arXiv subjects

Timo Fleig

Publications and source records attributed to Timo Fleig.

At least 19 recordsLinked to original sources

arXiv2025

Rotational Splittings in Diatomic Molecules of Interest to Searches for New Physics

Diatomic molecules with an energetically low-lying $^3 \Delta_1$ state are attractive platforms to detect new physics beyond the Standard Model, such as parity- and time-reversal violating phenomena. One of the advantages of using a $^3 \Delta_1$ state is its tiny $\Lambda$-splitting due to the coupling between the electronic and rotational angular momenta, which facilitates polarizing the molecules in small external electric fields. Theoretical estimation of the magnitude of the $\Lambda$-splitting is helpful for planning new experiments. In this study, we present a theoretical model to calculate the $\Lambda$-splitting. Our model integrates the relativistic four-component wavefunction and the traditional rotational Hamiltonian based on Hund's case (a). The multireference character of the wavefunction is taken into account. Our calculations for PtH and ThF$^+$ molecules qualitatively agree with experiment. The $\Lambda$-splitting of TaO$^+$ for the rotational ground state is predicted to be around 9 kHz. This tiny splitting can reduce the systematic uncertainty, but in a practical experiment, it may cause depolarization during rotation ramp-up.

physics.atom-ph↗

arXiv2024

Semi-Hadronic Charge-Parity Violation Interaction Constants in CsAg, FrLi and FrAg molecules

We present a systematic study of the nucleon-electron tensor-pseudotensor (Ne-TPT) interaction in candidate molecules for next-generation experimental searches for new sources of charge-parity violation. The considered molecules are all amenable to assembly from laser-cooled atoms, with the francium-silver (FrAg) molecule previously shown to be the most sensitive to the Schiff moment interaction in this set. Interelectron correlation effects are treated through relativistic general-excitation-rank configuration-interaction theory in the framework of the Dirac-Coulomb Hamiltonian. We find in FrAg the Ne-TPT interaction constant to be $W_T({\text{Fr}}) = 2.58 \pm 0.21 [\left<\Sigma\right>_A \mathrm{kHz}]$, considering the Francium atom as target of the measurement. Taking into account nuclear structure in a multi-source interpretation of a measured electric dipole moment, FrAg is found to be an excellent probe of physics beyond the Standard Model as this system will in addition to its sizeable Ne-TPT interaction constant greatly constrain fundamental parameters such as the quantum-chromo-dynamic $\bar{\theta}$ or the semileptonic four-fermion interaction $C_{lequ}$ from which nuclear and atomic ${\cal{CP}}$-violating properties arise.

physics.atom-ph↗

arXiv2024

Variational Calculation of the Hyperfine Stark Effect in Atomic $^{87}$Rb, $^{133}$Cs, and $^{169}$Tm

An electronically variational approach to the calculation of atomic hyperfine structure transition energies under the influence of static external electric fields is presented. The method avoids the calculation of intermediate atomic states entirely and requires only the wavefunctions of the electronic states involved in the respective hyperfine levels. These wavefunctions are obtained through relativistic general-excitation-rank configuration interaction theory. A variant of the method also enables for calculations on atoms with the most complicated of shell structures. Applications to $^{87}$Rb, $^{133}$Cs and a specific clock transition in $^{169}$Tm are presented. The final results $k_{\text{Rb}} = -1.234 \pm 0.0223$ [$10^{-10}$ Hz/((V/m)$^2$)] and $k_{\text{Cs}} = -2.347 \pm 0.084$ [$10^{-10}$ Hz/((V/m)$^2$)] obtained under inclusion of up to quintuple excitations in the atomic wavefunction expansion are compatible with previous calculations and, in the case of Cs, confirm that one of the earlier experimental measurements is not reliable. For $^{169}$Tm that is used in the development of atomic clocks the differential static scalar electric dipole polarizability between ground levels $J=\frac{7}{2}$ and $J=\frac{5}{2}$ is calculated to be $\Delta\alpha^s_0 = -0.134 \pm 0.11$ a.u. This result from a pure {\it{ab initio}} calculation confirms the result of $\Delta\alpha^s_0 = -0.063^{+0.01}_{-0.005}$ a.u. obtained in {\it{Nat. Comm.}} {\bf{10}} (2019) 1724 where a combination of measurement and theoretical modeling has been used.

physics.atom-ph↗

arXiv2023

${\cal{P,T}}$-Odd Weak Neutral Current Interactions in the TlF Molecule

Leptoquark models may explain deviations from the Standard Model observed in decay processes involving heavy quarks at high-energy colliders. Such models give rise to low-energy parity- and time-reversal-violating phenomena in atoms and molecules. One of the leading effects among these phenomena is the nucleon-electron tensor-pseudotensor interaction when the low-energy experimental probe uses a quantum state of an atom or molecule predominantly characterized by closed electron shells. In the present paper the molecular interaction constant for the nucleon-electron tensor-pseudotensor interaction in the thallium-fluoride molecule -- used as such a sensitive probe by the CeNTREX collaboration [Quantum Sci. Technol., 6:044007, 2021] -- is calculated employing highly-correlated relativistic many-body theory. Accounting for up to quintuple excitations in the wavefunction expansion the final result is $W_T({\text{Tl)}} = -6.25 \pm 0.31\, $[$10^{-13} {\langle\Sigma\rangle}_A$ a.u.] Interelectron correlation effects on the tensor-pseudotensor interaction are studied for the first time in a molecule, and a common framework for the calculation of such effects in atoms and molecules is presented.

physics.atom-ph↗

arXiv2023

Candidate Molecules for Next-Generation Searches of Hadronic Charge-Parity Violation

We systematically study a set of strongly polar heteronuclear diatomic molecules composed of laser-coolable atoms for their suitability as sensitive probes of new charge-parity violation in the hadron sector of matter. Using relativistic general-excitation-rank configuration interaction theory we single out the molecule francium-silver (FrAg) as the most promising system in this set and calculate its nuclear Schiff-moment interaction constant to $W^\mathrm{FrAg}_{SM}(\mathrm{Fr}) = 30168 \pm 2504\mathrm{a.u.}$ for the target nucleus Fr. Our work includes the development of system-tailored atomic Gaussian basis sets for the target atom in each respective molecule.

physics.atom-ph↗

arXiv2023

Atomic Clock States of Thulium have Near-Zero Electric Quadrupole Moment

A method for highly accurate calculations of atomic electric quadrupole moments (EQM) is presented, using relativistic general-excitation-rank configuration interaction wavefunctions based on Dirac spinors. Application to the clock transition states of the thulium atom employing up to full Quadruple excitations for the atomic wavefunction yields a final value of $Q_{zz}({^2F}_{7/2}) = 0.07 \pm 0.07$ a.u., establishing that the thulium electronic ground state has an exceptionally small EQM. A detailed analysis of this result is presented which has implications for EQMs of other atoms with unpaired $f$ electrons.

physics.atom-ph↗

arXiv2022

Spectroscopic and Electric Properties of the TaO$^+$ Molecule Ion for the Search of New Physics: A Platform for Identification and State Control

The TaO$^+$ cation is an attractive molecular species to search for parity- and time-reversal-violating interactions, in particular of hadronic origin. For the spectroscopic detection and preparation of TaO$^+$ cation in a desired state detailed knowledge of spectroscopic and electric properties in excited states is essential information. In this work we present spectroscopy constants for TaO$^+$ in the electronic ground and 29 excited states calculated with relativistic configuration interaction theory. The equilibrium bond lengths ($R_\mathrm{e}$), harmonic vibrational frequencies ($\omega_\mathrm{e}$), transition dipole moments (TDM), vertical excitation energies and static molecular dipole moments (PDM) are summarized. We include a detailed characterization of all electronic states in terms of their spinor occupations. This work supports the realization of experiments using TaO$^+$ ions to search for new physics beyond the standard model of elementary particles.

physics.atom-ph↗

arXiv2022

Electric dipole moments and the search for new physics

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework.

hep-ph↗

arXiv2022

Electric dipole moments due to nuclear Schiff moment interactions: A reassessment of the atoms $^{129}$Xe, $^{199}$Hg, and the molecule $^{205}$TlF

We present relativistic many-body calculations of atomic and molecular Schiff-moment interaction constants including interelectron correlation effects using atomic Gaussian basis sets specifically optimized for the Schiff interaction. Our present best results employing a Gaussian nuclear density function are $\alpha_{\text{SM}} = (0.364 \pm 0.025) \times 10^{-17} \frac{e \text{cm}}{e \text{fm}^3}$ for atomic $^{129}$Xe, $\alpha_{\text{SM}} = (-2.40 \pm 0.24) \times 10^{-17} \frac{e \text{cm}}{e \text{fm}^3}$ for atomic $^{199}$Hg, and $W_{\text{SM}} = (39967\pm 3600)$ a.u. for the thallium nucleus in the molecule $^{205}$TlF. We discuss agreements and discrepancies between our present results and those from earlier calculations on the atoms $^{129}$Xe and $^{199}$Hg. Using the most recent measurements of ${\cal{P,T}}$-odd electric dipole moments and the present interaction constants reliable upper bounds on the Schiff moments of the $^{199}$Hg and $^{205}$Tl nuclei are determined in the context of a single-source assumption.

physics.atom-ph↗

arXiv2021

Theoretical Aspects of Radium-Containing Molecules Amenable to Assembly from Laser-Cooled Atoms for New Physics Searches

We explore the possibilities for a next-generation electron-electric-dipole-moment experiment using ultracold heteronuclear diatomic molecules assembled from a combination of radium and another laser-coolable atom. In particular, we calculate their ground state structure and their sensitivity to parity- and time-reversal (${\cal{P,T}}$) violating physics arising from flavor-diagonal charge-parity (${\cal{CP}}$) violation. Among these species, the largest ${\cal{P,T}}$-violating molecular interaction constants -- associated for example with the electron electric dipole moment -- are obtained for the combination of radium (Ra) and silver (Ag) atoms. A mechanism for explaining this finding is proposed. We go on to discuss the prospects for an electron EDM search using ultracold, assembled, optically trapped RaAg molecules, and argue that this system is particularly promising for rapid future progress in the search for new sources of ${\cal{CP}}$ violation.

physics.atom-ph↗

arXiv2020

P,T-Odd Interactions in Atomic ${}^{129}$Xe and Phenomenological Applications

We calculate interaction constants for the contributions from \PT-odd scalar-pseudoscalar and tensor-pseudotensor operators to the electric dipole moment of ${}^{129}$Xe, for the first time in case of the former, using relativistic many-body theory including the effects of dynamical electron correlations. These interaction constants are necessary ingredients to relating the corresponding measurements to fundamental parameters in models of physics beyond the Standard Model. We obtain $\alpha_{C_S} = \left( 0.71 \pm 0.18 \right) [10^{-23}\, e~\text{cm}]$ and $\alpha_{C_T}= \left( 0.520 \pm 0.049 \right) [10^{-20}\, \left<\Sigma\right>_{\text{Xe}}\, e~\text{cm}]$, respectively. We apply our results to test a phenomenological relation between the two quantities, commonly used in the literature, and discuss their present and future phenomenological impact.

hep-ph↗

arXiv2020

The DIRAC code for relativistic molecular calculations

DIRAC is a freely distributed general-purpose program system for 1-, 2- and 4-component relativistic molecular calculations at the level of Hartree--Fock, Kohn--Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, coupled cluster and electron propagator theory. At the self-consistent-field level a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding, and frozen density embedding models. DIRAC was one of the earliest codes for relativistic molecular calculations and remains a reference in its field.

physics.chem-ph↗

arXiv2019

${\cal{P,T}}$-Violating and Magnetic Hyperfine Interactions in Atomic Thallium

We present state-of-the-art configuration interaction and coupled cluster calculations of the electron electric dipole moment, the nucleon-electron scalar-pseudoscalar, and the magnetic hyperfine interaction constants ($\alpha_{d_e}, \alpha_{C_S}, A_{||}$, respectively) for the thallium atomic ground state $^2P_{1/2}$. Our present best values are $\alpha_{d_e} = -559 \pm 28$, $\alpha_{C_S} = 6.77 \pm 0.34$ $[10^{-18} e$ cm$]$, and $A_{||} = 21172 \pm 1059$ [MHz]. These findings lead to a significant reduction of the theoretical uncertainties for ${\cal{P,T}}$-odd interaction constants but not to stronger constraints on the electron electric dipole moment, $d_e$, or the nucleon-electron scalar-pseudoscalar coupling constant, $C_S$.

physics.atom-ph↗

arXiv2018

${\cal{(P,T)}}$-Odd Tensor-Pseudotensor Interactions in atomic {$^{199}$Hg} and {$^{225}$Ra}

Highly correlated pure {\it{ab initio}} relativistic configuration interaction theory is in the present paper applied to the calculation of the tensor-pseudotensor ${\cal{(P,T)}}$-violating nucleon-electron interaction constant in the electronic ground states of atomic mercury and radium. The final best obtained results are $R_T$(Hg) = $-4.43$\, [$10^{-20}$ $\left<\sigma_N\right>$ $e$ cm] and $R_T$(Ra) = $-15.0$\, [$10^{-20}$ $\left<\sigma_N\right>$ $e$ cm]. The accuracy of the employed electronic-structure models are confirmed by determining the static electric dipole polarizability $\alpha_d$(Hg) = $35.7$ {\it{a.u.}} which is in accord with the experimental value to about $5$\%. $R_T$(Ra) will be useful for constraining (or obtaining) the ${\cal{(CP)}}$-violating parameter $C_T$ when combined with future measurements of the electric dipole moment of the radium atom.

physics.atom-ph↗

arXiv2018

Model-independent determinations of the electron EDM and the role of diamagnetic atoms

We perform model-independent analyses extracting limits for the electric dipole moment of the electron and the P,T-odd scalar-pseudoscalar (S-PS) nucleon-electron coupling from the most recent measurements with atoms and molecules. The analysis using paramagnetic systems, only, is improved substantially by the inclusion of the recent measurement on HfF+ ions, but complicated by the fact that the corresponding constraints are largely aligned, owing to a general relation between the coefficients for the two contributions. Since this same relation does not hold in diamagnetic systems, it is possible to find atoms that provide essentially orthogonal constraints to those from para\-magnetic ones. However, the coefficients are suppressed in closed-shell systems and enhancements of P,T-odd effects are only prevalent in the presence of hyperfine interactions. We formulate the hyperfine-induced time-reversal-symmetry breaking S-PS nucleon-electron interaction in general atoms in a mixed perturbative and variational approach, based on electronic Dirac-wavefunctions including the effects of electron correlations. The method is applied to the Hg atom, yielding the first direct calculation of the coefficient of the S-PS nucleon-electron coupling in a diamagnetic system. This results in additionally improved model-independent limits for both the electron EDM and the nucleon-electron coupling from the global fit. Finally we employ this fit to provide indirect limits for several paramagnetic systems under investigation.

hep-ph↗

arXiv2017

${\cal{P,T}}$-Odd and Magnetic Hyperfine Interaction Constants and Excited-State Lifetime for HfF$^+$

Parity- and time-reversal-symmetry violating interaction constants required for the interpretation of a recent measurement (arXiv:1704.07928 [physics.atom-ph]) of corresponding symmetry violations in the $\Omega=1$ (${^3\Delta}_1$) science state of the HfF$^+$ molecular ion are reported. Using a relativistic four-component all-electron multi-reference configuration interaction model the nucleon-electron scalar-pseudoscalar interaction constant is determined as $W_S = 20.0$ [kHz]. An updated result for the electron electric-dipole-moment effective electric field of $|E_{\text{eff}}| = 22.7 \left[\frac{\rm GV}{\rm cm}\right]$ is obtained. Further results of relevance in the context of the search for leptonic charge-parity violation such as magnetic hyperfine interaction constants and electronic $G$-tensor for HfF$^+$ are presented.

physics.atom-ph↗

arXiv2016

TaO$^+$, a Candidate Molecular Ion in Search of Physics Beyond the Standard Model

The TaO$^+$ molecular ion is proposed as a candidate system for detecting signatures of charge parity (${\cal{CP}}$) violating physics beyond the standard model of elementary particles. The electron electric dipole moment (EDM) effective electric field $E_{\text{eff}} = 20.2 \left[\frac{\rm GV}{\rm cm}\right]$, the nucleon-electron scalar-pseudoscalar (ne-SPS) interaction constant $W_{S} = 17.7$ [kHz] and the nuclear magnetic quadrupole interaction constant $W_M = 0.45$ [$\frac{10^{33} {\text{Hz}}}{e\, {\text{cm}}^2}$] are found to be sizeable ${\cal{P,T}}$-odd enhancements. The ratio of the leptonic and semi-leptonic enhancements differs strongly from the one for the ThO system which may provide improved limits on the electron EDM, $d_e$, and the SPS coupling constant, $C_S$. TaO$^+$ is found to have a ${^3\Delta_1}$ electronic ground state like the previously proposed ThF$^+$ molecular ion, but an order of magnitude smaller parallel G-tensor component which makes it less vulnerable to systematic errors in experiment.

physics.atom-ph↗

arXiv2016

Comment on "Theoretical study of thorium monoxide for the electron electric dipole moment search: Electronic properties of ${H}^3\Delta_1$ in ThO"

We present an updated EDM effective electric field of $E_{\text{eff}} = 75.2\left[\frac{\rm GV}{\rm cm}\right]$ and the electron-nucleon scalar-pseudoscalar interaction constant $W_S=107.8$ [kHz] for the ${^3\Delta}_1$ science state of ThO. The criticisms made in reference [J. Chem. Phys. 142, 024301 (2015)] are addressed and largely found to be unsubstantiated within the framework of our approach.

physics.atom-ph↗