Radiative Corrections and Parity Nonconservation in Heavy Atoms

The self-energy and the vertex radiative corrections to the effect of parity nonconservation in heavy atoms are calculated analytically in orders $Z{\alpha }^2$ and $Z^2{\alpha }^3\ln ({\lambda }_C/r_0)$, where ${\lambda }_C$ and $r_0$ are the Compton wavelength and the nuclear radius, respectively. The sum of the radiative corrections is $-0.85\%$ for Cs and $-1.41\%$ 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, $Q_{\mathrm{W}}=-72.90\left(28{)}_{\mathrm{e}\mathrm{x}\mathrm{p}}\right(35{)}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}}$ for Cs, and $Q_{\mathrm{W}}=-116.7\left(1.2{)}_{\mathrm{e}\mathrm{x}\mathrm{p}}\right(3.4{)}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}}$ for Tl, agree with predictions of the standard model. As an application of our approach, we have also calculated analytically the dependence of the Lamb shift on the finite size of the nucleus.