The effect of nuclear polarisation on the non-linearities of King plot for isotope shift in Ca + , Sr + and Yb + ions is studied. These ions are currently used in search for the manifestation of new interaction via non-linearities of King plot. The role of relativistic effects is also studied. The best way to achieve separation of electronic and nuclear variables (which is necessary for the linearity) is to present the field shift as F ′′ δ r λ , where the value of λ is the result of numerical relativistic calculations (2γ < λ < 2, γ = 1 − (Z/137.036) 2 ). Using this ansatz we demonstrated that the contribution of the relativistic effects to the non-linearity in spherical nuclei is very small.

Space-time variation of fundamental physical constants in expanding Universe is predicted by a number of popular models. The masses of second generation quarks are larger than first generation quark masses by several orders of magnitude, therefore space-time variation in quark masses may significantly vary between each generation. We evaluate limits on variation in the s and c quark masses from Big Bang nucleosynthesis, Oklo natural nuclear reactor, Yb + , Cs and Rb clock data. The construction of a 229 Th nuclear clock is expected to enhance these limits by several orders of magnitude. Furthermore, constraints are obtained on an oscillating scalar or pseudoscalar cold dark matter field, as interactions of the field with quarks produce variations in quark masses.