PHOTODISSOCIATION OF THE PROTON

Let us consider some beta-decay reaction

\[ Z \to (Z+1)+e^-+\nu+Q \tag{1} \]

(\(Z\) is the charge of the initial nucleus; \(e^-\), \(\nu\), and \(Q\) denote, respectively, the electron, the neutrino, and the energy difference of the initial and final nuclei). If reaction (1) is possible, then the reverse (endothermic) reaction must also proceed:

\[ (Z+1)+\gamma \to Z+e^+ + \nu \tag{2} \]

(\(e^+\), \(\gamma\) denote, respectively, the positron and the \(\gamma\)-quantum), provided only that the energy of the \(\gamma\)-rays is sufficiently large. It must be equal to the energy at rest of the pair of electrons—positron plus \(Q\). In particular, since the theory of beta decay predicts the radioactivity of the free neutron (reaction (1) for \(Z=0\)), one may expect the phototransformation of the proton into a neutron (reaction (2) for \(Z=0\)). For this a \(\gamma\)-ray with energy \(1.77\) MeV is required (the mass difference

Photodissociation of the Proton

of the neutron and proton is 0.75 MeV; the rest energy of the electron–positron pair is 1.02 MeV). Two notes are devoted to the theoretical and experimental investigation of this possibility.^1,2

In the experimental work^1 the transformation of a proton into a neutron under the action of γ-rays was compared with the photodisintegration of the deuteron and of beryllium (threshold γ-ray energies: 2.19 MeV for the deuteron, 1.63 MeV for beryllium). A γ-ray source (\(\mathrm{Mn}^{56}\), emitting four γ-lines with energies 0.845, 1.81, 2.13, and 2.7 MeV) was placed at the center of a cylindrical vessel containing 22.5 liters of distilled water. To detect neutrons, a silver cylinder was placed for three minutes between the source and the water; it was then quickly removed and positioned so that a thin-walled Geiger counter was inside it. The neutrons were registered by the activity induced by them in the silver. Then part of the water was successively replaced by known amounts of heavy water and of a beryllium chloride solution, and the same operations were carried out. Taking into account the activity produced in the silver by γ-rays and introducing a correction for the different numbers of H, D, and Be atoms present, the authors obtained the following ratios of effective cross sections for photodisintegration of the proton \((\sigma_{\mathrm H})\), the deuteron \((\sigma_{\mathrm D})\), and the beryllium nucleus \((\sigma_{\mathrm{Be}})\):

\[ \frac{\sigma_{\mathrm H}}{\sigma_{\mathrm{Be}}}<5\cdot 10^{-5}; \qquad \frac{\sigma_{\mathrm{Be}}}{\sigma_{\mathrm D}}=5. \]

The last ratio, as the authors point out, is not of substantial interest, since the numbers of γ-quanta causing disintegration of beryllium and of the deuteron are different. Only the 2.7 MeV quantum splits the deuteron, whereas Be is also split under the action of γ-rays with energies 1.81 and 2.13 MeV. However, the first ratio (indicating the practical absence of neutrons caused by photodisintegration of protons) can be used to estimate the upper limit of \(\sigma_{\mathrm H}\). Taking for \(\sigma_{\mathrm{Be}}\) at γ-ray energies of about 2 MeV the value^3 \(\sim 8\cdot 10^{-28}\ \mathrm{cm}^2\), the authors obtain:

\[ \sigma_{\mathrm H}<4\cdot 10^{-32}\ \mathrm{cm}^2 \quad \text{at γ-ray energy } \sim 2\ \mathrm{MeV}. \]

The theoretical study of the reaction of transformation of a proton into a neutron is carried out very simply on the basis of Fermi’s theory of beta decay.^2 Taking the scalar variant of the interaction of the electron–neutrino and proton–neutron fields, the author obtains:

\[ \sigma_{\mathrm H}\sim \frac{30}{\pi^2}\frac{e^2}{hc}G^2 \left(\frac{h}{m_e c}\right)^2 \left\{ \left[ \frac{E_\gamma-(M_n c^2-M_p c^2)}{m_e c^2} \right]^2 \cdot \frac{m_e c^2}{E_\gamma} \right\}, \tag{3} \]

where \(G\) is a dimensionless constant characterizing the magnitude of the Fermi interaction; \(m_e\), \(M_p\), \(M_n\) are the masses, respectively, of the electron, proton, and neutron; \(E_\gamma\) is the γ-ray energy.

For \(E_\gamma \sim 2\) MeV we have: \(\sigma_{\mathrm H}\sim 10^{-46}\ \mathrm{cm}^2\). This agrees excellently with the fact that the effect under investigation could not be detected experimentally.

Thus, the photodisintegration of the proton proves to be extremely improbable, which, however, does not diminish the fundamental significance of this reaction.

V. Averbakh

References

1. R. L. Burling and E. N. D. Kurie, Phys. Rev. 74, 109 (1948).
2. H. Primakoff, Phys. Rev. 74, 110 (1948).
3. B. Russell, D. Sachs, A. Wattenberg, and R. Fields, Phys. Rev. 73, 545 (1948).