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Abstract
Interest in the variation of fundamental constants has recently been stimulated by claims that the fine structure constant, α, was smaller in the past. Physicists are investigating whether α is currently varying using a number of methods including atomic clock experiments and quasar absorption spectra. To date atomic clock experiments have not reached the same level of precision as the quasar results but the precision to which transition frequencies are being measured is increasing dramatically and very soon atomic clock experiments based on Earth will be able to rival or surpass the quasar results. In order to relate the change in transition frequencies to a variation of α accurate calculations of relativistic effects in atoms and their dependence upon α are needed. Other effects, such as the small shift of transition frequencies due to blackbody radiation also need to be accounted for.
In this thesis we perform accurate calculations of the dependence of transition frequencies in two-valence-electron atoms and ions on a variation of α. The relativistic Hartree-Fock method is used with many-body perturbation theory and configuration interaction methods to calculate transition frequencies.
We also consider transitions with an enhanced sensitivity to α variation. In particular, narrow lines that correspond to atomic transitions between close lying, long-lived atomic states of different configurations. The small transition frequency, coupled with differences in the electron structure ensures a strong enhancement of the relative frequency change compared to a possible change in α .
We also show that using the modified form of the Dirac Hamiltonian, as suggested by Bekenstein, does not affect the analysis of the quasar data pertaining to a measurement of α variation, nor does it affect atomic clock experiments.
Finally we have performed calculations of the size of the frequency shift induced by a static electric field on the clock transition frequencies of the hyperfine splitting in Y b+, Rb, Cs, Ba+, and Hg+. The calculations are used to find the frequency shifts due to blackbody radiation which are needed for accurate frequency measurements and improvements of the limits on variation of α. Our result for Cs [δv/=E2 = -2:26(2) x 10-10Hz/(V/m)2] is in good agreement with early measurements and ab initio calculations. We present arguments against recent claims that the actual value might be smaller. The difference (~ 10%) is due to the continuum spectrum in the sum over intermediate states.