Electric Dipole Moment Operator Research Articles

A new quantum hydrodynamic description of ferroelectricity in spiral magnets

The strong coupling between magnetism and ferroelectricity was found in rare-earth manganites, where the electric polarization could be induced by special magnetic ordering. There is no theoretical model that would allow us to study the static and dynamic properties of electric polarization in strongly correlated magnetic dielectrics. In the presented research, we have taken the main step toward the construction of such a fundamental model and made a direct connection between the microscopic Katsura–Nagaosa–Balatsky theory and Mostovoy’s phenomenological model for magnetically induced polarization. A novel description of the ferroelectricity of spin origin is proposed within the framework of the many-particle quantum hydrodynamics method. It is applied to the study of cells of magnetic ions, where the electric dipole moment is proportional to the vector product of spins. Our approach is based on the many-particle Pauli equation, where the influence of an external magnetic field is considered. We define the electric dipole moment operator of the ion cell and introduce the macroscopic polarization as the quantum mechanical average of that operator. We formulate a model for the description of nonequilibrium polarization and derive a new polarization evolution equation. The polarization switching in ferroelectric magnets with the spiral spin-density-wave state is considered, and we demonstrate that the proposed model yields known results and can predict novel effects. The dynamic magnetoelectric effect can be investigated by employing this novel equation to study the evolution of polarization.

Lepton electric dipole moment and strong CP violation

Contribution of the strong CP angle, θ¯, to the Wilson Coefficients of electron and muon electric dipole moment (EDM) operators are discussed. Previously, θ¯ contribution to the electron EDM operator was calculated by Choi and Hong [1]. However, the effect of CP-violating three meson coupling was missing in [1]. We include this missing contribution for the first time in the literature, and reevaluate the Wilson coefficients of the lepton EDM operator. We obtain de=−(2.2–8.6)×10−28θ¯e-cm which is 15–70% of the result obtained in [1]. We also estimated the muon EDM as dμ=−(0.5–1.8)×10−25θ¯e-cm. Using |θ¯|≲10−10 suggested by the neutron EDM measurements, we obtain |de|≲8.6×10−38e-cm and |dμ|≲1.8×10−35e-cm. The θ¯ contribution to the muon EDM is much below the sensitivities of the current and near future experiments. Our result shows that the θ¯ contribution to de,μ can be larger than the CKM contributions by many orders of magnitude.

Permanent electric dipole moments of single-, two- and three-nucleon systems

A nonzero electric dipole moment (EDM) of the neutron, proton, deuteron or helion, in fact, of any finite system necessarily involves the breaking of a symmetry, either by the presence of external fields (i.e., electric fields leading to the case of induced EDMs) or explicitly by the breaking of the discrete parity and time-reflection symmetries in the case of permanent EDMs. We discuss two theorems describing these phenomena and report about the cosmological motivation for an existence of [Formula: see text] breaking beyond what is generated by the Kobayashi–Maskawa mechanism in the Standard Model and what this might imply for the permanent EDMs of the nucleon and light nuclei by estimating a window of opportunity for physics beyond what is currently known. Recent — and in the case of the deuteron even unpublished — results for the relevant matrix elements of nuclear EDM operators are presented and the relevance for disentangling underlying New Physics sources is discussed.

Photo-absorption sum rules σ–1 in different environments (Atoms, nuclei, nucleons)

Combining the spin-dependent dispersion GDH-sum rule, the isotopic-spin-dependent Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (i.e. generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector. Within the non-relativistic approach to photo-absorption sum rules for the 3N-nuclei a new σ–1 sum rule proposed which is based on general charge-symmetry (CS) consequences for the “CS-conjugated” triton and 3He.

Photo-absorption sum rules σ−1 in different environments

Combining the spin-dependent dispersion GDH-sum rule, the iso-vector, photo-excitation states projecting Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (or generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector.

Ab initio calculation of the rotational spectrum of methane vibrational ground state

In a previous article we have introduced an alternative perturbation scheme to the traditional one starting from the harmonic oscillator, rigid rotator Hamiltonian, to find approximate solutions of the spectral problem for rotation-vibration molecular Hamiltonians. The convergence of our method for the methane vibrational ground state rotational energy levels was quicker than that of the traditional method, as expected, and our predictions were quantitative. In this second article, we study the convergence of the ab initio calculation of effective dipole moments for methane within the same theoretical frame. The first order of perturbation when applied to the electric dipole moment operator of a spherical top gives the expression used in previous spectroscopic studies. Higher orders of perturbation give corrections corresponding to higher centrifugal distortion contributions and are calculated accurately for the first time. Two potential energy surfaces of the literature have been used for solving the anharmonic vibrational problem by means of the vibrational mean field configuration interaction approach. Two corresponding dipole moment surfaces were calculated in this work at a high level of theory. The predicted intensities agree better with recent experimental values than their empirical fit. This suggests that our ab initio dipole moment surface and effective dipole moment operator are both highly accurate.

Parametrization of linear dielectric response

The quantum linear response of a dielectric to an external electric field yields expressions for the dielectric susceptibility and the associated impulse response function. These are measured properties that, during analysis, are often "curve-fitted" to diverse forms of parametric functional forms that shall herein be referred to as fit-functions. The main purpose of this paper is to show, from a very general linear response formalism that encompasses virtually all microscopic models of dielectric response, that there are constraints on the forms that the susceptibilities must obey and to examine common parametrizations of the dielectric function in light of these constraints. Naturally these constraints should, whenever possible, be in-built into the fit-functions employed. The linear response approach due to Madden and Kivelson [Adv. Chem. Phys. 56, 467 (1984)], where the cause is considered to be a uniform external field, E(ext)(t), is utilized as it affords a much more straightforward interaction term, viz., -M·E(ext)(t), (M being the system's total electric dipole moment operator) than would be the case if the mean internal field (or "Maxwell field") were taken as the cause. It is shown that this implies definite relations between the quasipermittivity, ζ(ω), of the Madden-Kivelson approach and the normal permittivity, χ(ω)≡ε(ω)-ε(0). These relations indicate a condition for the divergence of the normal susceptibility, which, arguably, marks the onset of a ferroelectric transition in "sufficiently polar" dielectrics. Finally, some common parametric "fit-function" forms are investigated as to whether they comply with the constraints that the formalism imposes, and examples are given of their associated Cole-Cole plots in typical cases involving one or more relaxation times.

Quark-hadron duality sum rules for spin-dependent photon-nucleon and photon-photon resonance cross-section

We focus on the special kind sum rules, namely, the relativistic dipole-moment-fluctuation sum rules with only main valence quark configuration of hadrons taken into account and stress the specifics of these sum rules enabling to treat them as the quark-hadron duality sum rules in the processes initiated by real photons. A few relations, including the sum rule for the neutron charge radius, are discussed between different bremsstrahlung-weighted integrals of the nucleon resonance photoexcitation cross sections and correlation functions of the quark electric dipole moment operators in the nucleon ground state. These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector. In the meson sector, we mainly discuss the sum rules for the two-photon decay widths of the pseudoscalar mesons made of heavy charm quarks that are of the present interest. The obtained results are compared with predictions of other approaches.

High-precision calculationsj of the 3,1 P 1 0 →1 S 0 E1 amplitudes for magnesium, calcium, and strontium

High-precision calculations of the 3,1 P 1 0 (ns np→1 S 0(ns 2) E1 amplitudes were carried out for magnesium, calcium, and strontium (n=3, 4, and 5, respectively). The following results were obtained for the reduced matrix element 〈1 P 1 0 ‖d‖ 1 S 0〉 of electric dipole moment operator: 4.03(2) au for Mg, 4.91(7) au for Ca, and 5.28(9) au for Sr. These matrix elements are necessary for calculating the van der Waals coefficients C 6, which are used in evaluating the atomic scattering lengths. The latter determine the dynamics and stability of the Bose-Einstein condensate.

Electric dipole moment of a BPS monopole

Monopole ``superpartner'' solutions are constructed by acting with finite, broken supersymmetry transformations on a bosonic $N=2 \mathrm{BPS}$ monopole. The terms beyond first order in this construction represent the back reaction of the fermionic zero-mode state on the other fields. Because of the quantum nature of the fermionic zero modes, the superpartner solution is necessarily operator valued. We extract the electric dipole moment operator and show that it is proportional to the fermion zero-mode angular momentum operator with a gyroelectric ratio $g=2.$ The magnetic quadrupole operator is shown to vanish identically on all states. We comment on the usefulness of the monopole superpartner solution for a study of the long-range spin-dependent dynamics of BPS monopoles.

Rotational Energy Levels and Line Intensities for2S+1Σ–2S+1Σ Transitions in an Open-Shell Diatomic Molecule Weakly Bonded to a Closed-Shell Partner

This paper concerns rotational energy levels and line intensities for electronic, vibrational, and microwave transitions in an open-shell complex consisting of an open-shell diatomic molecule and a closed-shell partner. The electronic state of the open-shell diatomic fragment is a2S+1Σ state, whereS≥12, the close-shell partner could be a rare gas atom or a diatomic molecule or a planar polyatomic molecule. We are considering a near-rigid rotor model for a nonlinear complex, taking into account thoroughly all effects of the electron spin and the quartic centrifugal distortion correction terms. The total Hamiltonian is expressed as H=Hrot+Hsr+Hss+Hcd+Hsrcd+Hsscd. We have derived all the nonvanishing matrix elements of the Hamiltonian operators in the molecular basis set. The rotational energy levels are calculated by numerical diagonalization of the total Hamiltonian matrix for eachJvalue. The nonvanishing matrix elements of the electric dipole moment operator are derived in the molecular basis set for electronic, vibrational, and microwave transitions within the complex. Expectation values of the quantum numbers and of the parities of the rotational states are derived in the molecular basis set. Relative intensities of the allowed rotational transitions, expectation values of the quantum numbers and the parities are calculated numerically in the space of the eigenvectors obtained from diagonalization of the Hamiltonian matrix. The formalism and the computer program of this paper are considered as extensions to our previous work [W. M. Fawzy and J. T. Hougen,J. Mol. Spectrosc.137, 154–165 (1989); W. M. Fawzy,J. Mol. Spectrosc.160, 84–96 (1993)] and are expected to be particularly useful for analyzing and fitting high-resolution spectra of weakly bonded oxygen complexes. A brief discussion of the Hamiltonian operators, the matrix elements, and the computer program is given.

Implications of the strange spin of the nucleon for the neutron electric dipole moment in supersymmetric theories

Supersymmetric model contributions to the neutron electric dipole moment arise via quark electric dipole moment operators, whose matrix elements are usually calculated using the Naive Quark Model (NQM). However, experiments indicate that the NQM does not describe well the quark contributions Δq to the nucleon spin, and so may provide misleading estimates of electric dipole operator matrix elements. Taking the Δq from experiment, we indeed find consistently smaller estimates of the neutron electric dipole moment for given values of the supersymmetric model parameters. This weakens previous constraints on CP violation in supersymmetric models, which we exemplify analytically in the case where the lightest supersymmetric particle (LSP) is a U(1) gaugino B , and display numerically for other LSP candidates.

Rotational line strengths for the photoionization of diatomic molecules

We derive an expression for the probability that a diatomic molecule AB(n,v,N) in the electronic state n, vibrational state v, and rotational level N yields upon photoionization AB+(n+,v+,N+), where we assume Hund’s case (b) coupling. Our result is formally equivalent to the previous work of Buckingham, Orr, and Sichel [Phil. Trans. Roy. Soc. London, Ser. A 268, 147 (1970)] but differs substantially in that we use spherical tensor methods, which provide insight into the photoionization dynamics in terms of the contribution of different multipole moments. The total interaction term is given by the tensor product of the electric dipole moment operator T(1,μ0) and the multipole moment tensor T(l,m) describing the photoelectron in the lth partial wave. The interaction term is further simplified into a sum of reduced multipole moments T(k,p), where k=l±1 and p=μ0+m. For an isotropic distribution of initial states, the transition probability is given by P(N,N+)=1/3∑k Sk(N,N+)‖μ̄(k,q)‖2, where the factor of 1/3 arises from the use of a beam of polarized light, Sk(N,N+) is a generalized rotational line strength factor, and ‖μ̄(k,q)‖2=‖μl=k+1(k,q) ‖2+‖μl=k−1(k,q)‖2 is the sum of the squares of reduced multipole moment matrix elements. The summation over k is restricted to even values for a (±)↔(±) transition and to odd values for a (±)↔(∓) transition. Thus, for an unpolarized molecular sample, the integrated photoelectron intensity associated with an N→N+ transition is the incoherent sum of the multipole moments that contribute to this transition, and each such contribution is an incoherent sum over l=k+1 and l=k−1. If the molecular sample is polarized (aligned and/or oriented), then the expression for the N→N+ integrated photoelectron intensity becomes a coherent sum over different k values with the same l value. Moreover, if the photoelectron distribution is angle resolved, then the expression for the N→N+ transition probability is a coherent sum over l values with the same k value when the molecular sample is unpolarized and cannot be separated into incoherent parts when the molecular sample is polarized. The expression for P(N,N+) has been used to fit the results of the photoionization of H2 and NO. In both cases, the fit obtained, which required only one or two adjustable parameters, respectively, agrees well with the experimental data. This treatment may be readily extended to photoionization of polyatomic molecules and to molecules that follow different angular momentum coupling cases.

Supersymmetry and the neutron electric dipole moment.

The dimension-six $\mathrm{CP}$-violating operator ${f}_{\mathrm{abc}}{{{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}^{a}}_{\ensuremath{\mu}}}^{\ensuremath{\nu}}{{{G}^{b}}_{\ensuremath{\nu}}}^{\ensuremath{\rho}}{{{G}^{c}}_{\ensuremath{\rho}}}^{\ensuremath{\mu}}$, recently proposed by Weinberg as the dominant contribution to the neutron electric dipole moment ${d}_{n}$, cannot be supersymmetrized but will occur in the low-energy effective Lagrangian when supersymmetry is spontaneously broken. However, the dimension-five quark electric dipole moment and the quark color electric dipole moment operators contribute to ${d}_{n}$ even at one loop and become the dominant contributions, though the Weinberg contribution is still quite large.

The electric dipole moment function of HF

Based on experimental data with improved accuracy, a new determination of the electric dipole moment function of the molecule HF in the X 1 Sigma + electronic state has been made. The new results are presented in the forms both of a power series, valid within the range of internuclear separation 0.69( R/10-10m(1.45, and of a rational function at least qualitatively valid at all larger internuclear distances. The rotational dependence of expectation values of the electric dipole moment operator is also investigated.

Third-order theory of the line intensities in the allowed and forbidden vibrational-rotational bands of C 3 v molecules

A third-order theory of the intensities of the allowed and “forbidden” (perturbation-allowed) transitions to the fundamental vibrational levels of C 3 v semirigid molecules has been worked out by using the method of contact transformations applied to the electric dipole moment operator. Explicit expressions have been obtained for the linestrengths of the allowed (Δ k = 0, ±1) as well as forbidden (Δ k = ±2, ±3, ±4) transitions from the ground vibronic state to the fundamental vibrational levels of C 3 v molecules. The treatment takes into account all the important Coriolis and anharmonic interactions in a C 3 v molecule, including the effect of the “2, 2” and “2, −1” l-type interactions and the Δ k = ±3 interactions on the intensities of the allowed and forbidden vibrational-rotational transitions. The expressions for the linestrengths of the allowed and forbidden transitions are given here in a form suitable to fit the experimental data on the intensities in the vibrational-rotational spectra of C 3 v molecules.

Microwave Transient Phenomena of Symmetric Top Molecules. An Extended Bloch Type Description

Abstract The Bloch equations for the macroscopic polarization components Pr and Pi and the population difference ⊿N of a two-level system are derived with inclusion of diagonal elements of the electric dipole moment operator. The influence of such elements on the solutions is discussed. The effect of Stark-switching technique on the observed transient emission signal is considered.

The dipole moment expansion for a tetrahedral molecule in the ground vibronic state

The expansion of the electric dipole moment operator in terms of angular momentum operators is examined in detail for a tetrahedral molecule in the ground vibronic state. The components of this centrifugal distortion moment in the molecule fixed frame are formally expanded to arbitrary order, with the expansion coefficients being given in terms of rotation matrices. For terms of rank j less than 15, general expressions are given for the matrix elements in the symmetric top basis of the space-fixed components of the dipole moment. The dependence of these matrix elements on the K-quantum number is shown to factor in such a way that previous first order calculations can be extended to second order by replacing the first order dipole coupling constant μ 2 (2) with a function of J which involves μ 2 (2) and two second order constants, μ 2 (4) and μ 4 (4) . Different functions are required for Q- and R-branch matrix elements and explicit expressions are given for both. The third order terms are examined in detail in the Appendix. A recurrence relation is derived for j < 15 between the tetrahedral harmonics of types A 2 and F 2. The implications of this work for distortion moment spectroscopy in tetrahedral molecules are discussed.

An application of the concepts and methods of linear systems analysis to the scattering of resonance radiation by an atomic vapour

The semi-classical method for calculating the observable properties of light scattered from an optically thin atomic vapour is placed in the context of the well known input-output relations for random signals transmitted through a linear system. The autocorrelation of the scattered field amplitude, the statistic from which the mean intensity spectral density and intensity fluctuations may be deduced, is expressed in terms of the autocorrelation of the incident optical field and the autocorrelation of the scattering system; these latter are quantities that can be readily measured or calculated. An appendix contains a classical and a semi-classical calculation of the scattering system autocorrelation function for a vapour of atoms optically excited from a J=0 level under the conditions of a level crossing experiment. In the course of this calculation the relationship between the matrix element of the electric dipole moment operator and the corresponding classical quantity is carefully examined.

On the quantum theory of dispersion at resonance

The perturbation expansions of the wavefunction, under the action of external monochromatic radiation are obtained, which have no secular or divergent terms, in presence of resonance (without any damping factor). The expectation values of the electric dipole moment operator with respect to these characteristic states are calculated. The dispersion formulae are obtained in the neighbourhood of resonance; they are free from any divergences. The dispersion curves obtained from them have all the basic features of the usual dispersion curves in the neighbourhood of resonance.