  State-resolved laser spectroscopy at the 10$^{-12}$ precision level recently
reported in $arXiv$:2406.18719 determined the fractional change in nuclear
quadrupole moment between the ground and isomeric state of $^{229}\rm{Th}$,
$\Delta Q_0/Q_0$=1.791(2) %. Assuming a prolate spheroid nucleus, this allows
to quantify the sensitivity of the nuclear transition frequency to variations
of the fine-structure constant $\alpha$ to $K=5900(2300)$, with the uncertainty
dominated by the experimentally measured charge radius difference $\Delta
\langle r^2 \rangle$ between the ground and isomeric state. This result
indicates a three orders of magnitude enhancement over atomic clock schemes
based on electron shell transitions. We find that $\Delta Q_0$ is highly
sensitive to tiny changes in the nuclear volume, thus the constant volume
approximation cannot be used to accurately relate changes in $\langle r^2
\rangle$ and $Q_0$. The difference between the experimental and estimated
values in $\Delta Q_0/Q_0$ raises a further question on the octupole
contribution to the alpha-sensitivity.
