Enhanced Sensitivity to the Time Variation of the Fine-Structure Constant and $m_p/m_e$ in Diatomic Molecules

Sensitivity to temporal variation of the fundamental constants may be strongly enhanced in transitions between narrow close levels of different nature. This enhancement may be realized in a large number of molecules due to cancellation between the ground state fine-structure ${\omega }_f$ and vibrational interval ${\omega }_v$ [$\omega ={\omega }_f-n{\omega }_v\approx 0$, $\delta \omega /\omega =K(2\delta \alpha /\alpha +0.5\delta \mu /\mu )$, $K\gg 1$, $\mu =m_p/m_e$]. The intervals between the levels are conveniently located in microwave frequency range and the level widths are very small. Required accuracy of the shift measurements is about 0.01–1 Hz. As examples, we consider molecules $\mathrm{Cl}^{+}{}_2$, CuS, IrC, SiBr, and ${\mathrm{HfF}}^{+}$.