On Coupling Conditions in Light Nuclei and the Lifetimes of $\beta$-Radioactivities

Two series of $\beta$-activities are considered. The first series involves nuclei in which the number $n_p$ of protons exceeds the number $n_n$ of neutrons by 1. The second series involves the nuclei for which $n_p=n_n$ is odd. Similarly two coupling conditions are considered: in approximation 1, the forces do not depend on either ordinary or isotopic spin. In approximation 2 only the independence of isotopic spin is assumed. Apart from these coupling conditions, no use is made of any special model. The lifetimes of the disintegrations of the first series can be calculated on the basis of either coupling condition if one adopts Fermi's original theory. The transitions of the second series are forbidden in this theory. If one adopts the modification of Fermi's theory which has been proposed by Gamow and Teller, one can calculate the lifetimes for both series assuming the validity of the first approximation but this cannot be done if only the validity of the second approximation is assumed. The discussion of the experimental data indicates that the 1st approximation applies quite well for the normal states of nuclei up to a mass of about 30.