Hyperfine and Zeeman interactions of the $a(1)[{}^3{\Sigma }_1^{+}]$ state of PbO

The role of the interaction with the nearest electronic state ${}^3{\Sigma }_{0^{-}}^{+}$ on the hyperfine structure and magnetic properties of the $a(1)[{}^3{\Sigma }_1^{+}]$ state of PbO is assessed. The accounting for this contribution leads to the difference between $g$ factors of the $J=1$ $\Omega$-doublet levels $\Delta g=37\times {10}^{-4}$, which is in good agreement with the experimental data $\Delta g=30(8)\times {10}^{-4}$. The contribution of this interaction rapidly grows with $J$. For $J=30$, the difference of $g$ factors of $\Omega$-doublet states reaches 100%; for hyperfine constants, it reaches 18%. These differences also depend on the electric field, and, for $E=11$ V/cm for ${}^{207}\mathrm{Pb}$O, the difference in $g$ factors turns to zero. The latter is important for suppressing systematic effects in the electron electric dipole moment search experiment.

Figure 1

Calculated $g$ factors for $e$($g_e$) and $f$($g_f$) states. (a) Solid lines correspond to $J=1,\hspace{0.5em}F=1/2$ hyperfine levels of ${}^{207}\mathrm{Pb}$O, dashed lines correspond to $J=1$ rotational levels of ${}^{206,208}\mathrm{Pb}$O. (b) Solid lines correspond to $J=1,\hspace{0.5em}F=3/2,\hspace{0.5em}\left|M_F\right|=3/2$, dashed lines correspond to $J=1,\hspace{0.5em}F=3/2,\hspace{0.5em}\left|M_F\right|=1/2$ hyperfine levels of ${}^{207}\mathrm{Pb}$O.

Figure 2

The EDM induced Stark splitting between $M_F=\pm 1/2$ levels of $J=1,\hspace{0.5em}F=1/2$ state of ${}^{207}\mathrm{Pb}$O (solid line) and between $M=\pm 1$ levels of $J=1$ state of ${}^{206,208}\mathrm{Pb}$O (dashed line). Vertical and horizontal dotted lines show the “magic” electric field condition and the corresponding Stark splitting for ${}^{207}\mathrm{Pb}$O.