Higher-order Relativistic Effects Research Articles

Electron–ion collision and polarization of X-ray fluorescence radiation under hot quantum plasma conditions

In the current article, the spectral properties and electron collision (total and magnetic) excitation cross sections of ions taking placed in quantum plasmas are investigated. These cross sections are further used to study the polarization and angular distribution characteristics of the de-excitation radiation X-ray spectra, which play an important role in basic theoretical research, the diagnosis of the plasma environment, and the design of optical devices. To do so, a distorted wave method within the relativistic Dirac–Coulomb atomic structure scheme is suggested. The effective interaction potential between electrons and particles in hot quantum plasmas in the method is determined using a quantum approach that incorporates the influence of effective plasma screening effects caused by collective plasma oscillations. This potential replaces the traditional Coulomb interaction potential and is used in solving the modified Dirac equation to obtain the bound and continuum electron wave functions. Higher-order relativistic effects, such as the Breit interaction and the dominant quantum electrodynamics corrections, are added to enhance the accuracy of the method. Detailed calculations for the relativistic atomic structure and collision excitation dynamics process are carried out, taking the highly stripped H-like O7+ ion of astrophysical importance as an illustrative example. Detailed investigations are also conducted on the variation of energies, collision cross sections, and fluorescence polarizations as functions of the plasma parameters. Our results suggest that the joint effects of shielding and plasma coupling lead the energies, cross sections and fluorescence polarizations decrease (compared with the isolated case). The angular distribution of the X-ray fluorescence emission shows large change, suggesting their sensitivity to these effects. This study not only offers a valuable approach to investigating the plasma shielding and plasmon coupling effects in quantum plasmas but also holds significant relevance for applications in controlled nuclear fusion, astrophysical plasmas and so on.

Highly charged ion (HCI) clocks: Frontier candidates for testing variation of fine-structure constant

Attempts are made to unify gravity with the other three fundamental forces of nature. As suggested by higher dimensional models, this unification may require space and time variation of some of the dimensionless fundamental constants. In this scenario, probing temporal variation of the electromagnetic fine structure constant (α=e2ℏc) in a low energy regime at the cosmological time scale is of immense interest. Atomic clocks are ideal candidates for probing α variation because their transition frequencies are measured with ultra-high precision. Since atomic transition frequency is a function of α, measurement of a clock frequency at different temporal and spatial locations can yield signatures to ascertain variation of α. Highly charged ions (HCIs) are very sensitive to variation of α and are least affected by external perturbations, making them excellent platforms for searching for temporal variation of α. In this work, we overview HCIs suitable for building atomic clocks because of their spectroscopic features and sensitivity to variation of α. The selection of HCI clock candidates is outlined based on two general rules—by analyzing trends in fine structure splitting and level-crossing patterns along a series of isoelectronic atomic systems of the periodic table. Two variants of relativistic many-body methods in the configuration interaction and coupled-cluster theory frameworks are employed to determine the properties of HCIs proposed for atomic clocks. These methods treat electronic correlation and relativistic effects under the frame of the Dirac-Coulomb Hamiltonian rigorously, while other higher-order relativistic effects are included approximately. Typical systematic effects of the HCI clock frequency measurements are discussed using the calculated atomic properties. This review will help understand limits and potentials of the proposed HCIs as the prospective atomic clock candidates and guide future HCI clock experiments.

Enhanced Doppler Beaming for Dust-enshrouded Objects and Pulsars in the Galactic Center

Abstract Stars within the innermost part of the nuclear star cluster can reach orbital velocities up to a few percent of the light speed. As analyzed by Rafikov, Doppler boosting of stellar light may be of relevance at the pericenter of stellar orbits, especially with the upcoming high-precision photometry in the near- and mid-infrared bands. Here we analyze the previously neglected effect of the infrared spectral index of monitored objects on the Doppler-boosted continuum emission in a narrow photometric band. In contrast to main-sequence stars, the detected compact infrared-excess dust-enshrouded objects have an enhanced Doppler-boosting effect by as much as an order of magnitude, with the variability amplitude of the order of 10% for the most eccentric orbits. In a similar way, pulsars dominated by nonthermal synchrotron emission are also expected to exhibit a stronger Doppler-boosted signal by a factor of at least 4 in comparison with canonical S stars. In case the stellar orbit is robustly determined, the relative flux variation can thus provide hints about the nature of the objects. For extended dust-enshrouded objects, such as G1, that are variable due to tidal, ellipsoidal, bow-shock, and irradiation effects, the subtraction of the expected Doppler-boosting variations will help to better comprehend their internal physics. In addition, the relative flux variability due to higher-order relativistic effects is also modified for different negative spectral indices in a way that it can obtain both positive and negative values with the relative variability of the order of 1%.

Extended gravitoelectromagnetism. I. Variational formulation

This work presents a novel approach to well established concepts of gravity, formulating a new and consistent gravitoelectromagnetic theory. The long standing gravitoelectromagnetic field theory is considered in the framework of Hamilton’s principle. A variational formulation based on this principle describes the dynamics of a fully-relativistic perfect fluid in the presence of the gravitoelectromagnetic field in flat space, leading to the definition of the fluid and field energy-momentum tensors. A relativistic Cauchy invariant for a compressible fluid immersed in the gravitoelectromagnetic field is demonstrated. The gravitoelectromagnetic fluid equations of motion are written in covariant form suited for calculating higher-order relativistic effects. The integral form of the conservation theorems is presented, as well as equations that describe the excitation of gravitoelectromagnetic waves. As an application, the equations of motion are used to derive the equation that governs the galactic rotation according to gravitoelectromagnetism.

Accurate determination of energy levels, hyperfine structure constants, lifetimes and dipole polarizabilities of triply ionized tin isotopes

We have investigated the energies, magnetic dipole hyperfine structure constants (Ahyf) and electric dipole (E1) matrix elements of a number of low-lying states of triply ionized tin (Sn3+) by employing relativistic coupled-cluster theory. Contributions from the Breit interaction and lower-order quantum electrodynamic (QED) effects in the determination of the above quantities are also given explicitly. These higher-order relativistic effects are found to be important for the accurate evaluation of energies, while only QED contributions are seen to contribute significantly to the determination of Ahyf values. Our theoretical results for the energies are in agreement with one of the measurements but show significant differences for some states with another measurement. Reported Ahyf will be useful in guiding the measurements of hyperfine levels in the stable isotopes of Sn3+. The calculated E1 matrix elements are further used to estimate the oscillator strengths, transition probabilities and dipole polarizabilities (α) of many states. Large discrepancies between the present results and previous calculations of oscillator strengths and transition probabilities are observed among a number of states. The estimated α values will be useful for carrying out high precision measurements using the Sn3+ ion in future experiments.

Development of spin-orbit coupling for stochastic configuration interaction techniques.

To perform spin-orbit coupling calculations on atoms and molecules, good zeroth-order wavefunctions are necessary. Here, we present the software development of the Monte Carlo Configuration Interaction (MCCI) method, to enable calculation of such properties, where MCCI iteratively constructs a multireference wavefunction using a stochastic procedure. In this initial work, we aim to establish the efficacy of this technique in predicting the splitting of otherwise degenerate energy levels on a range of atoms and small diatomic molecules. It is hoped that this work will subsequently act as a gateway toward using this method to investigate singlet-triplet interactions in larger multireference molecules. We show that MCCI can generate very good results using highly compact wavefunctions compared to other techniques, with no prior knowledge of important orbitals. Higher-order relativistic effects are neglected and spin-orbit coupling effects are incorporated using first-order degenerate perturbation theory with the Breit-Pauli Hamiltonian and effective nuclear charges in the one-electron operator. Results are obtained and presented for B, C, O, F, Si, S, and Cl atoms and OH, CN, NO, and C2 diatomic radicals including spin-orbit coupling constants and the relative splitting of the lowest energy degenerate state for each species. Convergence of MCCI to the full configuration interaction result is demonstrated on the multireference problem of stretched OH. We also present results from the singlet-triplet interaction between the X3Σg- and both the a1Δg and b1Σg+ states of the O2 molecule. © 2017 Wiley Periodicals, Inc.

Persistent discrepancy between experimental and theoretical lifetimes forNi−

Recently the lifetime of the excited 3d94s22D3/2 in Ni- was measured to be 15.1±0.4 s [Phys. Rev. A 93, 012512 (2016)2469-992610.1103/PhysRevA.93.012512]. This deviates from results from nonrelativistic, within the LS-approximation, calculations for this forbidden magnetic-dipole transition of 18.88 s [J. Phys. B 50, 025001 (2017)JPAPEH0953-407510.1088/1361-6455/50/2/025001]. We here present elaborate and fully relativistic multiconfiguration Dirac-Hartree-Fock calculations, to explore this difference. Our calculated transition energy 1485.65cm-1 is in excellent agreement with the experimental 1485±3cm-1 [Phys. Rev. A 58, 2051 (1998)PLRAAN1050-294710.1103/PhysRevA.58.2051]. However the lifetime of 18.86 s, while agreeing well with the nonrelativistic analytical value, deviates from experiment by 25%. The uncertainties of our calculated wavelength and lifetime are estimated to be better than 0.1% and 1%, respectively. In spite of including a careful investigation of contributions from correlation as well as higher-order relativistic effects, we cannot find any explanation from the structure theory for this deviation. (Less)

Four-Component Relativistic Density Functional Theory Calculations of EPR g- and Hyperfine-Coupling Tensors Using Hybrid Functionals: Validation on Transition-Metal Complexes with Large Tensor Anisotropies and Higher-Order Spin-Orbit Effects.

The four-component matrix Dirac-Kohn-Sham (mDKS) implementation of EPR g- and hyperfine A-tensor calculations within a restricted kinetic balance framework in the ReSpect code has been extended to hybrid functionals. The methodology is validated for an extended set of small 4d(1) and 5d(1) [MEXn](q) systems, and for a series of larger Ir(II) and Pt(III) d(7) complexes (S = 1/2) with particularly large g-tensor anisotropies. Different density functionals (PBE, BP86, B3LYP-xHF, PBE0-xHF) with variable exact-exchange admixture x (ranging from 0% to 50%) have been evaluated, and the influence of structure and basis set has been examined. Notably, hybrid functionals with an exact-exchange admixture of about 40% provide the best agreement with experiment and clearly outperform the generalized-gradient approximation (GGA) functionals, in particular for the hyperfine couplings. Comparison with computations at the one-component second-order perturbational level within the Douglas-Kroll-Hess framework (1c-DKH), and a scaling of the speed of light at the four-component mDKS level, provide insight into the importance of higher-order relativistic effects for both properties. In the more extreme cases of some iridium(II) and platinum(III) complexes, the widely used leading-order perturbational treatment of SO effects in EPR calculations fails to reproduce not only the magnitude but also the sign of certain g-shift components (with the contribution of higher-order SO effects amounting to several hundreds of ppt in 5d complexes). The four-component hybrid mDKS calculations perform very well, giving overall good agreement with the experimental data.

More about excited bottomonium radiative decays

Radiative decays of bottomonium are revisited, focusing on contributions from higher-order relativistic effects. The leading relativistic correction to the magnetic spin-flip operator at the photon vertex is found to be particularly important. The combination of O(v^6) effects in the nonrelativistic QCD action and in the transition operator moves previous lattice results for excited Upsilon decays into agreement with experiment.

Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description

The gravitational-wave signal from inspiralling neutron-star--neutron-star (or black-hole--neutron-star) binaries will be influenced by tidal coupling in the system. An important science goal in the gravitational-wave detection of these systems is to obtain information about the equation of state of neutron star matter via the measurement of the tidal polarizability parameters of neutron stars. To extract this piece of information will require to have accurate analytical descriptions of both the motion and the radiation of tidally interacting binaries. We improve the analytical description of the late inspiral dynamics by computing the next-to-next-to-leading order relativistic correction to the tidal interaction energy. Our calculation is based on an effective-action approach to tidal interactions, and on its transcription within the effective-one-body formalism. We find that second-order relativistic effects (quadratic in the relativistic gravitational potential $u=G(m_1 +m_2)/(c^2 r)$) significantly increase the effective tidal polarizability of neutron stars by a distance-dependent amplification factor of the form $1 + \alpha_1 \, u + \alpha_2 \, u^2 +...$ where, say for an equal-mass binary, $\alpha_1=5/4=1.25$ (as previously known) and $\alpha_2=85/14\simeq6.07143$ (as determined here for the first time). We argue that higher-order relativistic effects will lead to further amplification, and we suggest a Pad\'e-type way of resumming them. We recommend to test our results by comparing resolution-extrapolated numerical simulations of inspiralling-binary neutron stars to their effective one body description.

On time transfer in X-ray pulsar navigation

X-ray pulsar navigation (XPNAV) is a new approach for spacecraft autonomous navigation. The system gets position information utilizing accurate timing methods. Among the timing models, the high-order relativistic effects on the propagated signal must be incorporated to attain precise timing. The time transfer model is provided in detail here in two parts: the time frame transformation and the relativistic effects.

COMMISSION 52: RELATIVITY IN FUNDAMENTAL ASTRONOMY

The tremendous progress in technology which we have witnessed during the last 30 years has led to enormous improvements of observational accuracy in all disciplines of fundamental astronomy. Relativity has been becoming increasingly important for modeling and interpretation of high accuracy astronomical observations during at least these 30 years. It is clear that for current accuracy requirements astronomical problems have to be formulated within the framework of General Relativity Theory. Many high-precision astronomical techniques have already required the application of relativistic effects, which are several orders of magnitude larger than the technical accuracy of observations. In order to interpret the results of such observations, one has to construct involved relativistic models. Many current and planned observational projects can not achieve their goals if relativity is not taken into account properly. The future projects will require the introduction of higher-order relativistic effects. To make the relativistic models consistent with each other for different observational techniques, to formulate them in the simplest possible way for a given accuracy, and to formulate them in a language understandable for astronomers and engineers who have little knowledge of relativity are the challenges of a multidisciplinary research field called Applied Relativity.

Small amplitude solitons in a warm plasma with smaller and higher order relativistic effects

Solitons have been investigated in a warm plasma through the Korteweg-de Vries (KdV) equation, considering a smaller relativistic effect for γ≈O(v2∕c2) and γe≈O(u2∕c2) and higher relativistic effects for γ≈O(v4∕c4) and γe≈O(u4∕c4). Compressive fast ion-acoustic solitons are observed to exist in the entire range (u0−v0) subject to a suitable mathematical condition satisfied by the initial streaming velocities u0,v0 of the electrons and the ions, respectively, electron to ion mass ratio Q(=me∕mi) and ion to electron temperature ratio σ(=Ti∕Te). Further, rarefactive solitons of pretty small amplitudes are observed in the small upper range of ∣u0−v0∣ for higher order relativistic effect which are found to change parabolically. It is essentially important to report in our model of plasma, that the higher order relativistic effect slows down the soliton speed to V⩽0.10 for all temperature ratios σ for small amplitude waves. On the other hand, the smaller order relativistic effect permits the soliton to exist even at a relatively much higher speed V<0.30. Solitons of high (negligible) amplitudes are found to generate at the smaller (greater) difference of initial streamings (u0−v0) corresponding to both the relativistic effects.

Comparison of ponderomotive self-channeling and higher-order relativistic effects on intense laser beams propagating in plasma channels

Nonlinear focusing of an intense laser beam propagating in a plasma channel is studied by means of the variational method including the effects of relativistic self-focusing (RSF), ponderomotive self-channeling (PSC), and higher-order relativistic nonlinearity (HRN). The effect of HRN defocuses the beam and has the same order of magnitude in the spot size evolution equation as that of PSC. The beam focusing singularity for laser power exceeding the critical power for RSF is prevented in the presence of HRN. And expression for the matched power is calculated.

Strengths and weaknesses of relativistic atomic structure calculations

Among the relativistic atomic structure theories developed in the last two decades, two methods - multiconfiguration Dirac-Fock (MCDF) and relativistic many-body perturbation theory (RMBPT) - have extensively been applied to calculate spectroscopic properties of neutral atoms as well as highly charged ions. The strengths and weaknesses of these methods are discussed with some examples. The MCDF method is based on the shell structure familiar to atomic physicists, and hence intuitively easier to understand. On the other hand, the RMBPT method is more systematic in introducing correlation and relativistic corrections and logically simpler to include quantum electrodynamic (QED) corrections and higher order relativistic effects than the MCDF method. A recent development in extensive relativistic configuration interaction is also described.

Correlation, relativistic and radiative effects for the energy levels of 1s22s22p5nl, 1s22s2p5nl (n = 3–6, l = s, p, d, f) configurations of Ne-Like ions with Z = 20–60

Calculations of energy levels of 1s22s22p5nl, 1s22s2p6nl (n = 3–6, l = s, p, d, f) configurations of Ne-like ions with Z = 20-60 have been carried out with use of an MZ program. The energy matrix in this method (1/Z method or Z–expansion) is represented in the form of a Z-expansion, where Z is the nuclear charge. Relativistic effects are taken into account in the framework of the Breit operator. The contributions of radiative and high order relativistic effects are also considered. The results of the calculations are compared with theoretical and experimental data.

Energy and fine structure of 1s2np states (n = 2, 3, 4 and 5) for the lithium isoelectronic sequence

The non-relativistic energies of 1s2np (n = 2, 3, 4 and 5) states for the lithium isoelectronic sequence from Li I to Ne VIII are calculated using the full-core plus correlation method. Relativistic and mass polarization effects on the energy are evaluated using first order perturbation theory. The fine structures are determined from the expectation values of the spin-orbit and spin-other-orbit interaction operators in the Pauli-Breit approximation. The higher order relativistic effects are estimated using the hydrogenic solution to the Dirac equation with an effective nuclear charge. The QED correction is also included. Our results are compared with the experimental and theoretical data in the literature. The fine structure results agree well with experiment. For 1s2np energies with n ⩾ 3, it appears that our results are quite accurate for all Z investigated. However, for the 1s22p systems, the discrepancy with experiment grows monotonically from 0.5 cm−1 for Li I to 29 cm−1 for Ne VIII. This is very different from all the other 1s2nl systems we have investigated using the same method. What separates 1s22p apart from the others is the unusually large orbit-orbit interaction and mass polarization effects. For Z > 6, the expectation values of these perturbation operators are opposite in sign to those of the 1s2 core. This energy increases quickly with Z.

The high order relativistic effects in millisecond pulsar timing

In this paper the second order relativistic effects of the Sun and the Earth in the deriving of the precise equation of transformation between proper atomic time on Earth and the PPN time in the solar system are considered. The time arrival formula is obtained from the null geodesic equation and various relativistic effects are estimated. Our results improve Hellings' to 10 −14 s. The high accuracy is necessary in the deriving of the period derivative of millisecond pulsars and in the study of their stability.

Inclusion of Relativistic Effects in Electronic Structure Calculations

The effects of relativity on atomic and molecular structure are discussed with an indication of their importance as a function of atomic number. Perturbation methods for the inclusion of relativistic effects are briefly analysed in terms of the Dirac equation; the multi-configuration Dirac-Fock method for the variational treatment of relativistic effects is then discussed in more detail. Finally, a case study on 2p ionisation in Ca is presented, in which higher-order relativistic effects are important.

Fine-structure splittings in the boron and fluorine isoelectronic sequences: comparison of perturbative (Breit-Pauli) and non-perturbative (MCDF-EAL) predictions

Numerical comparisons of Breit-Pauli and MCDF-EAL estimates of fine-structure splittings are presented for the boron and fluorine isoelectronic sequences up to Z=26. With simple modifications a single basis set is found to be very satisfactory over the entire range. The authors stress the importance of anomalous magnetic moment corrections and examine higher-order relativistic effects neglected in the perturbative approach. A discrepancy between Breit-Pauli and MCDF-EAL estimates in the fluorine sequence is explained in terms of the inclusion of exchange core polarisation but not electron correlation. The authors present evidence that these effects cancel to a large degree, at least for this system. Direct comparison is made with experiment for F to Fe17+.