We present numerical calculations for cesium and mercury to estimate the sensitivity of the scattering length to the variation of the fine-structure constant $\alpha$. The method used follows the ideas of Chin and Flambaum [Phys. Rev. Lett. 96, 230801 (2006)], where the sensitivity to the variation of the electron-to-proton mass ratio $\beta$ was considered. We demonstrate that for heavy systems, the sensitivity to the variation of $\alpha$ is of the same order of magnitude as to the variation of $\beta$. Near narrow Feshbach resonances, the enhancement of the sensitivity may exceed nine orders of magnitude.

• Received 6 March 2011

DOI:https://doi.org/10.1103/PhysRevA.83.052706