β-Decay and Spin of Light Nuclei

The $\beta$-decay of the nuclei ${\mathrm{He}}^6$, ${\mathrm{Be}}^7$, ${\mathrm{N}}^{13}$, ${\mathrm{O}}^{15}$ and ${\mathrm{F}}^{17}$ is investigated from a point of view of the Gamow-Teller modification of the Fermi-theory. It is assumed that the lowest state of each nucleus forms a spin-multiplet. The various transition probabilities are given as functions of the total angular momentum $I$ of the various states of the nuclei. An accurate knowledge of the $\beta$-spectrum would lead to a definite prediction of the spins of the nuclei. For the timeconstant in the $\beta$-theory a value of 3·${10}^3$ sec. is obtained as compared to the previous value of 11·${10}^3$ sec.