First-Principle Analysis of Strength of Parity Nonconservation in Atomic Thallium by Relativistic Many-Body Theory

With use of relativistic many-body perturbation theory, $E_1=(1.51\mathrm{}\pm 0.07)\left(i{\mu }_{\mathrm{B}}{Q}_W\right)\times {10}^{-10\mathrm{}}$ has been obtained for the $6P_{\frac{1}{2}}\to 7P_{\frac{1}{2}}$ dipole transition matrix element in the presence of parity-nonconserving weak electron-nucleon interaction effects explicitly, which on combination with the available experimental $M_1$ leads, for ${{sin}^2\theta }_{\mathrm{W}}=0.23\mathrm{}$, to $\delta =(1.65\mathrm{}\pm 0.24)\times {10}^{-3\mathrm{}} \mathrm{and} (1.68\mathrm{}\pm 0.25)\times {10}^{-3\mathrm{}}$ respectively, for ${}_{}{}^{203}{}_{}{}^{}\mathrm{Tl}$ and ${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$ in good agreement with the most recent experimental result for $\delta$.