Electric-field-dependent g factors of RaOCH 3 molecule

The sensitivity of experiments searching for the electron electric-dipole moment ($e\mathrm{EDM}$) using the symmetric top molecules can be greatly enhanced by laser cooling. A detailed understanding of the Zeeman structure of the $e\mathrm{EDM}$-sensitive levels is crucial for controlling systematic effects. We develop a method for calculating the $g$ factors of $K$-doublet levels in symmetric top molecules and apply it to ${\mathrm{RaOCH}}_{3}$. The electric-field-dependent $g$ factors of the first excited rotational level of ${\mathrm{RaOCH}}_{3}$ are calculated. We find that the $K$ doublet with a total angular momentum projection ${M}_{F}=2$ has a ratio $\mathrm{\ensuremath{\Delta}}g/g\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}{10}^{\ensuremath{-}6}$ for an electric field in the range from 500 mV/cm to 1 V/cm, where $\mathrm{\ensuremath{\Delta}}g$ is the difference in the $g$ factors for the $K$-doublet components.