Screening and enhancement of an oscillating electric field in molecules

Abstract

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.

Production of HD Molecules in Definite Hyperfine Substates

“…Polarized H + 2 and HD + ions in single spin-isomers are a perfect tool for precision spectroscopy of this most simple molecular ions, because the influence of the spindependent part of the transition-frequencies can be determined separately [17]. Another option to use these molecules can be the search for a static electric dipole moment (EDM) with oscillating electric fields [18] or even experiments searching for an oscillating nuclear EDM produced by the axion dark matter field [19]. For both methods the use of highly polarized HD molecules is beneficial, because the EDM effect would be proportional to the inverse nucleon charge z −1 that is at minimum for the hydrogen isotopes.…”

Electric field on nucleus in solids and interaction of CP-violating nuclear electric dipole moment with phonons

“…This paper is devoted to the extension of our previous results for atoms [9,10] and molecules [11] to the case of solid states. On the one hand, a crystal can be viewed as a molecule composed of a large number of atoms, and the general consideration developed in [11] is applicable.…”

“…This paper is devoted to the extension of our previous results for atoms [9,10] and molecules [11] to the case of solid states. On the one hand, a crystal can be viewed as a molecule composed of a large number of atoms, and the general consideration developed in [11] is applicable. However, the general formulas in [11] do not allow us to give specific numerical estimates as one needs to know the exact wave functions which take into account the positions of all atoms in the solid state including all excitations.…”

“…In molecules, the pattern of screening or resonant enhancement of the oscillating electric field is much more complex owing to the presence of rotational and vibrational states in addition to the electronic states [11]. Since the energies of rovibrational states are lower than the ones for electronic states, even the fields in the microwave region may strongly interact with nuclei.…”

“…On the one hand, a crystal can be viewed as a molecule composed of a large number of atoms, and the general consideration developed in [11] is applicable. However, the general formulas in [11] do not allow us to give specific numerical estimates as one needs to know the exact wave functions which take into account the positions of all atoms in the solid state including all excitations. On the other hand, in dielectrics and semiconductors, the electric field inside the solid state is well understood through the electric permittivity ε = (1 + χ )ε 0 , where χ is the electric susceptibility and ε 0 is the vacuum permittivity.…”