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

Nuclear laser spectroscopy at the 10^-12 precision level (Nature 633.8028 (2024): 63-70) determined the fractional change in the nuclear quadrupole moment of ²²⁹Th upon excitation, ΔQ₀/Q₀ = 1.791(2)%. Such high-accuracy nuclear parameters enable stringent tests and refinement of ²²⁹Th nuclear models. Using a semi-classical prolate-spheroid model, we quantify the transition frequency's sensitivity to fine-structure constant variations as K = 5900(2300), with uncertainty dominated by the measured charge-radius change Δ〈r²〉. This supports the predicted higher α-sensitivity of nuclear clocks over atomic clocks, important for new-physics searches. We find ΔQ₀ strongly dependent on nuclear volume, challenging the constant-volume approximation. The deviation between measured and predicted ΔQ₀/Q₀ underlines the need for improved modeling and measurement of additional nuclear parameters. We explicitly assess the octupole contribution to α-sensitivity.