A Note on the Theory of -Radioactivity

Abstract

THE ratio between the probability of absorption of a K-electron by a nucleus and the total probability of emission of a positron by the same nucleus can be calculated on the hypothesis put forward by Fierz¹ that the interaction term in the neutrino theory contains the five possible invariants. Let J_K be these invariants, obtained by scalar products from combinations of Dirac's matrices. If one puts the probability of the process of -radioactivity is proportional to H². Let W_el be the momentum of the neutrino, that of the electron, and the energy of the latter, these quantities being measured in units of mc and mc² (m = mass of the electron ; c = velocity of light). If the atomic number Z of the reacting nucleus is small, one obtains for the probability P(W)dW of the emission of an electron (a positron), the energy of which lies between W and W + dW: where k is a constant. The energy p of the neutrino is equal to the difference W_o between the energies of the initial and the final nucleus, minus the energy W_el of the emitted particle. The signs ± in (1) refer to an electron or a positron.