Rotating and vibrating symmetric-top molecule ${\mathrm{RaOCH}}_3$ in fundamental $\mathcal{P}, \mathcal{T}$-violation searches

We study the influence of the rotations and vibrations of the symmetric-top ${\mathrm{RaOCH}}_3$ molecule on its effectiveness as a probe for the $\mathcal{P}, \mathcal{T}$-violating effects, such as the electron electric dipole moment and the scalar-pseudoscalar electron-nucleon interaction. The corresponding enhancement parameters $E_{\mathrm{eff}}$ and $E_{\mathrm{s}}$ are computed for the ground and first excited rovibrational states with different values of the angular momentum component $K$. For the lowest $K$ doublet with $v_{\perp }=0$ and $K=1$ the values are $E_{\mathrm{eff}}=47.647\mathrm{GV}/\mathrm{cm}$ and $E_{\mathrm{s}}=62.109\mathrm{kHz}$. The results show larger deviation from the equilibrium values than in triatomic molecules.

Figure 1

The ${\mathrm{RaOCH}}_3$ molecule.

Figure 2

The angular dependence of the adiabatic potential at the equilibrium value $R=5.7\mathrm{a}.\mathrm{u}.$ The azimuthal angle is $\phi$, and the radial coordinate is $\theta$. The sector-dividing lines correspond to the directions of the hydrogen atoms.

Figure 3

The angular dependence of the $E_{\mathrm{eff}}$ at $R=5.7\mathrm{a}.\mathrm{u}.$

Figure 4

The angular dependence of the $E_{\mathrm{s}}$ at $R=5.7\mathrm{a}.\mathrm{u}.$

Figure 5

The angular dependence of the $E_{\mathrm{eff}}$ at $R=5.5\mathrm{a}.\mathrm{u}.$

Figure 6

The angular dependence of the $E_{\mathrm{s}}$ at $R=5.5\mathrm{a}.\mathrm{u}.$