Over a two-year duration, we have compared the frequency of the ${}^{199}\mathrm{H}\mathrm{g}^{+}$ $5d^{10}6s{}^{2}S_{1/2}(F=0)\leftrightarrow 5d^{9}6s^2{}^{2}D_{5/2}(F=2)$ electric-quadrupole transition at 282 nm with the frequency of the ground-state hyperfine splitting in neutral ${}^{133}\mathrm{C}\mathrm{s}$. These measurements show that any fractional time variation of the ratio ${\nu }_{\mathrm{C}\mathrm{s}}/{\nu }_{\mathrm{H}\mathrm{g}}$ between the two frequencies is smaller than $\pm 7\times {10}^{-15}{\mathrm{y}\mathrm{r}}^{-1}$ ($1\sigma$ uncertainty). According to recent atomic structure calculations, this sets an upper limit to a possible fractional time variation of $g_{\mathrm{C}\mathrm{s}}(m_e/m_p){\alpha }^{6.0}$ at the same level.

• Received 30 December 2002

DOI:https://doi.org/10.1103/PhysRevLett.90.150802