We show, at leading-order in the multipole expansion of the electron-nucleus interaction, that nucleon electric-dipole moments are completely shielded by electrons so that they contribute nothing to atomic electric-dipole moments, even when relativity in the nucleus is taken into account. It is well known that relativistic electron motion, by contrast, leads to dipole moments that are not screened; we discuss the reasons for the difference.
The electric dipole moments (EDMs) of diamagnetic atoms are expected to be sensitive to charge-parity violation particularly in nuclei through the nuclear Schiff moment. I explicitly demonstrate that the well-known form of the Schiff moment operator originating from the nucleon EDM is obtained by considering the screening of the nucleon EDMs in a neutral atom. Consequently, an additional contribution to the Schiff moment arises from the screening of the nuclear EDM induced by the interaction of the nucleon EDMs with the protons. This correction to the Schiff moment of $^{199}$Hg is evaluated i…
Parity (P) and time reversal (T) violating nuclear forces create P, T -odd moments in expansion of the nuclear electrostatic potential. We derive expression for the nuclear electric octupole field which includes the electron screening correction (similar to the screening term in the Schiff moment). Then we calculate the Z alpha corrections to the Schiff moment which appear due to the finite nuclear size. Such corrections are important in heavy atoms with nuclear charge Z > 50. The Schiff and octupole moments induce atomic electric dipole moments (EDM) and P, T -odd interactions in molecules wh…
We calculate the Schiff moments of the nuclei 199Hg and 211Ra in completely self-consistent odd-nucleus mean-field theory by modifying the Hartree-Fock-Bogoliubov code HFODD. We allow for arbitrary shape deformation, and include the effects of nucleon dipole moments alongside those of a CP-violating pion-exchange nucleon-nucleon interaction. The results for 199Hg differ significantly from those of previous calculations when the CP-violating interaction is of isovector character.
According to the Schiff theorem the nuclear electric dipole moment (EDM) is screened in neutral atoms. In ions this screening is incomplete. We extend a derivation of the Schiff theorem to ions and molecules. The finite nuclear size effects are considered including Z^2 alpha^2 corrections to the nuclear Schiff moment which are significant in all atoms and molecules of experimental interest. We show that in majority of ionized atoms the nuclear EDM contribution to the atomic EDM dominates while in molecules the contribution of the Schiff moment dominates. We also consider the screening of elect…
A partial screening of nucleon electric dipole moments (EDMs) in nuclear systems, which is related to the Schiff mechanism known for neutral atomic systems, is discussed. It is shown that the direct contribution from the neutron EDM to the deuteron EDM is partially screened by about 1% in a zero-range approximation calculation.
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…
According to the Schiff theorem an external electric field vanishes at atomic nucleus in a neutral atom, i.e. it is completely shielded by electrons. This makes a nuclear electric dipole moment (EDM) unobservable. In this paper an extension of the Schiff theorem to an oscillating electric field is considered. Such field can reach the nucleus and interact with the nuclear EDM. The enhancement effect appears if the field is in resonance with atomic or molecular transition. The shielding by electrons strongly affects low-energy nuclear electric dipole transition amplitudes in different nuclear re…
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…
The current status of electric dipole moments of diamagnetic atoms which involves the synergy between atomic experiments and three different theoretical areas -- particle, nuclear and atomic is reviewed. Various models of particle physics that predict CP violation, which is necessary for the existence of such electric dipole moments, are presented. These include the standard model of particle physics and various extensions of it. Effective hadron level combined charge conjugation (C) and parity (P) symmetry violating interactions are derived taking into consideration different ways in which a …
Current conservation, screening and the magnetic moment of the $Δ$ resonance: 2. Formulation with quark degrees of freedom 3. Magnetic moment of the $Δ^o$ and $Δ^-$ resonances
Using non-perturbative lattice method we studied hadronic screening correlators above and immediately below the deconfinement transition temperature, Tc, in the quenched approximation with lattice spacing of 1/(8T) using clover improved Wilson fermions. Simulations were performed at temperatures T /Tc = 0, 0.95 and 1.5. Mesonic screening correlators show no statistically significant thermal effects below Tc, and clear evidence for weakly interacting quarks above Tc . Baryon screening correlators yield similar physics above Tc, but show precursor effects for chiral symmetry restoration below Tc…
Interpretation of current and future neutrino oscillation and electron scattering experiments requires knowledge of lepton-nucleon and lepton-nucleus interactions at the percent level. We study the exchange of photons between charged particles and the nuclear medium for (anti)neutrino-, electron-, and muon-induced reactions inside a large nucleus. While quantum electrodynamics (QED)-medium contributions are formally suppressed by two powers of the electromagnetic coupling constant $α$ when compared to the leading-order cross sections, low-energy modes and the nuclear size enhance the effect by…
Electric dipole moments of diamagnetic atoms of experimental interest are calculated using the relativistic Hartree-Fock and random-phase approximation methods, the many-body perturbation theory and configuration interaction technique. We consider P,T-odd interactions which give rise to atomic electric dipole moment in the second order of the perturbation theory. These include nuclear Schiff moment, P,T-odd electron-nucleon interaction and electron electric dipole moment. Interpretation of a new experimental constraint of a permanent electric dipole moment of $^{199}$Hg [W. C. Griffith {\it et…
We calculate for the first time the electric dipole moment (EDM) of the deuteron, $^3$H, and $^3$He nuclei generated by the one-meson exchange CP-odd nuclear force in the standard model. The effective $|ΔS| = 1$ four-quark operators are matched to the $|ΔS| = 1$ standard model processes involving the CP phase of the Cabibbo-Kobayashi-Maskawa matrix at the electroweak scale and run down to the hadronic scale $μ= 1$ GeV according to the renormalization group evolution in the next-to-leading logarithmic order. At the hadronic scale, the hadron matrix elements are modeled in the factorization appr…
