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 201,199Hg and 87,85Rb, 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.Comment: 7 page
