Enhanced sensitivity to the time variation of the fine-structure constant and $m_p/m_e$ in diatomic molecules: A closer examination of silicon monobromide

Recently it was pointed out that transition frequencies in certain diatomic molecules have an enhanced sensitivity to variations in the fine-structure constant $\alpha$ and the proton-to-electron mass ratio $m_p/m_e$ due to a near cancellation between the fine structure and vibrational interval in a ground electronic multiplet [V. V. Flambaum and M. G. Kozlov, Phys. Rev. Lett. 99, 150801 (2007)]. One such molecule possessing this favorable quality is silicon monobromide. Here we take a closer examination of SiBr as a candidate for detecting variations in $\alpha$ and $m_p/m_e$. We analyze the rovibronic spectrum by employing the most accurate experimental data available in the literature and perform ab initio calculations to determine the precise dependence of the spectrum on variations in $\alpha$. Furthermore, we calculate the natural linewidths of the rovibronic levels, which place a fundamental limit on the accuracy to which variations may be determined.

Figure 1

Potential energy curves and the lowest few vibronic energy levels for the $X^2{\Pi }_r$ ground doublet of ${}^{28}\mathrm{Si}$${}^{79}\mathrm{Br}$. (a) The lower blue and upper red curves represent the potential energy curves for the ${}^2{\Pi }_{1/2}$ and ${}^2{\Pi }_{3/2}$ states, respectively, with the solid blue and dashed red horizontal lines illustrating the corresponding vibronic energy levels. (b) The energy separation between the quasidegenerate vibronic levels is magnified by a factor of 100. All energy differences are in cm${}^{-1}$.

Figure 2

Rovibronic levels of ${}^{28}\mathrm{Si}$${}^{79}\mathrm{Br}$ associated with the ${}^2{\Pi }_{1/2},v=1$ (solid blue lines) and ${}^2{\Pi }_{3/2},v=0$ (dashed red lines) quasidegenerate vibronic levels. Displayed are (a) the two vibronic levels and (b) all rovibronic levels for up to $J=9/2$. All energy differences are in cm${}^{-1}$.