The isotope shift is the difference between the transition frequencies of two isotopes of the same atom. The frequency spectrum is determined by the electronic interaction between the protons in the nucleus and the electrons. But the neutrons also make a small difference: carbon-12 and carbon-14, for example, have slightly different frequencies.

The isotope shift is important because, when searching for variation of α in quasar absorption spectra, we assume that the gas clouds have the same isotopic abundances as there are on Earth: the ratio of, say, magnesium-24 to magnesium-26 is the same everywhere. If the ratios differ, then the QSO lines will be shifted compared to the terrestrial lines, and this may incorrectly be accredited to a difference in α. In the case of magnesium, we know the isotope shift (it has been measured), but we still don't know the abundance ratios in the clouds. Nonetheless we can at least make estimates of the size of the systematic effect. In the case of most of the atoms used in this study, however, isotope shifts have not been measured. This has promped our group to calculate the isotope shifts, and this work has formed a large part of my PhD.

Ultimately we need measurements of the isotope shifts. If they are sufficiently accurate we can use them to measure the isotope abundances in gas clouds directly, and hence completely remove the systematic effect from the study of α variation. Actually, measuring the isotope abundances in gas clouds is interesting in itself because it allows us to test models of nuclear processes in stars.