Theoretical study ofThF+in the search forT,P-violation effects: Effective state of a Th atom inThF+

Abstract

We report the results of a theoretical investigation of the electronic structure of the ThF+ cation, which is one of the most interesting systems to search for the electron electric dipole moment (eEDM) [Science 342, 1220[Science 342, (2013] and other effects of violation of time reversal (T) and spatial parity (P) symmetries in fundamental interactions. For the working 3A , 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 ThF+ in terms of the eEDM. 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 ThF+ electronic structure with that of ThO. Also, we calculate other parameters of T,P-odd interactions: WT.P, which is needed for interpretation of the experiment in terms of the dimensionless constant kT P characterizing the strength of the 7\P-odd pseudoscalar-scalar electron-nucleus neutral current interaction (50 kHz); and WM, which is required to search for the 229Th nuclear magnetic quadrupole moment in 229ThF+ (0.88 1033 2 Z). A number of properties which can be measured are also calculated: the hyperfine structure constant, molecule-frame dipole moment, and g factor.

Enhanced effect of CP -violating nuclear magnetic quadrupole moment in a HfF+ molecule

“…(5) that W M parameter is mainly determined by the behavior of the electronic wave function in the region close to the heavy atom nucleus. We call such parameters as the Atoms-In-Compounds characteristics or properties [29][30][31]. Other examples are the hyperfine structure interaction constants, effective electric field, chemical shifts, etc.…”

“…[39]. GRECP and the restoration procedure were also successfully used for precise investigation of different diatomics [7,29,[40][41][42][43][44][45][46][47][48][49]. The two-step method allows one to consider high-order correlation effects and large basis sets with rather modest requirements to computer resources in comparison to 4-component approaches.…”

“…Other examples are the hyperfine structure interaction constants, effective electric field, chemical shifts, etc. To compute such parameters we have previously developed the two-step method [29,32,33] which allows us to avoid direct 4-component relativistic treatment. In the first stage, one considers the valence (and outer-core) part of the molecular wave function within the generalized relativistic effective core potential (GRECP) method [34][35][36].…”

“…Due to the corresponding savings one can use very large basis sets to consider basis set corrections and analyze its saturation. At the second step, one uses the nonvariational procedure developed in [29,32,33,38] to restore the correct 4-component behavior of the valence wave function in the spatial core region of a heavy atom. The procedure is based on a proportionality of the valence and low-lying virtual spinors in the inner-core regions of heavy atoms.…”

CHEMICAL SHIFTS OF X-RAY EMISSION SPECTRA AND EFFECTIVE STATES OF YTTERBIUM IN FLUORIDES: EMBEDDED CLUSTER MODELING OF YbF2 AND YbF3 CRYSTALS

“…The non-variation restoration code developed in references [14], [17], [29], [30] was used to obtain the correct four-component electronic wave function near the Yb nucleus. Chemical shifts of Kα1, 2 lines were calculated at experimental structural data [20], [21] by the method described in [4], assuming the core restoration radius Rc = 0.55 a.u.…”