Nuclear Photoeffect*

(Disintegration of the Deuteron by $\gamma$-Rays)

Chadwick and Goldhaber, Cambridge

By analogy with the excitation and ionization of atoms under the action of light, one may suppose that a complex nucleus also can be excited or “ionized,” i.e., disintegrated by rays of the corresponding energy. The latter is considerably easier to detect than excitation. In order for the disintegration of a nucleus to take place, it is necessary that the energy of the $\gamma$-ray exceed the binding energy of the complex nucleus. The $\gamma$-rays of thorium C'' with $h\nu = 2.62 \cdot 10^6$ electron-volts are, both in their energy and in their intensity, quite suitable for this purpose; and, using them, one may hope to produce disintegration with the emission of a heavy particle (such as, for example, a neutron, a proton, etc.) only in those nuclei which have a small or negative mass defect, for example, $\mathrm{D}^2$, $\mathrm{Be}^2$, and radioactive nuclei emitting $\alpha$-particles. The emission of a positive or negative electron upon absorption of a $\gamma$-ray would be difficult to detect, unless the nucleus obtained as a result were radioactive.

For investigation, heavy hydrogen was chosen first of all, since the mass defect of the deuteron is small, and it itself is the simplest of all nuclear systems; these properties have the same significance for nuclear theory as the properties of hydrogen have for atomic theory. The disintegration was assumed to proceed according to the scheme:

$$ \mathrm{D}_1^2 + h\nu \longrightarrow \mathrm{H}_1^1 + \mathrm{n}_0^1 . \tag{1} $$

Since the momentum of the quantum is small, and the masses of the proton and neutron are almost equal, the excess disintegration energy $h\nu - W$ (where $W$ is the binding energy of these particles) must be distributed almost equally between the proton and the neutron.

We give a description of the experiment. The ionization chamber was filled with 95% heavy hydrogen, kindly supplied by Dr. Oliphant. The chamber was connected in the usual arrangement to a linear amplifier and an oscillograph. When the heavy hydrogen was exposed to the $\gamma$-radiation of radiothorium, oscillograph deflections were observed.

* Nature, 134, 237, 1934; translated by A. A. Ilyina.

Investigation showed that these recoil particles should be attributed to protons produced as a result of the disintegration of the deuton. When a radium source of equal intensity of \(\gamma\)-radiation was used, only a negligible number of kicks was observed. On the basis of this fact we conclude that the disintegration cannot be effected to any appreciable extent by \(\gamma\)-rays with energy less than \(1.8\cdot 10^6\) electron-volts, which is precisely the case for the sharp line in the spectrum of radium C.

If the scheme (1) proposed by us for the nuclear process is correct, then it is possible to calculate the mass of the neutron with sufficient accuracy, since the masses of the atoms of hydrogen and heavy hydrogen are known very accurately. They are respectively 1.0078 and 2.0136. Since the deuton can be disintegrated by \(\gamma\)-rays with energy \(2.62\cdot 10^6\) electron-volts (the strong \(\gamma\)-rays of thorium C″), the value of the neutron mass must lie between 1.0058 and 1.0086. However, taking into account the absence of any appreciable action of the \(\gamma\)-rays of radium C with energy \(1.8\cdot 10^6\) electron-volts, one can calculate that the mass of the neutron must exceed 1.0077. If it were possible to measure the energy released from the proton nucleus in the disintegration (1), then the mass of the neutron would be determined very accurately. Rough estimates of the proton energy were made on the basis of measurements of the magnitude of the recoils of the oscillograph in the experiment described above. The value obtained turned out to be about 250,000 V, which gives \(2.1\cdot 10^6\) electron-volts for the binding energy of the deuton nucleus and 1.0080 for the neutron mass. These calculations of the proton energy, however, are very rough, and at present we can only accept for the neutron mass the value 1.0080 with an error limit of \(\pm 0.0005\). Preliminary calculations of the neutron mass, based on measurements of the energy in known nuclear reactions, gave values 1.007 and 1.010\(^{2,3}\). These calculations, however, are based not only on assumptions concerning nuclear processes, but also on changes obtained with the aid of mass spectrographs, whose accuracy may reach 0.001 mass units. It seems very important to determine the mass of the neutron with sufficient accuracy, and there is hope of accomplishing this by applying the new method set forth in the present article.

Experiments for observing the disintegration of the deuton will be carried out in a Wilson chamber. They will be able to confirm the nuclear process proposed by us and, at the same time, the hypothesis that the deuton consists of a proton and a neutron. From these experiments it will also be possible to obtain the energy of the protons and their angular distribution.

If the mass defect of the deuton is approximately \(2\cdot 10^6\) electron-volts, as follows from our experiments, then it is quite clear that the deuton cannot be disintegrated upon capture of a polonium \(\alpha\)-particle. When an \(\alpha\)-particle collides with a nucleus of mass \(M\), under the condition that the law of conservation of momentum is fulfilled, only a part of its kinetic energy, equal to \(\dfrac{M}{M+4}\), can be used for disintegration. In the case of the deuton this part will be \(1/3\)

NUCLEAR PHOTOEFFECT (DECOMPOSITION OF THE DEUTON BY γ-RAYS)

of the kinetic energy of the α-particle, which for a polonium α-particle will be considerably less than \(1.8 \cdot 10^{6}\) electron-V. Radium \(C'\) particles, possessing greater energy, should be precisely suitable for this case, and Dunning (Dunning)\(^{5}\) did in fact observe a small effect by placing heavy water in a radon tube.

Our experiments on the decomposition of the deuton by γ-rays of \(2.62 \cdot 10^{6}\) electron-V gave a value of the effective cross section of about \(10^{-28}\ \mathrm{cm}^{2}\). Bethe and Peierls (H. Bethe and R. Peierls), in a briefly published communication, calculated this effective cross section on the basis of the proton interaction force, whose magnitude is given by the theory of Heisenberg, Majorana, and Wigner. They obtained the transition probability by the ordinary quantum-mechanical method, and from their data one obtains a value of the effective cross section of the same order as the observed one, only slightly exceeding it under the condition that we take the neutron mass equal to 1.0080. If, conversely, from the experimental value of the effective cross section we obtain the neutron mass, we get 1.0085, which is already considerably higher. Thus the agreement of theory with experiment may be regarded as satisfactory, but not complete.

It is also necessary to mention further steps in this direction. Lea’s experiments found that paraffin bombarded by neutrons emits hard γ-radiation, greater in intensity and in quantum energy than in the bombardment of carbon alone. This can be explained by the fact that, in the collision of a neutron and a proton, these particles may sometimes combine in the form of a deuton with emission of a γ-quantum. This phenomenon is opposite to the processes described above. Now, if one assumes the validity of the principle of microscopic reversibility of all processes occurring in thermodynamic equilibrium among deutons, protons, neutrons, and radiation, we can calculate the relative probabilities of reaction (1), without any special hypotheses about the interaction forces. Using the value of the effective cross section from reaction (1), one can calculate the effective cross section for the capture of a neutron by a proton in the case where the kinetic energy of the neutron is \(2(h\nu - W) = 1.0 \cdot 10^{6}\) electron-V in the coordinate system of the proton before the collision. In this case the effective cross section \(\sigma_{c}\) for the union of the particles into the ground state of the deuton (we discard the possibility of higher states) is obtained as much smaller than the effective cross section \(\sigma_{p}\) for the photoeffect. It seems improbable that \(\sigma_{c}\) should become considerably larger for the more durable neutrons used in Lea’s experiments. Consequently, the interpretation of his observations at present appears almost impossible, since the effect of capture of neutrons by protons must be extremely small. A satisfactory explanation can be given only after further investigations.

References

1. K. T. Bainbridge, Phys. Rev. 44, 57, 1933.
2. J. Chadwick, Pros. Roy. Soc. A. 142, 1, 1933.
3. I. Curie and F. Joliot, Nature 133, 721, 1934.
4. Rutherford and A. E. Kompton, Proc. Roy. Soc., A. 143, 724, 1934.
5. Dunning, Phys. Rev. 45, 586, 1934.
6. Lea, Nature 133, 24, 1934.