Precision half-life measurement of $^{11}\mathrm{C}$: The most precise mirror transition $\mathcal{F}t$ value

Background: The precise determination of the Ft 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. C-11 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 C-11 Ft value is the half-life. Purpose: A high-precision measurement of the C-11 half-life was performed, and a new world average half-life was calculated. Method: C-11 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(26) s, is consistent with the previous values but significantly more precise. A new world average was calculated, t(1/2)(world) = 1220.41(32) 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 C-11 world average half-life allows the calculation of a Ft(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.