Improved experimental limit on the electric dipole moment of the electron

New results are reported in our search for the electric dipole moment ${\mathit{d}}_{\mathit{e}}$ of the electron in the ground 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$ state of ${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$. The atomic-beam magnetic resonance method is employed with separated oscillating fields. A magnetic field B defines the axis of quantization, and an electric field E, parallel to B, is applied in the region between the oscillating fields. Laser optical pumping is used for state selection and analysis, and the signal is fluorescence accompanying the decay of excited atoms in the analyzer region. The signature of a nonzero electric dipole moment is a dependence of the signal on the P,T-odd rotational invariant E⋅B (P and T denote parity and time reversal, respectively). Two counterpropagating atomic beams are employed to reduce a systematic effect due to the motional magnetic field E×v/c. Auxiliary experiments are performed to isolate and eliminate residual sources of systematic error. The result is ${\mathit{d}}_{\mathit{e}}$=[1.8±1.2(statistical)±1.0(systematic)]×${10}^{\mathrm{-}27}$ e cm. A detailed discussion is given of the experimental method, sources of systematic error and their elimination, and results.