Sensitivity of nuclear transition frequencies to temporal variation of the fine structure constant or the strong interaction

There exist in nature a few nuclear isomers with very low (eV) excitation energies, and the combination of low energy and narrow width makes them possible candidates for laser-based investigations. The best candidate is the lowest-energy excited state known in nuclear physics, the 7.6(5) eV isomer of 229Th. A recent study suggests that a measurement of the temporal variation of the excitation energy of this isomer would have 5-6 orders of magnitude enhanced sensitivity to a variation of the fine structure constant (α≅1/137.036) or of a strong interaction parameter (mq/ΛQCD). We reexamine the physics involved in these arguments. By invoking the Feynman-Hellmann Theorem we argue that there is no expectation of significantly enhanced sensitivity to a variation in the fine structure constant (beyond that obtained from experimental considerations such as the low energy and narrow width of the isomer). A similar argument applies for the strong interaction, but evaluating the shift due to temporal variations of the underlying parameters of the strong interaction may be beyond current nuclear structure techniques.