The Emission of Radiation in the Disintegration of Mesons

Abstract

The probability has been calculated that a meson of integral spin disintegrates into an electron, a neutrino, and a photon. This is essentially a classical process, the radiation being regarded as caused by the acceleration of charge in the disintegration. Because of the classical nature of the problem, the result is independent of the quantum mechanical properties (spin, coupling) of the meson field. For definiteness, the non-radiative decay is taken as being a two-body process in accordance with the original Yukawa theory, but several different types of couplings are used. The quantum mechanical probability for emission of one photon diverges at the low frequency end of the spectrum; this difficulty is avoided by using as a measure of the process the ratio of mean energy emitted to mean energy available for the process per unit time. This is of order $\frac{e^2}{\hslash c}$; the energy spectrum also is in agreement with the classical result.