SeD radical as a probe for the measurement of the time variation of the fine-structure constant $\alpha$ and proton-to-electron mass ratio $\mu$

Based on the spectroscopic constants derived from highly accurate potential-energy surfaces, the SeD radical is identified as a spectroscopic probe for measuring spatial and temporal variation of fundamental physical constants such as the fine-structure constant (denoted as $\alpha =\frac{e^2}{\hslash c}$) and the proton-to-electron mass ratio (denoted as $\mu =\frac{m_p}{m_e}$). The ground state of SeD $\left(X^2\Pi \right)$, due to spin-orbit coupling, splits into two fine-structure multiplets ${}^2{\Pi }_{\frac{3}{2}}$ and ${}^2{\Pi }_{\frac{1}{2}}$. The potential-energy surfaces of these spin-orbit components are derived from a state of the art electronic structure method, MRCI + Q inclusive of scalar relativistic effects with the spin-orbit effects accounted for through the Breit-Pauli operator. The relevant spectroscopic data are evaluated using a Murrel-Sorbie fit to the potential-energy surfaces. The spin-orbit splitting ${\omega }_f$ between the two multiplets is similar in magnitude with the harmonic frequency ${\omega }_e$ of the diatomic molecule. The amplification factor $K$ derived from this theoretical method for this particular molecule can be as large as 350; on the lower side it can be about 34. The significantly large values of $K$ indicate that the SeD radical can be a plausible experimental candidate for measuring variation in $\alpha$ and $\mu$.

Figure 1

The PESs of the ground state $X^2\Pi$ and the first excited state $A^2{\Sigma }^{+}$ of the SeD radical and partly magnified PESs of the SOC split states ${}^2{\Pi }_{\frac{3}{2}}$ and ${}^2{\Pi }_{\frac{1}{2}}$ near equilibrium separation $R_e$ (inset) at the MRCI + Q/a-V5Z-DK level of theory.

Figure 2

The curve for the vertical transition energy of the SeD $X^2{\Pi }_{\frac{3}{2}\to \frac{1}{2}}$ transition energy (in $\mathrm{cm}{}^{-1}$) versus the internuclear separation at the MRCI + Q/a-V5Z-DK level of theory.

Figure 3

(Left) The magnitude of vibronic levels of the two doublet states of ${}^{80}\mathrm{SeD}$. The blue and red lines represent the ${}^2{\Pi }_{\frac{3}{2}}$ and ${}^2{\Pi }_{\frac{1}{2}}$ MRCI + Q/a-V5Z-DK levels of theory, respectively. (Right) Rotational levels of the two doublet states. The blue (solid) and red (dashed) lines represent ${}^2{\Pi }_{\frac{3}{2}}$ and ${}^2{\Pi }_{\frac{1}{2}}$. Since $J$ is always $\ge$$\Omega$, for ${}^2{\Pi }_{\frac{3}{2}}$ the $J=\frac{1}{2}$ rotational level is not observed.