At present several groups are analysing quasar absorption spectra to search for variation of the fine structure constant, alpha, across space and time. These studies compare the wavelengths of several transitions observed in the absorption clouds with those seen in the laboratory, and interpret anomalies as variation in alpha. One group has already presented evidence that alpha may have been smaller at an early epoch. Other groups using different telescopes see no variation. These studies use the ???many-multiplet??? method, which relies on the utilisation of many transitions in many ions to enhance the size of the effects and remove sources of systematic error. While this method offers an order-of-magnitude improvement in sensitivity over the previously used alkali-doublet method, the alpha-dependence (relativistic shift) of every transition used in the analysis must be calculated ab initio. In this thesis we present a method for the precise calculation of relativistic shifts, based on an energy calculation involving combination of the configuration interaction method and many-body perturbation theory. The many-multiplet method also introduces a potential systematic error: if the relative isotope abundances of the absorbers differ from terrestrial abundances then there can be spurious shifts in the measured wavelengths, which may be incorrectly interpreted as variation of alpha. A ???conspiracy??? of several isotopic abundances may provide an alternative explanation for the observed spectral anomalies. To account for these systematic errors we need accurate values of the isotope shift. We calculate these shifts using the finite-field method to reduce the problem to that of an energy calculation, which in turn is done using the same method used for the relativistic shift. We present the results of our calculations for a variety of atoms and ions seen in quasar absorption spectra. The results of this research should allow astrophysicists to measure isotope abundances in the absorbers directly. This can provide a test for models of nuclear reactions in stars and supernovae, and of the chemical evolution of the Universe. Our calculations can also be used in conjunction with measurements to extract changes in nuclear charge radii between isotopes.

At present several groups are analysing quasar absorption spectra to search for variation of the fine structure constant, alpha, across space and time. These studies compare the wavelengths of several transitions observed in the absorption clouds with those seen in the laboratory, and interpret anomalies as variation in alpha. One group has already presented evidence that alpha may have been smaller at an early epoch. Other groups using different telescopes see no variation. These studies use the ???many-multiplet??? method, which relies on the utilisation of many transitions in many ions to enhance the size of the effects and remove sources of systematic error. While this method offers an order-of-magnitude improvement in sensitivity over the previously used alkali-doublet method, the alpha-dependence (relativistic shift) of every transition used in the analysis must be calculated ab initio. In this thesis we present a method for the precise calculation of relativistic shifts, based on an energy calculation involving combination of the configuration interaction method and many-body perturbation theory. The many-multiplet method also introduces a potential systematic error: if the relative isotope abundances of the absorbers differ from terrestrial abundances then there can be spurious shifts in the measured wavelengths, which may be incorrectly interpreted as variation of alpha. A ???conspiracy??? of several isotopic abundances may provide an alternative explanation for the observed spectral anomalies. To account for these systematic errors we need accurate values of the isotope shift. We calculate these shifts using the finite-field method to reduce the problem to that of an energy calculation, which in turn is done using the same method used for the relativistic shift. We present the results of our calculations for a variety of atoms and ions seen in quasar absorption spectra. The results of this research should allow astrophysicists to measure isotope abundances in the absorbers directly. This can provide a test for models of nuclear reactions in stars and supernovae, and of the chemical evolution of the Universe. Our calculations can also be used in conjunction with measurements to extract changes in nuclear charge radii between isotopes.