On the Continuous $\gamma$-Radiation Accompanying the $\beta$-Decay

Combining Fermi's theory of the $\beta$-decay with the ordinary principles of quantum electrodynamics one can treat the continuous radiation, to be expected from the acceleration of charges during the nuclear decay. Formulae for its spectral distribution and its total intensity are developed, applicable to light elements, where the effect of the nuclear Coulomb-field on the electrons can be neglected. The relative amount of energy, liberated in the form of radiation, increases monotonously with increasing total energy; in the case of radioactive boron it amounts to about 0.6 percent.