Title: Calculations of the Relativistic Effects in Many-Electron Atoms and Space-Time Variation of Fundamental Constants

Abstract: 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 provide 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 3). The combination of Fe II and Mg II, for which accurate laboratory frequencies exist, have already been used to constrain $\alpha$ variations. To use other atoms and ions, accurate laboratory values of frequencies of the strong E1-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.