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The 7.6 eV electromagnetic transition between the nearly degenerate groundstate and first excited state in the Th-229 nucleus may be very sensitive topotential changes in the fine-structure constant, $\alpha = e^2/\hbar c$.However, the sensitivity is not known, and nuclear calculations are currentlyunable to determine it. We propose measurements of the differences of atomictransition frequencies between thorium atoms (or ions) with the nucleus in theground state and in the first excited (isomeric) state. This will enableextraction of the change in nuclear charge radius and electric quadrupolemoment between the isomers, and hence the $\alpha$-dependence of the isomerictransition frequency with reasonable accuracy.

A proposed experimental method to determine $\alpha$-sensitivity of splitting between ground and 7.6 eV isomeric states in Th-229