Parity-violating electron scattering provides a largely model-independent way of measuring neutron densities in nuclei that has important implications for the structure of nuclei and neutron stars. In this paper we calculate radiative corrections to the parity-violating asymmetry $A_{\mathrm{pv}}$ in electron-nucleus scattering including vertex and vacuum polarization contributions. We find large cancellations between the vertex corrections to the vector and axial-vector vertices. As a result, the total radiative correction in second Born approximation is dominated by vacuum polarization and is of order $-0.5\%$. Coulomb distortions have modest effects on radiative corrections for ${}^{12}\mathrm{C}$ and ${}^{48}\mathrm{Ca}$ nuclei. For ${}^{208}\mathrm{Pb}$, Coulomb distortions reduce the total radiative correction to only about 0.1%. Therefore, these corrections are not important for the interpretation of the PREX and MREX experiments on ${}^{208}\mathrm{Pb}$ and for the CREX experiment on ${}^{48}\mathrm{Ca}$. However, radiative corrections must be carefully included for a precision measurement of the weak charge of ${}^{12}\mathrm{C}$.

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• Electroweak interactions in nuclear physics
• Electroweak radiative corrections
• Lepton induced nuclear reactions
• Neutron skin thickness