Sensitivity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Th</mml:mi><mml:mprescripts/><mml:none/><mml:mn>229</mml:mn></mml:mmultiscripts></mml:math> nuclear clock transition to variation of the fine-structure constant

Abstract

Peik and Tamm [Europhys. Lett. 61, 181 (2003)] proposed a nuclear clock 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, $\ensuremath{\alpha}$. 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 an accuracy high enough to resolve nonzero sensitivity. Here we determine this sensitivity using existing measurements of the change in the mean-square charge radius, coupled with the ansatz of constant nuclear density. The enhancement factor for $\ensuremath{\alpha}$ variation is $K=\ensuremath{-}(0.82\ifmmode\pm\else\textpm\fi{}0.25)\ifmmode\times\else\texttimes\fi{}{10}^{4}$. For the current experimental limit, $\ensuremath{\delta}\ensuremath{\alpha}/\ensuremath{\alpha}\ensuremath{\lesssim}{10}^{\ensuremath{-}17}$ per year, the corresponding frequency shift is $\ensuremath{\sim}200$ Hz per year. This shift is six orders of magnitude larger than the projected accuracy of the nuclear clock, paving the way for increased accuracy of the determination of $\ensuremath{\delta}\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}$ variation and calculate the effects of $\ensuremath{\alpha}$ variation in a number of M\"ossbauer transitions.

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