Precision half-life measurement of C11 : The most precise mirror transition Ft value

Abstract

Background: The precise determination of the $\mathcal{F}t$ value in $T=1/2$ mixed mirror decays is an important avenue for testing the standard model of the electroweak interaction through the determination of ${V}_{ud}$ in nuclear $\ensuremath{\beta}$ decays. $^{11}\mathrm{C}$ is an interesting case, as its low mass and small ${Q}_{EC}$ value make it particularly sensitive to violations of the conserved vector current hypothesis. The present dominant source of uncertainty in the $^{11}\mathrm{C}\phantom{\rule{4pt}{0ex}}\mathcal{F}t$ value is the half-life.Purpose: A high-precision measurement of the $^{11}\mathrm{C}$ half-life was performed, and a new world average half-life was calculated.Method: $^{11}\mathrm{C}$ was created by transfer reactions and separated using the TwinSol facility at the Nuclear Science Laboratory at the University of Notre Dame. It was then implanted into a tantalum foil, and $\ensuremath{\beta}$ counting was used to determine the half-life.Results: The new half-life, ${t}_{1/2}=1220.27(26)$ s, is consistent with the previous values but significantly more precise. A new world average was calculated, ${t}_{1/2}^{\text{world}}=1220.41(32)$ s, and a new estimate for the Gamow-Teller to Fermi mixing ratio $\ensuremath{\rho}$ is presented along with standard model correlation parameters.Conclusions: The new $^{11}\mathrm{C}$ world average half-life allows the calculation of a $\mathcal{F}{t}^{\text{mirror}}$ value that is now the most precise value for all superallowed mixed mirror transitions. This gives a strong impetus for an experimental determination of $\ensuremath{\rho}$, to allow for the determination of ${V}_{ud}$ from this decay.