Forbidden Transitions in β -decay and Orbital Electron Capture and Spins of Nuclei

A general formula giving minimum lifetimes for forbidden β-transitions of arbitrary order forbidden orbital electron capture is derived. Exact Coulomb wave functions are used for the electron. It is shown that the observed electron emission of K⁴⁰ requires Gamow-Teller selection rules. Combined with the Konopinski-Uhlenbeck result that only the tensor and vector interactions are compatible with the energy spectra of the β-rays from Na²⁴, P³², and RaE, it follows that the tensor interaction alone can explain both the lifetimes and energy spectra of forbidden β-transitions. The application of the tensor interaction to K⁴⁰ and to the other long-lived β-emitters, Rb⁸⁷, Lu¹⁷⁶, Be¹⁰, C¹⁴, and to existing data on orbital electron capture, leads to certain spin and parity predictions about parent and product nuclei---e.g., neither Be¹⁰ nor C¹⁴ can have a spin greater than 3, the 2-Mev γ-ray from K⁴⁰ is associated with K-electron capture to an excited state of A⁴⁰ having even parity, etc. The stability of the known neighboring isobars and the conditions under which L-electron capture becomes more probable than K-electron capture are also discussed.