A concept of CP-violating (T,P-odd) permanent molecular magnetic moments $μ^{CP}$ is introduced. We relate the moments to the electric dipole moment of electron (eEDM) and estimate $μ^{CP}$ for several diamagnetic polar molecules. The moments exhibit a steep, Z^5, scaling with the nuclear charge Z of the heavier molecular constituent. A measurement of the CP-violating magnetization of a polarized sample of heavy molecules may improve the present limit on eEDM by several orders of magnitude.
Heavy polar molecules offer a great sensitivity to the electron Electric Dipole Moment(EDM). To guide emerging searches for EDMs with molecular ions, we estimate the EDM-induced energy corrections for hydrogen halide ions $\mathrm{HBr}^{+}$ and $\mathrm{HI}^{+}$ in their respective ground $X ^2Π_{3/2}$ states. We find that the energy corrections due to EDM for the two ions differ by an unexpectedly large factor of fifteen. We demonstrate that a major part of this enhancement is due to a dissimilarity in the nature of the chemical bond for the two ions: the bond that is nearly of ionic characte…
The existence of a nuclear electric octupole moment (EOM) requires both parity and time invariance violation. The EOMs of odd $Z$ nuclei that are induced by a particular T- and P-odd interaction are calculated. We compare such octupole moments with the collective EOMs that can occur in nuclei having a static octupole deformation. A nuclear EOM can induce a parity and time invariance violating atomic electric dipole moment, and the magnitude of this effect is calculated. The contribution of a nuclear EOM to such a dipole moment is found, in most cases, to be smaller than that of other mechanism…
Nuclear magnetic quadrupole moments (MQMs), like intrinsic electric dipole moments of elementary particles, violate both parity and time-reversal symmetry and therefore probe physics beyond the Standard Model of particle physics. We report on accurate relativistic coupled cluster calculations of the nuclear MQM interaction constants in BaF, YbF, BaOH, and YbOH. We elaborate on estimates of the uncertainty of our results. The implications of experiments searching for nonzero nuclear MQMs are discussed.
We have calculated the atomic electric dipole moments (EDMs) induced in ^{199}Hg, ^{129}Xe, ^{223}Rn, ^{225}Ra, and ^{239}Pu by their respective nuclear Schiff moments S. The results are (in units 10^{-17}S(e {fm}^{3})^{-1}e cm): d(^{199}Hg)=-2.8, d(^{129}Xe)=0.38, d(^{223}Rn)=3.3, d(^{225}Ra)=-8.5, d(^{239}Pu)=-11. We have also calculated corrections to the parity- and time-invariance-violating (P,T-odd) spin-axis interaction constant in TlF. These results are important for the interpretation of atomic and molecular experiments on EDMs in terms of fundamental P,T-odd parameters.
We show that existing calculations of the interaction between nuclear Schiff moments and electrons in molecules use an inaccurate operator which gives rise to significant errors. By comparing the matrix elements of the accurate and imprecise Schiff moment operators, we calculated the correction factor as a function of the nuclear charge Z and presented corrected results for the T,P-violating interaction of the nuclear spin with the molecular axis in the TlF, RaO, PbO, TlCN, ThO, AcF molecules and in the ferroelectric solid PbTiO$_3$.
The CP-violating interaction of the nuclear magnetic quadrupole moment (MQM) of the $^{175}$Lu nucleus with electrons in the molecular cation LuOH$^+$ is studied. The resulting effect is expressed in terms of CP-odd parameters, such as quantum chromodynamics angle $\barθ$, quark electric dipole moment (EDM) and chromo-EDM. For this we have performed a calculation of the nuclear MQM as well as the molecular constant that characterises the interaction of this MQM of $^{175}$Lu with electrons. Additionally, we predict the hyperfine structure constants for the ground electronic state of LuOH$^+$. …
All-electron configuration interaction theory in the framework of the Dirac-Coulomb Hamiltonian has been applied to the TaN molecule, a promising candidate in the search for Beyond-Standard-Model physics in both the hadron and the lepton sector of matter. We obtain in the first excited {$^3Δ_1$} state a ${\cal{P,T}}$-odd effective electric field of $36.0 \left[\frac{\rm GV}{\rm cm}\right]$, a scalar-pseudoscalar ${\cal{P,T}}$-odd interaction constant of $32.8$ [kHz], and a nuclear magnetic-quadrupole moment interaction constant of $0.74$ [$\frac{10^{33} {\text{Hz}}}{e\, {\text{cm}}^2}$]. The l…
Nuclei with an octupole deformation have a non-zero electric octupole moment, electric dipole moment (EDM), Schiff moment and magnetic quadrupole moment (MQM) in the intrinsic frame which rotates with the nucleus. In a state with definite angular momentum in the laboratory frame, these moments are forbidden by parity (P) and time reversal invariance (T) conservation, meaning their expectation values vanish due to nuclear rotation. However, nuclei with an octupole deformation have doublets of close opposite parity rotational states with the same spin, which are mixed by T,P-odd nuclear forces. …
Octupole deformation results in a strongly enhanced collective Schiff moment in 229Th nucleus. An additional enhancement of time reversal (T) and parity (P) violating effects (such as T,P-violating electric dipole moments) appears in the ground 1Sigma state and in the metastable 3Delta_1 state of diatomic molecule 229ThO. Similar enhancements exist in molecular ions 229ThOH+, 229ThF+ and 225,223RaOH+. Corresponding experiments may be used to test CP-violation theories predicting T,P-violating nuclear forces and to search for axions.
We propose a direct method of detection of the nuclear anapole moment. It is based on the existence of a linear Stark shift for alkali atoms in their ground state perturbed by a quadrupolar interaction potential and a magnetic field. This shift is proportional to the T-even pseudoscalar built from the quadrupolar potential symmetry axis, the directions of the applied electric and magnetic fields.It involves on the one hand the anisotropy of the hyperfine interaction induced by the quadrupolar interaction and, on the other,the static electric dipole moment arising from electroweak interactions …
The electric dipole moments of closed-shell atoms are sensitive to the parity and time-reversal violating phenomena in the nucleus. The nuclear Schiff moment is one such property, it arises from the parity and time reversal violating quark-quark interactions and the quark-chromo electric dipole moments. We calculate the electric dipole moment of atomic $^{199}{\rm Hg}$ arising from the nuclear Schiff moment using the relativistic coupled-cluster theory. This is the most accurate calculation of the quantity to date. Our calculations in combination with the experiment data provide important insi…
The exchange of an axion-like particle between atomic electrons and the nucleus may induce electric dipole moments (EDMs) of atoms and molecules. This interaction is described by a parity- and time-reversal-invariance-violating potential which depends on the product of a scalar $g^s$ and a pseudoscalar $g^p$ coupling constant. We consider the interaction with the specific combination of these constants, $g_e^s g_N^p$, which gives significant contributions to the EDMs of diamagnetic atoms. In this paper, we calculate these contributions to the EDMs of $^{199}$Hg, $^{129}$Xe, $^{211}$Rn and $^{2…
In the presence of P,T-violating interactions, the exchange of axion-like particles between electrons and nucleons in atoms and molecules induces electric dipole moments (EDMs) of atoms and molecules. We perform calculations of such axion-exchange-induced atomic EDMs using the relativistic Hartree-Fock-Dirac method including electron core polarisation (RPA) corrections. We present analytical estimates to explain the dependence of these induced atomic EDMs on the axion mass and atomic parameters. From the experimental bounds on the EDMs of atoms and molecules, including $^{133}$Cs, $^{205}$Tl, …
The existence of permanent electric dipole moments (EDMs) and magnetic quadrupole moments (MQMs) violate both time reversal invariance ($T$) and parity ($P$). Following the $CPT$ theorem they also violate combined $CP$ symmetry. Nuclear EDM are completely screened in atoms and molecules while interaction between electrons and MQM creates atomic and molecular EDM which can be measured and used to test CP-violation theories. Nuclear MQM are produced by the nucleon-nucleon $T,P$-odd interaction and by nucleon EDM. In this work we study the effect of enhancement of the nuclear MQM due to the nucle…
Relativistic many-body methods at different levels of approximations are employed to gain insights into the passage of the electron correlations from lower to higher levels in the accurate determination of the electric dipole polarizability ($α_d$) and electric dipole moment (EDM) due to the electron-nucleus tensor-pseudotensor (T-PT) and nuclear Schiff moment (NSM) interactions of the $^{199}$Hg ground state. Moreover, plausible reasons for the differences in the previous calculations are pointed out. Comparison between the calculated and experimental results of $α_d$ indicates that our EDM c…
Deformed nuclei possess enhanced moments violating time reversal invariance ($T$) and parity ($P$). Collective magnetic quadrupole moments (MQM) appear in nuclei with a quadrupole deformation (which have ordinary $T$,$P$-conserving collective electric quadrupole moments). Nuclei with an octupole deformation have a collective electric octupole moment, electric dipole moment (EDM), Schiff moment and MQM in the intrinsic frame which rotates with the nucleus. In a state with definite angular momentum in the laboratory frame, these moments are forbidden by $T$ and $P$ conservation, meaning their ex…
HfF$^+$ cation is a very promising system to search for the electron electric dipole moment (EDM), and corresponding experiment is carried out by E. Cornell group. Here we theoretically investigate the cation to search for another T,P-odd effect -- the nuclear magnetic quadrpole moment (MQM) interaction with electrons. We report the first accurate ab initio relativistic electronic structure calculations of the molecular parameter $W_M$=0.494 $\frac{10^{33}\mathrm{Hz}}{e~{\rm cm}^2}$ that is required to interpret the experimental data in terms of the MQM of Hf nucleus. For this we have implemen…
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 ($α_{d_e}, α_{C_S}, A_{||}$, respectively) for the thallium atomic ground state $^2P_{1/2}$. Our present best values are $α_{d_e} = -559 \pm 28$, $α_{C_S} = 6.77 \pm 0.34$ $[10^{-18} e$ 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 constrai…
We perform calculations of the CP-violating atomic and molecular electric dipole moments (EDM) induced by the interaction of the nuclear Schiff moments with electrons. EDM of atoms Eu, Dy, Gd, Ac, Th, Pa, U, Np and Pu are of special interest since they have isotopes with strongly enhanced nuclear Schiff moments caused by the octupole nuclear deformation or soft octupole vibration mode. These atoms have open 4f or 5f shells making the calculations complicated. We use our special version of the configuration interaction method combined with the many-body perturbation theory method adopted for op…
We report rigorous calculations of electric dipole moment (EDM) in $^{225}$Ra due to parity and time-reversal violating tensor-pseudotensor (T-PT) and nuclear Schiff moment (NSM) interactions between the electrons and nucleus by employing the relativistic all order coupled-cluster (RCC) methods at various levels of approximation. The most accurate EDM ($d_A$) results are obtained as $d_A=-10.04\times 10^{-20} C_T <σ_n>|e|cm$ and $d_A^{NSM}=-6.79 \times 10^{-17} S (|e|fm^3)^{-1} |e|cm$ with $C_T$ and $S$ are the T-PT coupling constant and NSM respectively. Due to exhaustive treatment of the ele…
CP-violating interaction of the nuclear magnetic quadrupole moment (MQM) with electrons in the ytterbium mono-hydroxide molecule, $^{173}$YbOH, is considered. Both the magnetic quadrupole moment (MQM) of the $^{173}$Yb nucleus and the molecular interaction constant WM are estimated. Electron correlation effects are taken into account within the relativistic Fock-space coupled cluster method. Results are interpreted in terms of the strength constants of CP-violating nuclear forces, neutron EDM, QCD vacuum angle $θ$, quark EDM and chromo-EDM.
Collisions and chemical reactions of molecules in Bose-Einstein condensates (BECs) are extremely sensitive to weak fields. This sensitivity arises due to the high density of compound resonances and a macroscopic number of molecules with kinetic energy E=0 (perfect energy resolution). We suggest that chemical reactions in molecular BECs could be used to enhance effects produced by small external perturbations and search for a parity-violating energy difference in chiral molecules.
Measurements of nuclear spin-dependent parity-violating (NSD-PV) effects provide an excellent opportunity to test nuclear models and to search for physics beyond the Standard Model. Molecules possess closely-spaced states with opposite parity which may be easily tuned to degeneracy to greatly enhance the observed parity-violating effects. A high-sensitivity measurement of NSD-PV effects using light triatomic molecules is in preparation [E. B. Norrgard, et al., Commun. Phys. 2, 77 (2019)]. Importantly, by comparing these measurements in light nuclei with prior and ongoing measurements in heavie…
Combining the recently reported electric dipole moment (EDM) of $^{199}$Hg atom due to breaking of parity and time-reversal symmetries with the improved relativistic atomic calculations, precise limits on the tensor-pseudotensor (T-PT) electron-nucleus (e-N) coupling coefficient and the nuclear Schiff moment (NSM) interactions are determined. Using these limits with the nuclear calculations, we infer limits on the EDMs of neutron and proton as $d_n < 2.2 \times 10^{-26} |e| \rm{cm}$ and $d_p < 2.1 \times 10^{-25} |e| \rm{cm}$, respectively, and on the quantum chromodynamics (QCD) parameter and…
We demonstrate that electron electric dipole moment experiments with molecules in paramagnetic state are sensitive to $P,T$-violating nuclear forces and other $CP$-violating parameters in the hadronic sector. These experiments, in particular, measure the coupling constant $C_{SP}$ of the $CP$-odd contact semileptonic interaction. We establish relations between $C_{SP}$ and different $CP$-violating hadronic parameters including strength constants of the $CP$-odd nuclear potentials, $CP$-odd pion-nucleon interactions, quark-chromo EDM and QCD vacuum angle. These relations allow us to find limits…
