Calculation of radiative corrections to the effect of parity nonconservation in heavy atoms

Abstract

We calculate the self-energy and the vertex radiative corrections to the effect of parity nonconservation in heavy atoms. The sum of the corrections is of the form ${\cal A}\ln(\lambda_C/r_0)+{\calB}$, where ${\cal A}$ and ${\cal B}$ are functions of $Z\alpha$, and $\lambda_C$ and $r_0$ are the Compton wavelength and the nuclear radius, respectively. The function ${\cal A}$ is calculated exactly in $Z\alpha$ and the function ${\cal B}$ is calculated in the leading order. In the leading order ${\cal A}\propto \alpha(Z\alpha)^2$ and ${\cal B}\propto \alpha(Z\alpha)$. The sum of the corrections is -0.85% for Cs and -1.48% for Tl. Using these results we have performed analysis of the experimental data on atomic parity nonconservation. The values obtained for the nuclear weak charge, $Q_W=-72.81(28)_{exp}(36)_{theor}$ for Cs and $Q_W=-116.8(1.2)_{exp}(3.4)_{theor}$ for Tl, agree with predictions of the standard model within $0.6\sigma$. As an application of our approach we have also calculated dependence of the Lamb shift on the finite nuclear size.