New analysis ofO14β decay: Branching ratios and conserved vector current consistency

The ground-state Gamow-Teller transition in the decay of ${}^{14}\mathrm{O}$ is strongly hindered and the electron spectrum shape deviates markedly from the allowed shape. A reanalysis of the only available data on this spectrum changes the branching ratio assigned to this transition by seven standard deviations: Our new result is $(0.54\pm 0.02)\%$. The Kurie plot data from two earlier publications are also examined, and a revision to their published branching ratios is recommended. The required nuclear matrix elements are calculated with the shell model, and, for the first time, consistency is obtained between the M1 matrix element deduced from the analog γ transition in ${}^{14}\mathrm{N}$ and that deduced from the slope in the shape-correction function in the β transition, a requirement of the conserved-vector current hypothesis. This consistency is obtained, however, only if renormalized rather than free-nucleon operators are used in the shell-model calculations. In the mirror decay of ${}^{14}\mathrm{C}$, a similar situation occurs. Consistency among the ${}^{14}\mathrm{C}$ lifetime, the slope of the shape-correction function, and the M1 matrix element from γ decay can be achieved only with renormalized operators in the shell-model calculation.