Numerical evaluation of systematics in the experiment for electron electric dipole moment measurement in ${\mathrm{HfF}}^{+}$

The energy shifts of hyperfine structure levels of the ground rotational level of the metastable ${}^3{\mathrm{\Delta }}_1$ electronic state of ${}^{180}{\mathrm{HfF}}^{+}$ ions are calculated in the presence of variable external electric and magnetic fields. The calculations are required for the analysis of systematic effects in the experiment for the search of the electron electric dipole moment ($e\mathrm{EDM}$). Different perturbations in the molecular spectra important for $e\mathrm{EDM}$ spectroscopy are taken into account.

Figure 1

Calculated ratios $f^{\mathcal{B}}/f^{\mathcal{B}\mathcal{D}}$ [dashed (red) curve] and $f^0/f^{\mathcal{D}}$ [dotted (blue) curve] as functions of the $\mathrm{component}{f}^0$. Also, the constant value $({\mathrm{g}}^u+{\mathrm{g}}^l)/({\mathrm{g}}^u-{\mathrm{g}}^l)=-473$ is indicated as a black horizontal line.

Figure 2

Calculated ${10}^4{f}^{\mathcal{B}\mathcal{D}}$ [solid (black) curve] and $f^{\mathcal{B}}$ [dashed (red) curve] as functions of the phase $\phi$.

Figure 3

Calculated $\mathrm{\Delta }\mathrm{g}/E$ as a function of the external static electric field $E$. Solid (black) curve: magnetic interaction with both ${}^3{\mathrm{\Pi }}_{0^{\pm }}$ and ${}^3{\mathrm{\Delta }}_2$ is taken into account. Dashed (red) curve: the interaction with ${}^3{\mathrm{\Pi }}_{0^{\pm }}$ is omitted.