On the Continuous Gamma-Radiation Accompanying the Beta-Decay of Nuclei

The quantum mechanical calculations of Knipp and Uhlenbeck, and F. Bloch of the continuous $\gamma$-spectrum associated with the sudden change of nuclear charge during $\beta$-decay have been extended to forbidden $\beta$-transitions and to the different types of $\beta$-interactions. It is shown that the $\gamma$-spectrum has practically the same shape, and the ratio of total $\gamma$-intensity to $\beta$-intensity is almost the same for forbidden transitions as for allowed transitions, irrespective of the $\beta$-interaction. This accounts for the good agreement of the theory for allowed transitions with the experiments of C. S. Wu on ${}_{15}{}^{}{}_{}{}^{}\mathrm{P}_{}^{32}{}_{}{}^{}$, a "forbidden" $\beta$-emitter. A simple classical analogue is given to explain this uniformity and is shown to justify the interpretation that the probabilities for the $\beta$- and $\gamma$-emission processes may in a very good approximation be taken as independent.