Relativistic energy shifts in Ge II, Sn II and Pb II and search for cosmological variation of the fine structure constant

Sensitivity of atomic transition frequencies to variation of the fine structure constant $\alpha=e^2/\hbar c$ increases proportional to $Z^2$ where $Z$ is the nuclear charge. Recently several lines of heavy ions Ge II, Sn II and Pb II have been detected in quasar absorption spectra. We have performed accurate many-body calculations of $\alpha^2$-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 Pb II is highly non-linear dependence on $\alpha^2$ due to the level pseudo-crossings.