Search for cosmological variation of the fine-structure constant using relativistic energy shifts in $\mathrm{Ge}\mathrm{II}$, $\mathrm{Sn}\mathrm{II}$, and $\mathrm{Pb}\mathrm{II}$

The sensitivity of atomic transition frequencies to variation of the fine structure constant $\alpha =e^2∕\hslash c$ increases proportional to $Z^2$ where $Z$ is the nuclear charge. Recently several lines of heavy ions $\mathrm{Ge}\mathrm{II}$, $\mathrm{Sn}\mathrm{II}$, and $\mathrm{Pb}\mathrm{II}$ have been detected in quasar absorption spectra. We have performed accurate many-body calculations of the ${\alpha }^2$ dependence of transition frequencies ($q$ coefficients) for these atoms and found an order-of-magnitude increase in sensitivity in comparison with atomic transitions which were previously used to search for temporal and spatial variation of $\alpha$ in quasar absorption systems. An interesting feature in $\mathrm{Pb}\mathrm{II}$ is a highly nonlinear dependence on ${\alpha }^2$ due to the level pseudocrossings.

Figure 1

Energies of lowest even-parity multiplets of $\mathrm{Pb}\mathrm{II}$ as functions of ${\alpha }^2$. Standard ${}^{2S+1}L_J$ notations are used for atomic states. Dotted lines correspond to $J=1∕2$, short-dashed lines correspond to $J=3∕2$, and long-dashed lines correspond to $J=5∕2$.