Sensitivity of Th229 nuclear clock transition to variation of the fine-structure constant

Abstract

A nuclear clock has been proposed based on the isomeric transition between the ground state and the first excited state of thorium-229. This transition was recognized as a potentially sensitive probe of possible temporal variation of the fine-structure constant, α. The sensitivity to such a variation can be determined from measurements of the mean-square charge radius and quadrupole moment of the different isomers. However, current measurements of the quadrupole moment are yet to achieve accuracy high enough to resolve non-zero sensitivity. Here we determine this sensitivity using existing measurements of the change in mean-square charge radius, coupled with the ansatz of constant nuclear density. The enhancement factor for α-variation is K = −(0.9 ± 0.3) × 10 4 . For the current experimental limit δα/α 10 −17 per year, the corresponding frequency shift is ∼ 200 Hz. This shift is six orders of magnitude larger than the projected accuracy of the nuclear clock, paving the way for increased accuracy for determination of δα and interaction strength with low mass scalar dark matter. We verify that the constant-nuclear-density ansatz is supported by nuclear theory and propose how to verify it experimentally. We also consider a possible effect of the octupole deformation on the sensitivity to α-variation.

Relativistic coupled-cluster calculation of hyperfine-structure constants of $^{229}$Th$^{3+}$ and evaluation of the electromagnetic nuclear moments of $^{229}$Th

“…The magnetic dipole moment, µ, and the electric quadrupole moment, Q has been obtained by combining our atomic calculation with the measured HFS A B values. We find our determined µ values, 0.359 (9), is in very good agreement with the SDpT results, 0.360 (7). While our electric quadrupole moment, Q = 2.95 (7), is smaller than their recommended value, Q = 3.11 (6), about 5%, owing to the electron correlation represent by the nonlinear terms, which omitted in SDpT calculations, contribute significantly to the electric quadrupole moment and reduce the values.…”

“…We found that our CCSD values matched perfectly with the SDpT results 0.360 (7), but lower than other reported results. The comparison of our CCSD result and SDpT result shows that the contribution of the partial triple excitations and the non-linear term on A/µ to the first three states are small.…”

“…229 Th possess an extremely low first excited isomeric state of only several eV [1,2], which opens the possibility to construct a high-precision nuclear optical clock [3][4][5] and provides a strongly enhanced sensitivity for searching for new physics beyond the standard model [6,7]. To achieve these attractive objects, accurate knowledge of the nuclear and electronic properties of 229 Th, such as the nuclear moments, plays a fundamental role.…”

“…The accurate nuclear moment values not only can help to grasp the hyperfine structures (HFS) of 229 Th atoms and related ions, but also provide a benchmark tool to improve the nuclear model theory thereby helping to reliably predict the properties of its isomers such as the isomer transition rate and the nuclear moments [8]. The nuclear quadrupole moment of 229 Th also can be used to assess the sensitivity of the isomeric transition to the possible variation of α and other fundamental constants [7,9,10].…”

SpaceQ -- Direct Detection of Ultralight Dark Matter with Space Quantum Sensors

“…A solidstate nuclear clock could be particularly attractive for a space mission. Molecular clocks provide sensitivity to m e /m p variation and a nuclear clock is highly sensitive to hadronic sector, with possible K = 10 4 sensitivity to the variation of m q /Λ QCD [102,111].…”