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

We report the results of theoretical investigation of electronic structure of ThF$^+$ cation which is one of the most interesting systems to search for the electron electric dipole moment (eEDM) [H. Loh, K.C. Cossel, M.C. Grau, K.-K. Ni, E.R. Meyer, J.L. Bohn, J. Ye, E.A. Cornell, Science {\bf 342}, 1220 (2013)] and other effects of violation of time reversal (T) and spacial parity (P) symmetries in fundamental interactions. For the working $^3\Delta_1$ state we have found 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 planed on ThF$^+$ in terms of eEDM. Within the concept of atoms in compounds [A.V. Titov, Y.V. Lomachuk, and L.V. Skripnikov, Phys. Rev. A {\bf 90}, 052522 (2014)] we have compared the ThF$^+$ electronic structure with that of ThO. Also we have calculated 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); $W_M$, which is required to search for the Th nuclear magnetic quadrupole moment in $^{229}$ThF$^+$ (0.88 $\frac{10^{33}\mathrm{Hz}}{e {\rm cm}^2}$). A number of properties which can be measured are also calculated: hyperfine structure constant, the molecule-frame dipole moment, and g-factor

Theoretical study of the parity and time reversal violating interaction in solids

A new theoretical approach to study the properties in solids, which are sensitive to a change of densities of the valence electrons in atomic cores (hyperfine structure constants, parameters of space parity (P) and time reversal (T) violation interaction, etc.) is proposed and implemented. It uses the two-step concept of calculation of such properties which was implemented earlier for the case of molecules [Progr.\ Theor.\ Chem.\ Phys. B 15, 253 (2006)]. The approach is applied to evaluate the parameter $X$ describing electronic density gradient on the Pb nucleus that is required to interpret the proposed experiment on PbTiO$_3$ crystal [PRA, 72, 034501 (2005)] to search for the Schiff moment of the $^{207}$Pb nucleus because of its high sensitivity to the corresponding P,T-violating interactions. For comparison the $X$ parameter has also been calculated on the Pb nucleus for the $^1\Sigma^+$ state of $^{207}$PbO molecule using the same density functionals as those utilized in PbTiO$_3$ studies. The relativistic coupled-clusters approach with single, double and perturbative triple cluster amplitudes, applicable to a few atom systems and providing high accuracy for $X$, is also applied to the PbO case to estimate the accuracy of density functional studies

Theoretical study of ThO for the electron electric dipole moment search

An experiment to search for the electron electric dipole moment (\eEDM) on the metastable $H^3\Delta_1$ state of ThO molecule was proposed and now in the final stage of preparation by the ACME collaboration [http://www.electronedm.org]. To interpret the experiment in terms of \eEDM\ and dimensionless constant $k_{T,P}$ characterizing the strength of the scalar T,P-odd electron-nucleus neutral current interaction, an accurate theoretical study of effective electric field on electron, Eeff, and $W_{T,P}$ constants is required. We report calculation of \Eeff\ (84 GV/cm) and a parameter of T,P-odd scalar neutral currents interaction, $W_{T,P}$ (116 kHz), together with the hyperfine structure constant, molecule frame dipole moment and $H^3\Delta_1\to X^1\Sigma^+$ transition energy, which can serve as a measure of reliability of the obtained \Eeff\ and $W_{T,P}$ values. Besides, our results include a parity assignment and evaluation of the electric-field dependence for the magnetic $g$ factors for the $\Omega$-doublets of $H^3\Delta_1$

Many body study of gg-factor in boron-like argon

Highly accurate measurements of the $g$-factor of boronlike Ar are currently implemented within the ARTEMIS experiment at GSI (Darmstadt, Germany) and within the ALPHATRAP experiment at the MPIK (Heidelberg, Germany). A comparison with the corresponding theoretical predictions will allow one to test the modern methods of bound-state QED. However, at least three different theoretical values of the \emph{g}-factor have been published up to date. The systematic study of the \emph{g} factor value of Ar$^{13+}$ in the ground $[(1s)^2(2s)^2 2p]^2P_{1/2}$ and the first excited $[(1s)^2(2s)^2 2p]^2P_{3/2}$ states is performed within the high order coupled cluster and configuration interaction theories up to the full configuration interaction treatment. Correlation contributions are discussed and results are compared with previous studies.Comment: 7 pages, no figure

Evaluation of CP-violation in HfF+^+

CP violation effects produced by the nuclear magnetic quadrupole moment (MQM), electron electric dipole moment (EDM) and scalar$-$pseudoscalar nucleus$-$electron neutral current (SP) interaction in $^{177}$Hf$^{19}$F$^+$ and $^{179}$Hf$^{19}$F$^+$ are calculated. The role of the hyperfine interaction is investigated. It is shown that the MQM shift can be distinguished from the electron EDM and SP ones due to the implicit dependence of MQM shift on the hyperfine sublevel. The MQM effect is expressed in terms of the proton (EDM), QCD vacuum angle $\theta$ and quark chromo-EDMs

Centrifugal correction to hyperfine structure constants in the ground state of lead monofluoride, PbF

The sensitivity of the PbF molecule to the electron electric dipole moment has motivated detailed microwave spectroscopy. Previous theoretical approaches cannot fully explain the spectra. In turn, the explanation from "first principles" is very important both for molecular theory and for confirmation of the correctness of the interpretation of experimental data obtained with high precision. All of these issues are decisively addressed here. We have determined centrifugal correction parameters for hyperfine structure constants, both on lead and fluorine nuclei, of the $X^2\Pi_{1/2}$ state of lead monofluoride. These parameters were obtained by fitting experimentally observed pure rotational transitions and from {\it ab initio} calculations. We show that taking this correction into account is required to reproduce the experimental transition energies obtained in [Phys. Rev. A 84, 022508 (2011)]

Manifestations of nuclear CP-violation in ThO molecule

Investigations of CP violation in hadron sector may be done using measurements in the ThO molecule. Recent measurements in this molecule improved the limit on electron EDM by an order of magnitude. Another time reversal (T) and parity (P) violating effect in $^{229}$ThO is induced by the nuclear magnetic quadrupole moment. We have performed nuclear and molecular calculations to express this effect in terms of the strength constants of T,P-odd nuclear forces, neutron EDM, QCD vacuum angle $\theta$, quark EDM and chromo-EDM

TaN molecule as a candidate to search for New physics

It is demonstrated that the TaN molecule is the best candidate to search for T,P-violating nuclear magnetic quadrupole moment (MQM), it also looks promising to search for other T,P-odd effects. We report results of coupled-cluster calculations of T,P-odd effects in TaN produced by the Ta nucleus MQM, electron electric dipole moment (EDM), scalar$-$pseudoscalar nucleus$-$electron interactions, also of the molecule-axis hyperfine structure constant and dipole moment. Nuclear calculations of $^{181}$Ta MQM are performed to express the T,P-odd effect in terms of the strength constants of T,P-odd nuclear forces, proton and neutron EDM, QCD parameter $\theta$ and quark chromo-EDM

Towards the search of electron electric dipole moment: correlation calculations of the P,T-violation effect in the Eu++^{++} cation

Recently the Eu$_{0.5}$Ba$_{0.5}$TiO$_{3}$ solid was suggested as a promising candidate for experimental search of the electron electric dipole moment. To interpret the results of this experiment one should calculate the effective electric field acting on an unpaired (spin-polarized) electrons of europium cation in the crystal because the value of this field cannot be measured experimentally. The Eu$^{++}$ cation is considered in the paper in the uniform external electric field $E_{\rm ext}$ as our first and simplest model simulating the state of europium in the crystal. We have performed high-level electronic structure correlation calculation using coupled clusters theory (and scalar-relativistic approximation for valence and outer core electrons at the molecular pseudopotential calculation stage that is followed by the four-component spinor restoration of the core electronic structure) to evaluate the enhancement coefficient $K= E_{\rm eff}/E_{\rm ext}$ (where $E_{\rm ext}$ is the applied external electric field and $E_{\rm eff}$ is the induced effective electric field acting on an unpaired electron in Eu$^{++}$). A detailed computation analysis is presented. The calculated value of $K$ is -4.6

Calculation of the parity and time reversal violating interaction in ^{225}RaO

The 10-electron generalized relativistic effective core potential and the corresponding correlation spin-orbital basis sets are generated for the Ra atom and the relativistic coupled cluster calculations for the RaO molecule are performed. The main goal of the study is to evaluate the P,T-odd parameter X characterized by the molecular electronic structure and corresponding to a "volume effect" in the interaction of the ^{225}Ra nucleus Schiff moment with electronic shells of RaO. Our final result for X(^{225}RaO) is -7532 which is surprisingly close to that in ^{205}TlF but has different sign. The obtained results are discussed and the quality of the calculations is analyzed. The value is of interest for a proposed experiment on RaO [PRA 77, 024501 (2008)] due to a very large expected Schiff moment of the ^{225}Ra nucleus.Comment: 5 pages, corrected the erroneous signs of H_eff and w_ex_e from 10.1103/PhysRevA.87.02010