Nuclear magnetic quadrupole moment of ${}^{175}\mathrm{Lu}$ and parity-violating polarization degree of levels in ${}^{175}\mathrm{Lu}{\text{OH}}^{+}$

A calculation is performed of the parity-violating polarizations in the external electric field, which are associated with the electron electric dipole moment ($e\mathrm{EDM}$) and magnetic quadrupole moment (MQM) of the ${}^{175}\mathrm{Lu}$ nucleus, as well as the determination of the rovibrational structure for the ${}^{175}\mathrm{Lu}{\mathrm{OH}}^{+}$ cation. Beyond the bending of the molecule, the slight effect of the stretching of the distance between Lu and OH is taken into account. This study is required for the preparation of the experiment and for the extraction of the $e\mathrm{EDM}$ and MQM values of ${}^{175}\mathrm{Lu}$ from future measurements.

Figure 1

The Jacobi coordinates for the $\mathrm{Lu}{\mathrm{OH}}^{+}$ cation are defined as follows: $R$ is the distance between Lu and the center of mass of OH, while $\theta$ denotes the angle between the OH axis and the axis directed from Lu to the OH center of mass (the $z$ axis of the molecular frame).

Figure 2

The potential-energy surface $V(\theta ,R)$ obtained at the CCSD(T) level and using polynomial interpolation. Data and fitting coefficients are available in the Supplemental Material.

Figure 3

Calculated polarizations $P_e/7$ (solid) and $P_M$ (dashed) for the selected levels numbered 43–56 in Tables 2 and 3 (see text for details) for the different values of $M_F$ of the lowest $N=1$ rotational level of the first-excited ${\nu }_2=1$ bending vibrational mode of ${}^{175}\mathrm{Lu}{\mathrm{OH}}^{+}$ as functions of the external electric field. Since the influence of the hydrogen nuclear spin is very small, some curves for the states which differ by only projection $M_I^{\mathrm{H}}=\pm 1/2$ coincide. It looks like the curves are labeled by two figures.