The Disintegration of High Energy Protons

The coupling between light and heavy particles assumed in the Fermi theory of $\beta$-decay makes it possible for high energy protons in passing through matter to transfer a considerable fraction of their energy to electrons and neutrinos. If we suppose that this coupling is a maximum for relative energies of the light and heavy particles of the order $\frac{\hslash c}{R}$, with $R$ the range of nuclear forces, and is small for much higher relative energies, the most important process which occurs, for sufficiently energetic protons, can be pictured as a sort of photodisintegration of the proton by the contracted Coulomb field of a passing nucleus, the proton changing into a neutron and emitting a positron and a neutrino. With a coupling of the type described, and of the magnitude required by the proton-neutron forces, processes involving more than one pair of light particles will be relatively rare. The cross section for the disintegration of a proton of energy $E$ is found to be of the order $2\pi \left(\frac{\hslash }{\mathrm{Mc}}\right)R{Z}^2{\alpha }^2{\ln }^2 \left(\frac{E}{M{c}^2}\right),$ and is very small, even for heavy nuclei. The mean energy given to the positron per disintegration is of the order $\frac{2\left(\frac{\hslash c}{R}\right)\left(\frac{E}{M{c}^2}\right)}{\ln \left(\frac{E}{M{c}^2}\right)}.$ The positrons emitted in these disintegrations can account in order of magnitude for the incidence of showers observed under thick absorbers.