The Production of Soft Secondaries by Mesotrons

I. Cosmic-ray evidence shows that the soft component, which persists even under great thicknesses of matter, consists, primarily at least, of electrons and $\gamma$-rays. The observations of the magnitude and variation with depth of the soft component and showers, and of the size and material dependence of bursts, lead to the following rough phenomenological description: In addition to ordinary ionization losses, the mesotrons have an appreciable chance of transferring a considerable fraction of their energy to the soft component. For transfers above 2×${10}^{10}$ v this probability is roughly independent of mesotron energy. Under ${10}^{10}$ v the probability of large transfers is much greater, roughly 20 times as great as at higher energies. II. The production of secondaires of energy <${10}^{10}$ v can be accounted for by a familiar process: the Lorentz contracted Coulomb field of the mesotron, in sweeping over an atom, ejects a high energy electron. This mechanism, however, is inadequate to explain the very large energy transfers, >${10}^{10}$ v, involved in bursts. The theory which has been developed to describe the mesotron of spin one associates with transitions in which the direction of the mesotron spin changes an intrinsic dipole moment; this dipole field favors high energy transfers, and, roughly, can account for the observed bursts. However, the dipole filed also gives probabilities of high energy bremsstrahlung, >${10}^{10}$ v, much too large to be compatible with the observations. III. The cross sections for the production of electron secondaires and bremsstrahlung by the intrinsic mesotron dipole field have been estimated under the assumption that the coupling of mesotron and electromagnetic field is small; when this is not so the formula cannot be right. Examination of the approximation made indicates that the estimate of the cross section for electron secondaries should be valid up to mesotron energies of ∼${10}^{12}$ v, and is thus applicable to the bursts. The bremsstrahlung formula, on the other hand, fails at ${10}^{10}$ v; it thus cannot be used for bursts, while for energies ${10}^9<E<\mathrm{}{10}^{10}$ it leads to no contradiction with the experimental evidence. The problem of extending the formulae above these critical energies probably goes beyond the framework of present theory. The evidence indicates that it is the largeness of the coupling, and not the occurrence of lengths smaller than the critical $\frac{\hslash }{\mu c\sim 2\times {10}^{-13\mathrm{}}}$ cm, that limits the applicability of the quantum mechanics.