Relativistic Many-body Theory Research Articles

Scalar Breit interaction for molecular calculations.

Variational treatment of the Dirac-Coulomb-Gaunt or Dirac-Coulomb-Breit two-electron interaction at the Dirac-Hartree-Fock level is the starting point of high-accuracy four-component calculations of atomic and molecular systems. In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac-Coulomb-Gaunt and Dirac-Coulomb-Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac-Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin-spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Aun (n = 2-8) show that the scalar Dirac-Coulomb-Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac-Coulomb-Breit Hamiltonian. The scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.

Investigating effects of relativistic kinematics, dimensionality, interactions, and short-range correlations on the ratio of quartic over quadratic nuclear symmetry energies

While ample evidence for the so-called empirical parabolic law of the equation of state (EOS) of isospin asymmetric nuclear matter (ANM) has been obtained in many studies within both nonrelativistic and relativistic nuclear many-body theories using various interactions, it has been unclear if there is any fundamental physics reason for the small quartic symmetry energy compared to the quadratic one even as the ANM approaches pure neutron matter. Within both relativistic and nonrelativistic free Fermi gas (FFG) models in coordinate spaces of arbitrary dimension $d$ with and without considering short-range correlations (SRCs) as well as nonlinear relativistic mean field models, we study effects of relativistic kinematics, dimensionality, interactions, and SRC on the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ of quartic over quadratic symmetry energies in ANM EOSs. We found that the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ in the FFG model depends strongly on the dimension $d$. While it is very small already in the normal three-dimensional space, it could be even smaller in spaces with reduced dimensions for subsystems of particles in heavy-ion reactions and/or whole neutron stars due to constraints, collectivities, and/or symmetries. We also found that the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ could theoretically become very large only at the ultrarelativistic limit far above the density reachable in neutron stars. However, nuclear interaction directly and/or indirectly through SRC-induced high-momentum nucleons affects significantly the density dependence of $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ compared to the relativistic FFG model prediction. The SRCs affect significantly not only the kinetic energy of symmetric nuclear matter but also the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ while the relativistic corrections are found negligible. Although we found no fundamental physics reason for the $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ to be very small especially at high densities, the results may help better understand the EOS of dense neutron-rich matter.

P,T -odd interactions in atomic Xe129 and phenomenological applications

We calculate interaction constants for the contributions from $\mathcal{P},\mathcal{T}$-odd scalar-pseudoscalar and tensor-pseudotensor operators to the electric dipole moment of $^{129}\mathrm{Xe}$ using relativistic many-body theory including the effects of dynamical electron correlations. These interaction constants are necessary ingredients to relating the corresponding measurements to fundamental parameters in models of physics beyond the standard model. We obtain ${\ensuremath{\alpha}}_{{C}_{S}}=\left(0.71\ifmmode\pm\else\textpm\fi{}0.18\right)({10}^{\ensuremath{-}23}\phantom{\rule{0.16em}{0ex}}e\phantom{\rule{3.33333pt}{0ex}}\text{cm})$ and ${\ensuremath{\alpha}}_{{C}_{T}}=\left(0.520\ifmmode\pm\else\textpm\fi{}0.049\right)({10}^{\ensuremath{-}20}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\langle}\mathrm{\ensuremath{\Sigma}}\ensuremath{\rangle}}_{\text{Xe}}\phantom{\rule{0.16em}{0ex}}e\phantom{\rule{3.33333pt}{0ex}}\text{cm})$, respectively. We apply our results to test a phenomenological relation between the two quantities, commonly used in the literature, and discuss their present and future phenomenological impact.

A new view on the origin of zero-bias anomalies of Co atoms atop noble metal surfaces

Many-body phenomena are paramount in physics. In condensed matter, their hallmark is considerable on a wide range of material characteristics spanning electronic, magnetic, thermodynamic and transport properties. They potentially imprint non-trivial signatures in spectroscopic measurements, such as those assigned to Kondo, excitonic and polaronic features, whose emergence depends on the involved degrees of freedom. Here, we address systematically zero-bias anomalies detected by scanning tunneling spectroscopy on Co atoms deposited on Cu, Ag and Au(111) substrates, which remarkably are almost identical to those obtained from first-principles. These features originate from gaped spin-excitations induced by a finite magnetic anisotropy energy, in contrast to the usual widespread interpretation relating them to Kondo resonances. Resting on relativistic time-dependent density functional and many-body perturbation theories, we furthermore unveil a new many-body feature, the spinaron, resulting from the interaction of electrons and spin-excitations localizing electronic states in a well defined energy.

Background field method in thermo field dynamics for wave propagation in unmagnetized spinor QED plasmas

In this paper, we propose a relativistic quantum many-body theory for the collective modes in spinor quantum electrodynamic plasma. Different from the usual quantization scheme, we use the self-consistency nontrivial background field method in the framework of thermo field dynamics, in which the resulting quanta are temperature-dependent particles instead of the observable ones such as electrons, positrons, and photons. The theory provides a general scheme for many-body physics, which overcomes the disadvantages of random phase, Hartree–Fock, or other equivalent mean-field approximations. The essential point for our theory is to exactly evaluate the background fields. In this paper, we propose a general and efficient method to determine them, which we name as the “classical limit method” for convenience. To demonstrate how to apply the theory, we discuss the collective modes in unmagnetized electron–positron plasma, in both the low-energy and high-energy limits. It yields the well-known dispersion relations of longitudinal and transverse modes for non-relativistic degenerate plasmas, at zero and nonzero temperature. Furthermore, it gives the additional relativistic and vacuum fluctuation corrections, including increasing mass, decreasing effective charge, finite light velocity influence on the dispersion relation, and virtual charge redistribution. The last effect is reported for the first time.

Tidal deformation of neutron stars from microscopic models of nuclear dynamics

The observation of the gravitational wave signal GW170817, consistent with emission from the inspiral of a binary neutron-star system, provided information on the tidal deformation of the participating stars. The available data may be exploited to constrain the equation of state of densenuclear matter, as well as to shed light on the underlying models describing nuclear dynamics at microscopic level. In this paper we compare the experimental results to the predictions of different theoretical models, based on non relativistic nuclear many-body theory, the relativistic field-theoretical formalism, and a more phenomenological approach constrained by observed nuclear properties. While the precision of the available data does not allow to resolve the degeneracy of the models, our analysis shows a distinct sensitivity to the star compactness predicted by the different equations of state, which turns out to be significantly affected by relativistic boost corrections to the nucleon-nucleon potential.

The Role of Relativistic Many-Body Theory in Electron Electric Dipole Moment Searches Using Cold Molecules

In this review article, we survey some of our results pertaining to the search for the electric dipole moment of the electron (eEDM), using heavy polar molecules. In particular, we focus on the relativistic coupled cluster method (RCCM) and its applications to eEDM searches in YbF, HgX (X = F, Cl, Br, and I), BaF, HgA (A = Li, Na, and K), and YbOH. Our results are presented in a systematic manner, by first introducing the eEDM and its measurement using molecules, the importance of relativistic many-body theory, and finally our results, followed by future prospects.

The role of relativistic many-body theory in probing new physics beyond the standard model via the electric dipole moments of diamagnetic atoms

The observation of electric dipole moments (EDMs) in atomic systems due to parity and time-reversal violating (P,T-odd) interactions can probe new physics beyond the standard model and also provide insights into the matter-antimatter asymmetry in the Universe. The EDMs of open-shell atomic systems are sensitive to the electron EDM and the P,T-odd scalar-pseudoscalar (S-PS) semi-leptonic interaction, but the dominant contributions to the EDMs of diamagnetic atoms come from the hadronic and tensor-pseudotensor (T-PT) semi-leptonic interactions. Several diamagnetic atoms like 129Xe, 171Yb, 199Hg, 223Rn, and 225Ra are candidates for the experimental search for the possible existence of EDMs, and among these 199Hg has yielded the lowest limit till date. The T or CP violating coupling constants of the aforementioned interactions can be extracted by combining the EDM measurements from with atomic and nuclear calculations. In this work, we report the calculations of the EDMs of the above atoms by including both the electromagnetic and P,T-odd violating interactions simultaneously. These calculations are performed by employing relativistic many-body methods based on the random phase approximation (RPA) and the singles and doubles coupled-cluster (CCSD) method starting with the Dirac-Hartree-Fock (DHF) wave function in both cases. The differences in the results from both the methods shed light on the importance of the non-core-polarization electron correlation effects that are accounted for by the CCSD method. We also determine THE electric dipole polarizabilities of these atoms, which have computational similarities with EDMs and compare them with the available experimental and other theoretical results to assess the accuracy of our calculations.

Estimation of the blackbody-radiation shift due to the Stark effect for the microwave Cd+113 ion clock

The microwave clock frequency of the $|5s~^2S_{1/2}, F=0,m_F=0 \rangle \leftrightarrow |5s~^2S_{1/2}, F=1,m_F=0 \rangle$ transition in the $^{113}$Cd$^+$ ion has been reported as 15199862855.0192(10) Hz [Opt. Lett. {\bf 40}, 4249 (2015)]. Fractional systematic due to the black-body radiation (BBR) shift ($\beta$) arising from the Stark effect in the above clock transition was used as $-1.1 \times 10^{-16}$ from our unpublished preliminary estimation. We present here a precise value as $\beta=-1.815(77) \times 10^{-16}$ by carrying out rigorous calculations of third-order polarizabilities of the hyperfine levels associated with the clock transition. This is determined by evaluating matrix elements of the magnetic dipole hyperfine interaction Hamiltonian, electric dipole operator and energies between many low-lying states of $^{113}$Cd$^+$. We employ all-order relativistic many-body theories in the frameworks of Fock-space coupled-cluster and relativistic multi-configuration Dirac-Fock methods.

Relativistic coupled-cluster-theory analysis of unusually large correlation effects in the determination of gj factors in Ca+

We investigate roles of electron correlation effects in the determination of the $g_j$ factors of the $4s ~ ^2S_{1/2}$, $4p ~ ^2P_{1/2}$, $4p ~ ^2P_{3/2}$, $3d ~ ^2D_{3/2}$, and $3d ~ ^2D_{5/2}$ states, representing to different parities and angular momenta, of the Ca$^+$ ion. Correlation contributions are highlighted with respect to the mean-field values evaluated using the Dirac-Hartree-Fock method, relativistic second order many-body theory, and relativistic coupled-cluster (RCC) theory with the singles and doubles approximation considering only the linear terms and also accounting for all the non-linear terms. This shows that it is difficult to achieve reasonably accurate results employing an approximated perturbative approach. We also find that contributions through the non-linear terms and higher-level excitations such as triple excitations, estimated perturbatively in the RCC method, are found to be crucial to attain precise values of the $g_j$ factors in the considered states of Ca$^+$ ion.

Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms: A unique window to hadronic and semi-leptonic CP violation

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 nucleon interacts with other nucleons as well as with electrons. Nuclear structure calculations of the CP-odd nuclear Schiff moment are discussed using the shell model and other theoretical approaches. Results of the calculations of atomic electric dipole moments due to the interaction of the nuclear Schiff moment with the electrons and the P and time-reversal (T) symmetry violating tensor-pseudotensor electron-nucleus are elucidated using different relativistic many-body theories. The principles of the measurement of the electric dipole moments of diamagnetic atoms are outlined. Upper limits for the nuclear Schiff moment and tensor-pseudotensor coupling constant are obtained combining the results of atomic experiments and relativistic many-body theories. The coefficients for the different sources of CP violation have been estimated at the elementary particle level for all the diamagnetic atoms of current experimental interest and their implications for physics beyond the standard model is discussed. Possible improvements of the current results of the measurements as well as quantum chromodynamics, nuclear and atomic calculations are suggested.

Thermal effects in dense matter beyond mean field theory

The formalism of next-to-leading order (NLO) Fermi Liquid Theory (FLT) is employed to calculate the thermal properties of symmetric nuclear and pure neutron matter in a relativistic many-body theory beyond the mean field level which includes two-loop (TL) effects. For all thermal variables, the semi-analytical NLO corrections reproduce results of the exact numerical calculations for entropies per baryon up to 2. This corresponds to excellent agreement down to subnuclear densities for temperatures up to [Formula: see text] MeV. In addition to providing physical insights, a rapid evaluation of the equation of state (EOS) in the homogeneous phase of hot and dense matter is achieved through the use of the zero-temperature Landau effective mass function and its derivatives.

Hyperfine-induced quadrupole moments of alkali-metal-atom ground states and their implications for atomic clocks

Spherically-symmetric ground states of alkali-metal atoms do not posses electric quadrupole moments. However, the hyperfine interaction between nuclear moments and atomic electrons distorts the spherical symmetry of electronic clouds and leads to non-vanishing atomic quadrupole moments. We evaluate these hyperfine-induced quadrupole moments using techniques of relativistic many-body theory and compile results for Li, Na, K, Rb, and Cs atoms. For heavy atoms we find that the hyperfine-induced quadrupole moments are strongly (two orders of magnitude) enhanced by correlation effects. We further apply the results of the calculation to microwave atomic clocks where the coupling of atomic quadrupole moments to gradients of electric fields leads to clock frequency uncertainties. We show that for $^{133}$Cs atomic clocks, the spatial gradients of electric fields must be smaller than $30 \, \mathrm{V}/\mathrm{cm}^2$ to guarantee fractional inaccuracies below $10^{-16}$.

On the theory of electronic states of heavy elements

Versions of the relativistic many-body theory that make it possible to develop the theory of electronic states and spectroscopy of heavy elements have been proposed. Asymptotic estimates of the atomic terms have been made. It has been shown that the physical cause of the formation of the layered structure of electron shells is directly related to the repulsion of electrons in the electron plasma of the atom.

All-order relativistic many-body theory of low-energy electron-atom scattering

A generalization of the box-variational method is developed to describe particle scattering with the Dirac equation. The method is applied to extract phase shifts from all-order single + double relativistic many-body perturbation theory calculations of the electron-helium, electron-neon, and electron-krypton systems. Comparisons with experimental elastic and momentum transfer cross sections are made. Agreement at the 1% to 2% level is achieved for helium and neon. The scattering length for krypton is 4% smaller in magnitude than experimental estimates derived from swarm experiments.

Contribution of the4f-core-excited states in determination of atomic properties in the promethium isoelectronic sequence

The atomic properties of Pm-like ions were comprehensively studied using relativistic atomic codes. Excitation energies of the $4{f}^{14}nl$ (with $nl=5s$, $6s$, $5p$, $6p$, $5d$, $6d$, and $5f$) states in Pm-like ions with nuclear charge $Z$ ranging from 74 to 100 are evaluated within the framework of relativistic many-body theory (RMBPT). First- and second-order Coulomb energies and first- and second-order Breit corrections to the energies are calculated. Two alternative treatments of the Breit interaction are investigated. In the first approach we omit Breit contributions to the Dirac-Fock potential and evaluate Coulomb and Breit-Coulomb corrections through second order perturbatively. In the second approach were included both Coulomb and Breit contributions on the same footing via the Breit-Dirac-Fock potential and then treat the residual Breit and Coulomb interactions perturbatively. The results obtained from the two approaches are compared and discussed. The important question of what is the ground state in Pm-like ions was answered. Properties of the $4f$-core-excited states are evaluated using the multiconfiguration relativistic Hebrew University Lawrence Livermore atomic code (hullac code) and the Hartree-Fock-relativistic method (cowan code). We evaluate excitation energies and transition rates in Pm-like ions with nuclear charge $Z$ ranging from 74 to 92. Our large scale calculations include the following set of configurations: $4{f}^{14}5s$, $4{f}^{14}5p$, $4{f}^{13}5{s}^{2}$, $4{f}^{13}5{p}^{2}$, $4{f}^{13}5s5p$, $4{f}^{12}5{s}^{2}5p$, $4{f}^{12}5s5{p}^{2}$, and $4{f}^{12}5{p}^{3}$. Trends of excitation energies as function of $Z$ are shown graphically for selected states. Excitation energies, transition rates, and lifetimes in Pm-like tungsten are evaluated with additional inclusion of the $4{f}^{11}5{s}^{2}5{p}^{2}$, $4{f}^{11}5s5{p}^{3}$, $4{f}^{10}5{s}^{2}5{p}^{3}$, and $4{f}^{10}5s5{p}^{4}$ configurations. This represents an unusual example of an atomic system where the even-parity complex [$4{f}^{14}5s+4{f}^{13}5s5p+4{f}^{12}5s5{p}^{2}+4{f}^{11}5s5{p}^{3}+4{f}^{10}5s5{p}^{4}$] and the odd-parity complex [$4{f}^{14}5p+4{f}^{13}5{s}^{2}+4{f}^{12}5{s}^{2}5p+4{f}^{11}5{s}^{2}5{p}^{2}+4{f}^{10}5{s}^{2}5{p}^{3}$] include so different configurations. Wavelengths of the $4{f}^{14}5s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}$-$4{f}^{14}5p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{J}$ transition obtained by the cowan, hullac, and RMBPT codes are compared with other theoretical results and available measurements.

Reliability test for the experimental results of electric-quadrupole hyperfine-structure constants and assessment of nuclear quadrupole moments in135Ba and137Ba

We investigate electric quadrupole hyperfine structure constant ($B$) results in $^{135}$Ba$^+$ and $^{137}$Ba$^+$ and compare their ratios with the reported measurements of the ratio between the nuclear quadrupole moment ($Q$) values of these isotopes. We carry out confidence tests for the reported experimental $B$ values and calculations of $B/Q$ from the present work. Inconsistencies in the experimental $B$ values are observed in both the isotopes from different experiments performed using the same techniques. The present calculations are carried out using an all order relativistic many-body theory considering only single and double excitations in the coupled-cluster ansatz. After a detailed analysis of the results, the values of $Q$ we obtain for $^{135}$Ba and $^{137}$Ba are 0.153(2)$b$ and 0.236(3)$b$, respectively, which differ by about 4% from the currently referred precise values.

Relativistic many-body calculation of energies, lifetimes, polarizabilities, and hyperpolarizabilities in Li-like Be+

Excitation energies of the $ns$, $np$, $nd$, and $nf$ ($n\ensuremath{\le}$ 9) states in Li-like Be${}^{+}$ are evaluated within the framework of relativistic many-body theory. First-, second-, third-, and all-order Coulomb energies and first- and second-order Breit corrections to the energies are calculated. Two alternative treatments of the Breit interaction are investigated. In the first approach, we omit Breit contributions to the Dirac-Fock potential and evaluate Coulomb and Breit-Coulomb corrections through second order perturbatively. In the second approach, we include both Coulomb and Breit contributions on the same footing via the Breit-Dirac-Fock potential and then treat the residual Breit and Coulomb interactions perturbatively. The results obtained from the two approaches are compared and discussed. All-order calculations of reduced matrix elements, oscillator strengths, transition rates, and lifetimes are given for levels up to $n$ = 9. Electric-dipole ($2s--np$), electric-quadrupole ($2s--nd$), and electric-octupole ($2s--nf$) matrix elements are evaluated in order to obtain the corresponding ground-state multipole polarizabilities using the sum-over-states approach. Recommended values are provided for a large number of electric-dipole matrix elements. Scalar and tensor polarizabilities for the $ns$, $n{p}_{1/2}$, $n{p}_{3/2}$, $n{d}_{3/2}$, and $n{d}_{5/2}$ states with $n\ensuremath{\le}9$ are also calculated. The scalar hyperpolarizability for the ground $2s$ state is evaluated and compared with the result of a nonrelativistic calculation.

Relativistic many-body theory: A new field-theoretical approach

Relativistic many-body theory: A new field-theoretical approach

Relativistic many-body XMCD theory including core degenerate effects

A many-body relativistic theory to analyze X-ray Magnetic Circular Dichroism (XMCD) spectra has been developed on the basis of relativistic quantum electrodynamic (QED) Keldysh Green's function approach. This theoretical framework enables us to handle relativistic many-body effects in terms of correlated nonrelativistic Green's function and relativistic correction operator Q, which naturally incorporates radiation field screening and other optical field effects in addition to electron-electron interactions. The former can describe the intensity ratio of L2/L3 which deviates from the statistical weight (branching ratio) 1/2.In addition to these effects, we consider the degenerate or nearly degenerate effects of core levels from which photoelectrons are excited. In XPS spectra, for example in Rh 3d sub level excitations, their peak shapes are quite different: This interesting behavior is explained by core-hole moving after the core excitation. We discuss similar problems in X-ray absorption spectra in particular excitation from deep 2p sub levels which are degenerate in each sub levels and nearly degenerate to each other in light elements: The hole left behind is not frozen there. We derive practical multiple scattering formulas which incorporate all those effects.