Relativistic energy shifts of atomic excitation energies, showing the dependence of these energies on the value of the fine-structure constant $\alpha$, are needed to extract past changes in $\alpha$ from spectra of distant quasars. These shifts are calculated by the Fock-space coupled cluster method and its extrapolated intermediate Hamiltonian extension, which allow high-accuracy treatment of electron correlation. The accuracy of the method is tested by comparing 33 transition energies in heavy atoms (obtained with the laboratory $\alpha$) with experiment; the average error is $258{\mathrm{cm}}^{-1}$, and the largest error is $711{\mathrm{cm}}^{-1}$. This may be compared with an average error of $432{\mathrm{cm}}^{-1}$ and a maximum error of $2150{\mathrm{cm}}^{-1}$ in the work of Dzuba et al., who reported most of the available energy shift calculations. The enhanced accuracy is due to more extensive inclusion of electron correlation. To obtain the energy shifts, we repeated the calculations with different values of $\alpha$ (within 0.1% of the current value). Our shifts differ by up to 30% from the values given by Dzuba et al., with an average difference of 9%. Based on the better quality of the present-day excitation energies, we believe the energy shifts reported here are more accurate than earlier work.

• Received 11 October 2006

DOI:https://doi.org/10.1103/PhysRevA.74.062505