Relativistic Shift Research Articles

Relativistic corrections for screening effects on the energies of hydrogen-like atoms embedded in plasmas

The influence of relativistic and plasma screening effects on energies of hydrogen-like atoms embedded in plasmas has been studied. The Dirac equation with a more general exponential cosine screened potential has been solved numerically and perturbatively, by employing the direct perturbation theory. Properties of spectra corresponding to bound states and to different sets of the potential parameters have been studied both in nonrelativistic and relativistic approximations. Binding energies, fine-structure splittings, and relativistic energy shifts have been determined as functions of parameters of the potential. The results have been compared with the ones known from the literature.

Spin-asymmetric laser-driven relativistic tunneling frompstates

The tunneling ionization of an electron from a p-state in a highly charged ion in the relativistic regime is investigated in a linearly polarized strong laser field. In contrast to the case of an s-state, the tunneling ionization from the p-state is spin asymmetric. We have singled out two reasons for the spin asymmetry: first, the difference of the electron energy Zeeman splitting in the bound state and during tunneling, and second, the relativistic momentum shift along the laser propagation direction during the under-the barrier motion. Due to the latter, those states are predominantly ionized where the electron rotation is opposite to the electron relativistic shift during the under-the-barrier motion. We have investigated the dependence of the ionization rate on the laser intensity for different projections of the total angular momentum and identified the intensity parameter which governs this behaviour. The significant change of the ionization rate is originated from the different precession dynamics of the total angular momentum in the bound state at high and low intensities.

Is Emotion Perception Relative? Evaluating Sleep Effects on Relativity of Emotion Perception

The present study examines whether valence strength causes relativistic shifts in emotion perception form faces across sleep (filled vs deprived) nights. A group of twelve volunteers participated twice (sleep/no-sleep) with fourteen days gap between participation. Subjects evaluated low valenced facial expressions (targets) in the presence on high valence facial expressions (anchors) before sleep/no sleep nights and again the following morning. Analysis of results using 2 × 2 × 2 (groups, anchor, sessions) split plot analysis of variance suggest that larger relativistic shifts were apparent in the no-sleep group. Also post sleep relativistic shifts in emotion perception were the least (p < 0.001). Sleep consolidates emotional memory for faces.

The conceptual design of an electron cyclotron emission imaging system for studying ITER-like high temperature plasmas

The design of an electron cyclotron emission imaging (ECEI) system for two-dimensional (2D) observation of the magnetohydrodynamical modes in high temperature ITER (from ‘International Thermonuclear Experimental Reactor’) H-mode-like plasmas (5.3 T and 25 keV) based on fundamental ordinary mode (O1-mode) and second-harmonic extraordinary mode (X2-mode) measurements is explored conceptually. For studying the spatial resolution in high temperature plasmas, the relativistic broadening and inward shift of the emission layer in the mid-plane are calculated. The radial spatial resolution is significantly degraded in the range R < 5.1 m for the O1-mode and in the range R < 6.9 m for the X2-mode. The region with R < 6.5 m is inaccessible for X2-mode study. The emission layer width is enlarged in a narrow region of the pedestal due to the magnetic field being modified by the large pressure gradient. The broadening and shift in the poloidal plane are also calculated, to investigate their effects on 2D measurements. The frequency range of electron cyclotron emission measurements is selected to protect the system from stray radiations of the 170 GHz electron cyclotron resonance heating source and to avoid harmonic overlap. The frequency ranges of 115–160 GHz for the O1-mode and 230–320 GHz for the X2-mode provide radial coverage of 5.9 < R < 8.2 m or −0.15 < r/a < 1.The ECEI system utilizes a dual-array detection technique which provides a simultaneous measurement at two radial positions, and each array has 8 by 16 (radial by vertical) channels. The radial image size with 8 channels is ∼41–76 cm for the O1-mode and ∼19–36 cm for the X2-mode, with sufficient resolution. The front-end optics, which focuses the electron cyclotron emission to the low loss corrugated transmission waveguides, is designed with two flat mirrors and two focusing mini-lens arrays. The vertical image size with 16 channels is ∼150 cm and the spot size of each channel is 8–15 cm in the plasma region, taking into account the sensitivity pattern of the waveguide. The refraction effect due to inhomogeneous plasma enlarges the vertical image size up to 20% and 5% for the O1-mode and X2-mode cases, respectively. The horizontal distortion due to the relativistic inwards shift is reduced by the increased toroidal field in the core region.

Validity of the relativistic phase shift model for the extrinsic spin Hall effect in dilute metal alloys

Recently, a generalized relativistic phase shift model was proposed (Fedorovet al 2013 Phys. Rev. B 88 085116) for the description of the skew-scattering contribution to the spin Hall effect caused by impurities. Here, we inspect this model by means of a systematic comparison with the results of first-principles calculations performed for several metallic host systems with different substitutional impurities. It is found that for its proper application, the differences between impurity and host phase shifts should be used as input parameters. Generally, the model provides good qualitative agreement with ab initio results for hosts with a free-electron-like Fermi surface and a relatively weak spin–orbit coupling, but fails otherwise.

An Investigation on the Fine Structure Levels in the Ground State Configuration for the Antimony Anion

We have investigated the correlation, relativistic, and isotope shift effects on the fine structure levels in the ground state configuration for the antimony anion ( Sb-). Energies and radiative transition probabilities (for magnetic dipole, M1, and electric quadrupole, E2) have been obtained using the multiconfiguration Hartree-Fock method within the framework of the Breit-Pauli Hamiltonian. Therefore, the most important configuration interaction and relativistic effects have been included. Comparisons with other available works are presented. For some M1 and E2 lines the considered transition probabilities are reported for the first time

Rashba splitting and relativistic energy shifts in In/Si(111) nanowires

A numerically efficient methodology that allows for relativistic calculations including spin-orbit coupling for spatially anisotropic potentials is employed to study the energetics and electronic properties of In/Si(111)($4\ifmmode\times\else\texttimes\fi{}1$)/($8\ifmmode\times\else\texttimes\fi{}2$) nanowires within density-functional theory. For the subtle total energy balance between the metallic In zigzag chain structure observed at room temperature and the insulating In hexagons that form below the critical temperature, scalar-relativistic corrections to the kinetic energy are clearly far more important than the spin-orbit coupling. On the other hand, a relativistic treatment including spin-orbit coupling is required to describe correctly the electronic band structure that shows a large, strongly anisotropic $k$-point-dependent spin splitting of the In-related states at the $X$ point of the surface Brillouin zone. Suitably combined with the metal-insulator transition, the resulting quasi-1D Rashba effect may be used for spin filtering.

The α-dependence of transition frequencies

Using multiconfiguration Dirac-Hartree-Fock (MCDHF) method we calculated the dependence of the transition frequencies on fine-structure constant α. The energies and relativistic energy shifts are compared with results from Dzuba et al [1], Berengut et al [2] and King et al [3].

Two-Body Orbit Expansion Due to Time-Dependent Relative Acceleration Rate of the Cosmological Scale Factor

By phenomenologically assuming a slow temporal variation of the percent acceleration rate S̈S -1 of the cosmic scale factor S(t), it is shown that the orbit of a local binary undergoes a secular expansion. To first order in the power expansion of S̈S -1 around the present epoch t0, a non-vanishing shift per orbit (Δr) of the two-body relative distance r occurs for eccentric trajectories. A general relativistic expression, which turns out to be cubic in the Hubble parameter H0 at the present epoch, is explicitly calculated for it in the case of matter-dominated epochs with Dark Energy. For a highly eccentric Oort comet orbit with period Pb ≈ 31 Myr, the general relativistic distance shift per orbit turns out to be of the order of (Δr) ≈ 70 km. For the Large Magellanic Cloud, assumed on a bound elliptic orbit around the Milky Way, the shift per orbit is of the order of (Δr) ≈ 2–4 pc. Our result has a general validity since it holds in any cosmological model admitting the Hubble law and a slowly varying S̈S-1(t). More generally, it is valid for an arbitrary Hooke-like extra-acceleration whose “elastic” parameter κ is slowly time-dependent, irrespectively of the physical mechanism which may lead to it. The coefficient κ1 of the first-order term of the power expansion of κ(t) can be preliminarily constrained in a model-independent way down to a κ1 ≲ 2 x 10-13 year-3 level from latest Solar System’s planetary observations. The radial velocities of the double lined spectroscopic binary ALPHA Cen AB yield κ1 ≲ 10-8 year-3.

Four‐component relativistic chemical shift calculations of halogenated organic compounds

The calculation of nuclear magnetic resonance (NMR) properties of organic compounds with heavy elements has been a computational challenge due to the importance of relativistic effects and the cost of relativistic calculations capable of capturing these effects. The heavy‐atom effect on the chemical shift of light atoms also challenges the interpretation of NMR spectra of organic compounds, since relativistic effects can affect the predicted values of protons bonded to heavy atoms by as much as 20 ppm. Here, we investigate the chemical shifts of six organic compounds with/without halogen atoms using non‐relativistic and state‐of‐the‐art four‐component relativistic methods, comparing the results to available experimental data. Our study confirms the importance of relativistic effects in modeling NMR properties of organic compounds involving heavy atoms and shows that these effects cannot be properly described by non‐relativistic methods. We also demonstrate that relativistic four‐component calculations of NMR chemical shifts now have reached a level of maturity that allows these methods to be used routinely in theoretical studies of NMR properties of large organic compounds containing heavy elements. The accuracy of these calculations is high enough to allow them to be used in assisting in the structural characterization of natural compounds. Comparison of the GGA functionals used in the four‐component relativistic density functional theory calculations shows that the PBE functional seems to be well suited for such studies. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Accurate bond dissociation energy of water determined by triple-resonance vibrational spectroscopy and ab initio calculations

Triple-resonance vibrational spectroscopy is used to determine the lowest dissociation energy, D0, for the water isotopologue HD16O as 41239.7±0.2cm−1 and to improve D0 for H216O to 41145.92±0.12cm−1. Ab initio calculations including systematic basis set and electron correlation convergence studies, relativistic and Lamb shift effects as well as corrections beyond the Born–Oppenheimer approximation, agree with the measured values to 1 and 2cm−1 respectively. The improved treatment of high-order correlation terms is key to this high theoretical accuracy. Predicted values for D0 for the other five major water isotopologues are expected to be correct within 1cm−1.

Ris3: A program for relativistic isotope shift calculations

An atomic spectral line is characteristic of the element producing the spectrum. The line also depends on the isotope. The program ris3 (Relativistic Isotope Shift) calculates the electron density at the origin and the normal and specific mass shift parameters. Combining these electronic quantities with available nuclear data, isotope-dependent energy level shifts are determined. Program summaryProgram title:ris3Catalogue identifier: ADEK_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEK_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5147No. of bytes in distributed program, including test data, etc.: 32869Distribution format: tar.gzProgramming language: Fortran 77.Computer: HP ProLiant BL465c G7 CTO.Operating system: Centos 5.5, which is a Linux distribution compatible with Red Hat Enterprise Advanced Server.Classification: 2.1.Catalogue identifier of previous version: ADEK_v1_0Journal reference of previous version: Comput. Phys. Comm. 100 (1997) 81Subprograms used:Cat IdTitleReferenceADZL_v1_1grasp2K VERSION 1_1to be publishedDoes the new version supersede the previous version?: YesNature of problem:Prediction of level and transition isotope shifts in atoms using four-component relativistic wave functions.Solution method:The nuclear motion and volume effects are treated in first order perturbation theory. Taking the zero-order wave function in terms of a configuration state expansion |ΨPJMJ〉=∑μcμ|Φ(γμPJMj)〉, where P, J and MJ are, respectively, the parity and angular quantum numbers, the electron density at the nucleus and the normal and specific mass shift parameters may generally be expressed as ∑μ,νcμcν〈γμPJMj|V|γνPJMj〉 where V is the relevant operator. The matrix elements, in turn, can be expressed as sums over radial integrals multiplied by angular coefficients. All the angular coefficients are calculated using routines from the grasp2K version 1_1 package [1].Reasons for new version:This new version takes the nuclear recoil corrections into account within the (αZ)4m2/M approximation [2] and also allows storage of the angular coefficients for a series of calculations within a given isoelectronic sequence. Furthermore, the program JJ2LSJ, a module of the grasp2K version 1_1 toolkit that allows a transformation of ASFs from a jj-coupled CSF basis into an LSJ-coupled CSF basis, has been especially adapted to present ris3 results using LSJ labels of the states. This additional tool is called RIS3_LSJ.Summary of revisions:This version is compatible with the new angular approach of the grasp2K version 1_1 package [1] and can store necessary angular coefficients. According to the formalism of the relativistic nuclear recoil, the “uncorrected” expression of the normal mass shift has been fundamentally modified compared with its expression in [3].Restrictions:The complexity of the cases that can be handled is entirely determined by the grasp2K package [1] used for the generation of the electronic wave functions.Unusual features:Angular data is stored on disk and can be reused. LSJ labels are used for the states.Running time:As an example, we evaluated the isotope shift parameters and the electron density at the origin using the wave functions of Be-like system. We used the MCDHF wave function built on a complete active space (CAS) with n=8 (296 626 CSFs-62 orbitals) that contains 3 non-interacting blocks of given parity and J values involving 6 different eigenvalues in total. Calculations take around 10 h on one AMD Opteron 6100 @ 2.3 GHz CPU with 8 cores (64 GB DDR3 RAM 1.333 GHz). If angular files are available the time is reduced to 20 min. The storage of the angular data takes 139 MB and 7.2 GB for the one-body and the two-body elements, respectively.

Relativistic Corrections for Calculating Ionization Energies of One- to Five-Electron Isoelectronic Atomic Ions

We have previously proposed a simple empirical equation to reproduce the literature values of the ionization energies of one-electron to four-electron atomic ions with very good agreement. However, we used a potential energy approach in our equation, which has no theoretical basis. This paper discusses an alternative kinetic energy expression for one to five electrons with simple corrections for relativistic and Lamb shift effects and for two- to-five electron ions additional effects including electron relaxation and residual interactions. For calculated values of one-electron (hydrogen-like) and two electron (helium like) atomic ions, the difference with the literature values is typically 0.001% or less. Agreement with the literature values for three-, four-, and five-electron ions is 99% or better. First electron affinities calculated by our expression also agree fairly well with generally recommended values. These results show that there is strong evidence that our methodology can be developed to reliably predict, with fairly good accuracy, ionization energies of multielectron atomic ions that have not been measured.

Relativistic terahertz pulse generation by non-linear interaction of a high-power fs laser with underdense plasmas

Generation of a terahertz radiation by the interaction of a highly intense laser (IL ⩾ 1018 W cm−2) and an underdense plasma with relativistic effects has been investigated. The results of two-dimensional particle-in-cell simulations for the relativistic frequency shift of the emitted THz pulse are presented. It was found that the emitted THz frequency is shifted down with the scaling of γ−α, where γ is the Lorentz factor of the driving laser pulse and α is roughly 0.2 and slightly depends on the laser spot size. Furthermore, the monotonic linear dependence of the THz field strength on the incident laser power was observed. Comparison of the non-relativistic and relativistic laser power regime is shown as well.

Project 8: Using Radio-Frequency Techniques to Measure Neutrino Mass

The shape of the beta decay energy distribution is sensitive to the mass of the electron neutrino. Attempts to measure the endpoint shape of tritium decay have so far seen no distortion from the zero-mass form. Here we show that a new type of electron energy spectroscopy could improve future measurements of this spectrum and therefore of the neutrino mass. We propose to detect the coherent cyclotron radiation emitted by an energetic electron in a magnetic field. For mildly relativistic electrons, like those in tritium decay, the relativistic shift of the cyclotron frequency allows us to extract the electron energy from the emitted radiation. As the technique inherently involves the measurement of a frequency in a non-destructive manner, it can, in principle, achieve a high degree of resolution and accuracy.

Relativistic energy shifts of negative-ion bound states: the rational function Thomas–Fermi potential model

The rational function Thomas–Fermi (RTF) potential recently used for describing electron–atom scattering interactions is investigated as to its bound (negative-ion) states. Although the (static) RTF potential may account for some relativistic and many-body corrections, this study focuses on (relativistic) dynamical aspects of the ‘extra’ electron in the negative-ion bound states. Some exotic states near threshold are shown to exist in the Dirac equations but not in the Schrödinger equation that neglects the spin of the ‘extra’ electron. Results are presented for the two large atomic charge numbers Z = 54 and Z = 64.

Relativistic effects in comparisons of time scales by means of transportable quantum clocks time and frequency measurements

Formulas to describe the action of relativistic effects on the timing frequency of a clock are derived. Estimates of the relativistic shifts in frequency that occur as a clock travels by airplane or motor vehicle are given. The influence of gravitational anomalies on the Earth on the precision with which a relativistic correction is determined as a function of the route followed by the clock is estimated. A formula for calculating the correction with the use of GPS–GLONASS is presented.

Relativistic effects in the screened Coulomb potentials

The expansion of wavefunction into Sturmian functions is used to compute nonrelativistic energies for the Yukawa and Hulthén potentials. Using nonrelativistic solutions, the first-order relativistic corrections for bound states with n ⩽ 4 Dirac particles bounded in these potentials are calculated in the framework of direct perturbation theory. The dependence of the relativistic energy shifts and the fine structure splittings on the parameters of the potentials for several states are examined.

On relativistic shifts of negative-ion resonances

Results from a Dirac approach to electron- (neutral) atom resonance calculations are compared with those from nonrelativistic ones. A recently developed amplitude-phase method for the Dirac equations that is valid also in the non-relativistic limit is applied. The main conclusion is that significant energy differences are expected for long-lived resonances.

Isotope shifts and relativistic shifts of Cr ii for the study ofαvariation in quasar absorption spectra

We use the combination of configuration interaction and many-body perturbation theory method (CI+MBPT) to perform ab initio calculations the low-energy spectra of Cr II with high accuracy. It is found that second-order MBPT diagrams should be included in a consistent and complete way for the MBPT to improve the accuracy of calculations in this five-valence-electron system. This contrasts with previous ions with fewer valence electrons where it was found that single-valence-electron diagrams dominate the corrections. Isotope shifts and relativistic shifts (q-values) are calculated for use in astronomical determination of the fine-structure constant in quasar absorption spectra.