Fine-structure constant sensitivity of the Th-229 nuclear clock transition

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.