Nuclear magnetization distribution effect in molecules: Ra${}^{+}$ and RaF hyperfine structure

Abstract

Recently the first laser spectroscopy measurement of the radioactive RaF molecule has been reported by Ruiz \textit{et al.} [Nature \textbf{581}, 396 (2020)]. This and similar molecules are considered to search for the New Physics effects. The radium nucleus is of interest as it is octupole-deformed and has close levels of opposite parity. The preparation of such experiments can be simplified if there are reliable theoretical predictions. It is shown that the accurate prediction of the hyperfine structure of the RaF molecule requires to take into account the finite magnetization distribution inside the radium nucleus. For atoms, this effect is known as the Bohr-Weisskopf (BW) effect. Its magnitude depends on the model of the nuclear magnetization distribution which is usually not well known. We show that it is possible to express the nuclear magnetization distribution contribution to the hyperfine structure constant in terms of one magnetization distribution dependent parameter: BW matrix element for $1s$-state of the corresponding hydrogen-like ion. This parameter can be extracted from the accurate experimental and theoretical electronic structure data for an ion, atom, or molecule without the explicit treatment of any nuclear magnetization distribution model. This approach can be applied to predict the hyperfine structure of atoms and \textit{molecules} and allows one to separate the nuclear and electronic correlation problems. It is employed to calculate the finite nuclear magnetization distribution contribution to the hyperfine structure of the ${}^{225}$Ra${}^{+}$ cation and ${}^{225}$RaF molecule. For the ground state of the ${}^{225}$RaF molecule, this contribution achieves 4\%.

References in corpus (10)

• Combined 4-component and relativistic pseudopotential study of ThO for the electron electric dipole moment search
• Evolution of Octupole Deformation in Radium Nuclei from Coulomb Excitation of Radioactive ${}^{222}$Ra and ${}^{228}$Ra Beams
• Ab initio study of radium monofluoride, RaF, as a candidate to search for P- and T,P- violation effects
• Theoretical study of thorium monoxide for the electron electric dipole moment search, II: Electronic properties of $H^3{\Delta }_1$ in ThO
• Theoretical study of ThF${}^{+}$ in the search for T,P-violation effects: Effective state of a Th atom in ThF${}^{+}$ and ThO compounds
• $\mathcal{P},\mathcal{T}$-Odd and Magnetic Hyperfine Interaction Constants and Excited-State Lifetime for HfF${}^{+}$
• Concept of effective states of atoms in compounds to describe properties determined by the densities of valence electrons in atomic cores
• Electron correlation and nuclear charge dependence of parity-violating properties in open-shell diatomic molecules
• Study of the scalar-pseudoscalar interaction in the francium atom
• Ground-state hyperfine splitting for Rb, Cs, Fr, Ba^+, and Ra^+