Forbidden Transitions inβ-decay and Orbital Electron Capture and Spins of Nuclei

Abstract

A general formula giving minimum lifetimes for forbidden $\ensuremath{\beta}$-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 ${\mathrm{K}}^{40}$ 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 $\ensuremath{\beta}$-rays from ${\mathrm{Na}}^{24}$, ${\mathrm{P}}^{32}$, and RaE, it follows that the tensor interaction alone can explain both the lifetimes and energy spectra of forbidden $\ensuremath{\beta}$-transitions. The application of the tensor interaction to ${\mathrm{K}}^{40}$ and to the other long-lived $\ensuremath{\beta}$-emitters, ${\mathrm{Rb}}^{87}$, ${\mathrm{Lu}}^{176}$, ${\mathrm{Be}}^{10}$, ${\mathrm{C}}^{14}$, and to existing data on orbital electron capture, leads to certain spin and parity predictions about parent and product nuclei---e.g., neither ${\mathrm{Be}}^{10}$ nor ${\mathrm{C}}^{14}$ can have a spin greater than $3\ensuremath{\hbar}$, the 2-Mev $\ensuremath{\gamma}$-ray from ${\mathrm{K}}^{40}$ is associated with $K$-electron capture to an excited state of ${\mathrm{A}}^{40}$ 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.