According to the Schiff theorem, the atomic electrons completely screen the atomic nucleus from an external static electric field. However, this is not the case if the field is time-dependent. Electronic orbitals in atoms either shield the nucleus from an oscillating electric field when the frequency of the field is off the atomic resonances or enhance this field when its frequency approaches an atomic transition energy. In molecules, not only electronic, but also rotational and vibrational states are responsible for the screening of oscillating electric fields. As will be shown in this paper, the screening of a low-frequency field inside molecules is much weaker than it appears in atoms owing to the molecular ro-vibrational states. We systematically study the screening of oscillating electric fields inside diatomic molecules in different frequency regimes,i.e., when the field's frequency is either of order of ro-vibrational or electronic transition frequencies. In the resonance case, we demonstrate that the microwave-frequency electric field may be enhanced up to six orders in magnitude due to rovibrational states. We also derive the general formulae for the screening and resonance enhancement of oscillating electric field in polyatomic molecules. Possible applications of these results include nuclear electric dipole moment measurements and stimulation of nuclear reactions by laser light.

According to the Schiff theorem, a nuclear electric dipole moment (EDM) is completely shielded in a neutral atom by electrons. We consider the extension of Schiff theorem to the cases of timedependent external electric fields and nuclear EDMs. A time-dependent external electric field penetrates to the nucleus and causes nuclear spin rotation. Interaction with the axion dark matter field generates nuclear EDM d = d0 cos(ωt) oscillating with the frequency ω = mac 2 / . This EDM generates atomic and molecular EDM proportional to ω 2 . However, this EDM does not lead to the nuclear spin rotation in the constant external electric field. Nevertheless, if the nuclear EDM and the external electric field oscillate with the same frequency then the nuclear spin rotation angle grows linearly with time. The molecular EDMs induced by nuclear EDMs are strongly enhanced since nuclei move slowly and do not produce as efficient screening of oscillating nuclear EDM as electrons do. An additional strong enhancement comes from the small energy interval between rotational molecular levels. Finally, if the nuclear EDM oscillation frequency is in resonance with a molecular transition, there may be a significant resonance enhancement. Numerical estimates for the molecules HF, LiF, YbF, BaF, TlF, HfF + , ThF + , ThO and WC are provided.

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Experiments with paramagnetic ground or metastable excited states of molecules (ThO, HfF+, YbF, YbOH, BaF, PbO, etc.) provide strong constraints on the electron electric dipole moment (EDM) and the coupling constant CSP of contact semileptonic interaction. We compute new contributions to CSP arising from the nucleon EDMs due to the combined electric and magnetic electron-nucleon interaction. This allows us to improve limits from the experiments with paramagnetic molecules on the CP-violating parameters, such as the proton EDM, |dp| < 1.1 × 10−23e·cm, the QCD vacuum angle, $$ \left|\overline{\theta}\right| $$ θ ¯ < 1.4 × 10−8, as well as the quark chromo-EDMs and the π-meson-nucleon couplings. Our results may also be used to search for the axion dark matter which produces oscillating $$ \overline{\theta} $$ θ ¯ .

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 PbTiO3.