Precise Test of Electroweak Theory from a New Measurement of Parity Nonconservation in Atomic Thallium

We report a new measurement of parity nonconserving (PNC) optical rotation near the 1.28 $\mu$m, ${6P}_{1/2}\to {6P}_{3/2}$ magnetic dipole transition in thallium. We find the ratio of the PNC $E1\mathrm{}$ amplitude to the $M1\mathrm{}$ amplitude to be $R=(-14.68\mathrm{}\pm 0.17)\times {10}^{-8\mathrm{}}$, which within the present uncertainty of atomic theory yields the thallium weak charge $Q_w\left({}_{}{}^{205}{}_{}{}^{}T\mathrm{l}\right)=-114.2\mathrm{}\pm 3.8$ and the electroweak parameter $S=-2.2\mathrm{}\pm 3.0$. Separate measurements on the $F=1\mathrm{}$ and $F=0\mathrm{}$ ground-state hyperfine components of the transition yield $R_1-R_0=(0.15\pm 0.20)\times {10}^{-8\mathrm{}}$, which limits the size of nuclear spin-dependent PNC in Tl.