Calculations of the relativistic effects in many-electron atoms and space-time variation of fundamental constants

Theories unifying gravity and other interactions suggest the possibility of spatial and temporal variation of physical “constants” in the Universe. Detection of high-redshift absorption systems intersecting the sight lines towards distant quasars provides a powerful tool for measuring these variations. We have previously demonstrated that high sensitivity to the variation of the fine-structure constant $\alpha$ can be obtained by comparing spectra of heavy and light atoms (or molecules). Here we describe new calculations for a range of atoms and ions, most of which are commonly detected in quasar spectra: Fe II, Mg II, Mg I, C II, C IV, N V, O I, Al III, Si II, Si IV, Ca I, Ca II, Cr II, Mn II, Zn II, Ge II (see the results in Table III). The combination of Fe II and Mg II, for which accurate laboratory frequencies exist, has already been used to constrain $\alpha$ variations. To use other atoms and ions, accurate laboratory values of frequencies of the strong $E1\mathrm{}$ transitions from the ground states are required. We wish to draw the attention of atomic experimentalists to this important problem. We also discuss a mechanism which can lead to a greatly enhanced sensitivity for placing constraints on variation on fundamental constants. Calculations have been performed for Hg II, Yb II, Ca I, and Sr II where there are optical transitions with the very small natural widths, and for hyperfine transition in Cs I and Hg II.