  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
$^{229}$Th. 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
($\alpha \cong 1/137.036$) or of a strong interaction parameter
($m_q/\Lambda_{QCD}$). 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 to 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.
