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 $\beta$ 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 ${}^{11}\mathrm{C}\mathcal{F}t$ 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 $\beta$ counting was used to determine the half-life.

Results: The new half-life, $t_{1/2}=1220.27\left(26\right)$ s, is consistent with the previous values but significantly more precise. A new world average was calculated, $t_{1/2}^{\text{world}}=1220.41\left(32\right)$ s, and a new estimate for the Gamow-Teller to Fermi mixing ratio $\rho$ 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 $\rho$, to allow for the determination of $V_{ud}$ from this decay.

• Received 28 August 2017
• Revised 18 December 2017

DOI:https://doi.org/10.1103/PhysRevC.97.035503