Electric dipole moments of atoms and molecules produced by enhanced nuclear Schiff moments

Abstract

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 open f -shell case. To validate the method we perform similar calculations for simpler atoms (Xe, Hg, Tl + , Pb, Pb ++ , Rn, Ra) where some earlier results are available. In addition we present the estimates of the CP-violating nuclear spin -molecular axis interaction constants for molecules which may be of experimental interest including AcF, AcN, AcO + , EuN, EuO + , ThO, PbO and TlF. We also present updated values of the nuclear Schiff moments and atomic and molecular EDM expressed in terms of the CP-violating π-meson -nucleon interaction constantsḡ0, g1,ḡ2, QCD parameterθ and quark chromo-EDMs. The results may be used to test CP-violation theories and search for axion dark matter in atomic, molecular and solid state experiments.1 Nuclear EDM and magnetic quadrupole produced by the T,Podd nuclear forces are also enhanced due to an opposite parity level with the same spin close to the ground state [9,15]. Collective enhancement of the magnetic quadrupole moments in deformed nuclei have been demonstrated in [16].9 Some older molecular calculations presented constant X = W S /6. Table I to the energy shift W T,P = W S S J J · n gives for the fully polarised molecule the energy difference between the J z = J and J z = −J states: Substitution of the Schiff moment from

Limits on CP-violating hadronic interactions and proton EDM from paramagnetic molecules

“…In particular, our limit on the neutron EDM obtained from the results of experiments with paramagnetic molecules is almost three order of magnitude weaker than the recent experimental measurements of EDM of neutron |d n | < 1.8 × 10 −26 e • cm [67]. However, for the proton EDM our limit (5.1) is just about 20 times weaker than the recent constraint on this parameter |d p | < 5 × 10 −25 e • cm [68] which was based on the measurements on EDM of 199 Hg atom [14]. 6 Remarkably, the constraint (5.1) on the proton EDM is nearly 30 times more stringent than that found in recent 129 Xe EDM experiments [70,71].…”

“…Note that this constraint is approximately two times weaker than that in ref [69]. because the authors of ref [68]. revisited earlier calculations of nuclear Shiff moments.…”

Parity and Time Reversal Invariance Violation in Neutron-Nucleus Scattering

“…After neutron capture, it is possible that 140 57 La 83 has an excited isomeric state with octupole deformation. Further, the spectra of the stable 153 63 Eu 90 isotope (I P = 5/2 + ) indicates octupole deformation in the ground state [66,68], with an energy band gap of 97 keV. This is a good candidate to search for PV and PTRIV effects.…”

“…It is also important to note that octupole deformation is required in the nucleus excited by the neutron capture. Information regarding octupole deformation can be extracted from the nuclear rotational spectra presented in the database [67] (see also [66,68]). In nuclei with nonzero spin with octupole deformation, doublets of opposite parity states with the same spin (along the rotational bands) can be seen.…”

Probing Fundamental Symmetries of Deformed Nuclei in Symmetric Top Molecules

“…One demonstrated method for increasing experimental sensitivity is to use a polar molecule, whose internal fields can be easily oriented to provide an enhancement of ≳100 over atoms in EDM measurements [21][22][23]. TlF, for instance, is sensitive to the Schiff moment of 205 Tl nuclei [24][25][26], and theoretical proposals have identified a wide variety of diatomic [27][28][29][30][31][32][33] and triatomic molecules [28,34,35] suitable for Schiff moment measurements. Combining enhancements due to nuclear deformation and the polarizability of molecules results in ≳10 5 sensitivity increase relative to atomic Schiff moment measurements with spherical nuclei.…”