Atomic microwave clocks based on hyperfine transitions, such as the caesium standard, tick with a frequency that is proportional to the magnetic moment of the nucleus. This magnetic moment varies strongly between isotopes of the same atom, while all atomic electron parameters remain the same. Therefore the comparison of two microwave clocks based on different isotopes of the same atom can be used to constrain variation of fundamental constants. In this paper, we calculate the neutron and proton contributions to the nuclear magnetic moments, as well as their sensitivity to any potential quark-mass variation, in a number of isotopes of experimental interest including 201,199 Hg and 87,85 Rb, where experiments are underway. We also include a brief treatment of the dependence of the hyperfine transitions to variation in nuclear radius, which in turn is proportional to any change in quark mass. Our calculations of expectation values of proton and neutron spin in nuclei are also needed to interpret measurements of violations of fundamental symmetries.

We statistically analyse a recent sample of data points measuring the fine-structure constant α (relative to the terrestrial value) in quasar absorption systems, where a spatial gradient in α was recently reported. We find agreement with previous authors that the dipole model is a robust, well-justified fit to the data. Using a simple analysis we find that the monopole term (the constant offset in Δα/α) may be caused by non-terrestrial magnesium isotope abundances in the absorbers. Finally we test the domain-wall model against the data.Key words. cosmology: theory -methods: statistical -large-scale structure of Universe -cosmology: miscellaneous Optical quasar absorption spectra provide a probe of variations in the fine-structure constant, α = e 2 / c, along a past-light cone centred on present-day telescopes. In this paper we analyse the results of a large sample of quasar absorption systems where values of Δα/α have been measured using the many-multiplet method (Dzuba et al. 1999a,b). Here Δα/α = (α(r) − α 0 )/α 0 is the relative variation in α at a particular position r in the Universe where the absorption occurs.The data used in this paper are taken from Murphy et al. (2003 and King et al. (2012, Very Large Telescope), kindly supplied by the King in a usable text format including the location of each absorber and its measured value of Δα/α. In total there are 293 points in our data file including 140 from Keck and 153 from VLT of which seven absorbers are seen in both the Keck and VLT samples. The data is described fully in King et al. (2012) (see Berengut et al. 2012 for a discussion pertinent to the current analysis). In Webb et al. (2011), the combined data sample is interpreted as providing evidence for variation in α throughout the Universe with an angular-dependence. This "dipole" model is found to be preferred to a monopole (constant offset) model of the variation at the 4.1σ level.Note that both the Keck and VLT samples account for unknown sources of scatter in the data by including extra systematic errors, σ rand , that are added in quadrature with the underlying statistical error. The data we use includes a conservative (large) value which will tend to reduce the significance of the dipole relative to a monopole model. In practice the results of this paper are relatively insensitive to the exact σ rand used.The In this paper we test the dipole interpretation B(z) ∼ r. In this form (1) represents a gradient in the value α throughout the Universe, and r cos θ is the distance to a quasar absorption system along that gradient. Of course, r itself is model dependent at large redshifts. In this work we use the standard Λ CDM cosmology parametrized by WMAP5 (Hinshaw et al. 2009) to determine r = ct (t is lookback time) from the redshift z:Again, this reflects the fact that we are taking measurements along a past light cone centred on present-day Earth. An alternative approach is to use the comoving distance:In this case the dipole model (1) is modified to use B(z) = B d(z). This parameterisatio...