of a telescope of proportional counters connected in a coincidence circuit. The thickness of the target was chosen as a compromise between comparison with the range of the protons. The target and the telescope could rotate independently about an axis passing through the center of the target, which made it possible to carry out measurements at various angles to the axis of the γ-ray beam.

To eliminate the electron background present near the cyclotron beam, the coincidence circuit was adjusted to register only sufficiently large pulses. Operation of the circuit could be caused only by the simultaneous stopping (within \(\sim 0.5\) μsec) at the beginning and end of the counter of two electrons, which is a rather improbable event. In addition, the absence of coincidences produced by electrons is confirmed by the following facts: a) the relative effective cross section is proportional to \(Z\), not \(Z^2\); b) the effective cross section in Pb falls in the region of low energies because of the Coulomb barrier.

The possibility of recording particles of another kind was excluded by investigating the distribution of pulses in the counter by magnitude. Accidental coincidences did not exceed 15%. The greatest error in the results was introduced by the uncertainty in measuring proton ranges.

The obtained cross section was referred to the effective number of γ-quanta, equal to the total beam energy divided by the maximum γ-ray energy (320 MeV).

The energy spectrum of protons for carbon, copper, and lead, obtained at an angle of 90° to the direction of the γ-ray beam, is shown in Fig. 1.

The dependence of the differential cross section on energy can in general be represented as \(E^{-S}\), where \(E\) is the proton energy, and \(S = 1.2 \pm 0.1\) for carbon, \(1.9 \pm 0.1\) for copper, and \(2.2 \pm 0.2\) for lead. The fall of the cross section for Pb at an energy of \(\sim 10\) MeV is connected, in all probability, with the Coulomb barrier, which prevents the emission of protons.

Figure 2 presents the behavior of the relative value of the cross section at 40 MeV at an angle of 90° for Be, C, Al, Zn, Cu, Ag, Pb, and W. From the figure it can be seen that, to the accuracy attained in the experiment, the cross section for the production of protons by photons increases with increasing atomic weight proportionally to \(Z\), the number of protons in the nucleus.

In addition, the angular distribution of protons was measured for Be, C, and Cu at 10 and 40 MeV.

For protons with an energy of 10 MeV the cross section is close to isotropic; with an increase of the energy to 40 MeV, a predominance of protons scattered forward (at angles \(< 90^\circ\)) is observed.

To explain the results obtained, two different pictures of the mechanism of interaction of γ-rays with the nucleus are possible. The first consists in

Fig. 1. Energy dependence of the cross section for C, Cu, and Pb at 90°.

Fig. 2. Relative cross section as a function of atomic number.

in that the nucleus, absorbing a γ-quantum, passes into an excited state and then emits a proton, transferring to it the excitation energy. The second proceeds from the fact that the γ-quantum interacts directly with a constituent part of the nucleus (a proton, an α-particle, etc.) that contains a proton. The experimental data, in all probability, testify in favor of the predominance, at proton energies \(>30\) MeV, of the second interaction mechanism. This is confirmed both by the energy

Fig. 3. Energy dependence of the cross section.

dependence (when protons are evaporated by an excited nucleus, the cross section should vary more strongly with energy) and by the presence, in the angular distribution at \(40^\circ\), of a peak elongated forward (in the case of the first mechanism, isotropy in the angular distribution would have been observed).

In conclusion, in the paper, on the basis of simple considerations concerning the character of the direct interaction of a γ-ray with a proton, the dependence of the cross section on the energy and its absolute magnitude have been calculated. The results of the calculation are shown in Fig. 3. Discrepancies between the calculations and the experimental data at low energies are clearly visible. The absolute value of the cross section found in the calculation is \(8.3 \cdot 10^{-28}\ \text{cm}^2\); from experiment \(\sigma = 3.1 \cdot 10^{-28}\ \text{cm}^2\).

The authors explain the discrepancies by the excessively crude assumption about the form of the wave function of the proton in the nucleus adopted in the calculation.^2

V. F.

CITED LITERATURE

1. C. Levinthal and A. Silverman, Phys. Rev. 82, 882 (1951).
2. G. F. Chew and M. L. Goldberger, Phys. Rev. 77, 470 (1950).