Theoretical study of ${\mathrm{ThF}}^{+}$ in the search for $T,P$-violation effects: Effective state of a Th atom in ${\mathrm{ThF}}^{+}$ and ThO compounds

We report the results of a theoretical investigation of the electronic structure of the ${\mathrm{ThF}}^{+}$ cation, which is one of the most interesting systems to search for the electron electric dipole moment $\left(e\mathrm{EDM}\right)$ [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science 342, 1220 (2013)] and other effects of violation of time reversal (T) and spatial parity (P) symmetries in fundamental interactions. For the working ${}^3{\Delta }_1$ state we find a quite high value of the effective electric field acting on unpaired electrons (37.3 GV/cm). The field will be required to interpret the experiment planned on ${\mathrm{ThF}}^{+}$ in terms of the $e\mathrm{EDM}$. Within the concept of atoms in compounds [A. V. Titov, Y. V. Lomachuk, and L. V. Skripnikov, Phys. Rev. A 90, 052522 (2014)], we compare the ${\mathrm{ThF}}^{+}$ electronic structure with that of ThO. Also, we calculate other parameters of T,P-odd interactions: $W_{T,P}$, which is needed for interpretation of the experiment in terms of the dimensionless constant $k_{T,P}$ characterizing the strength of the $T,P$-odd pseudoscalar-scalar electron-nucleus neutral current interaction (50 kHz); and $W_M$, which is required to search for the ${}^{229}\mathrm{Th}$ nuclear magnetic quadrupole moment in ${}^{229}{\mathrm{ThF}}^{+}$ (0.88 $\frac{{10}^{33}\mathrm{Hz}}{e{\mathrm{cm}}^2})$. A number of properties which can be measured are also calculated: the hyperfine structure constant, molecule-frame dipole moment, and $g$ factor.

Figure 1

Large components of the $5s_{1/2},6s_{1/2}$, and $7s_{1/2}$ spinors of Th for the $7s^{2}7p^{1}6d^1$ configuration. Inset: Large components of $5s_{1/2},6s_{1/2}$, and $7s_{1/2}$ spinors in the core region; the scaling factor is chosen in such a way that the amplitudes of large components of these spinors are equal at $R_c$ = 0.25 a.u.