Related Treatment Research Articles

Relativistic effects on the linear polarization and angular distribution of x-ray radiation emitted by inner-shell photoionization of atoms

We present a theoretical study of relativistic effects on the linear polarization and angular distribution of x-ray radiation for the L () characteristic line following inner-shell single photoionization of Cd, Ba, Yb and Ra atoms. The analysis is performed based on the multi-configuration Dirac–Fock method and the density matrix theory. To explore the nature of these effects, calculations are carried out based on detailed analyses of the total and magnetic sublevel cross sections, the linear polarization, and the angular distribution of the x-ray photoemission, as well as on corresponding data calculated in the nonrelativistic limit. Our results show a significant difference in the above parameters compared to the nonrelativistic treatment, which is mainly due to the relativistic treatment of the target. Higher multipole contributions are also estimated, and found to be generally weaker. The importance of inclusion of the relativistic effects grows with increasing atomic number and the incoming photon energy.

Probing the Spinning of the Massive Black Hole in the Galactic Center via Pulsar Timing: A Full Relativistic Treatment

Abstract Pulsars around the massive black hole (MBH) in the Galactic center (GC) are expected to be revealed by upcoming facilities (e.g., the Square Kilometer Array). Under a full relativistic framework with the pulsar approximated as a test particle, we investigate the constraints on the spinning of the MBH by monitoring the timing of surrounding pulsars. For GC pulsars orbiting closely around the MBH (e.g., ≲1000 au), we find that full relativistic treatment in modeling accurately their timing signals can be necessary, as the relativistic signals are orders of magnitude larger than the time-of-arrival measurement accuracies. Although usually there are near degeneracies among MBH spin parameters, the constraints on the spinning of the MBH are still very tight. By continuously monitoring a normal pulsar in orbits with a period of ∼2.6 yr and an eccentricity of 0.3–0.9 under a timing precision of 1–5 ms, within ∼8 yr the spin magnitude and the orientations of the GC MBH can be constrained with error of and , respectively. Even for pulsars in orbits similar to the detected star S2/S0-2 or S0-102, we find that the spinning of the MBH can still be constrained within 4–8 yr, with the most significant constraints provided near the pericenter passage. If the proper motion of the pulsars with astrometric accuracy of 10 μas can also be collected along with the timing measurement, then the position, velocity, mass, and distance to the solar system of the MBH can be constrained to ∼10 μas, ∼1 μas yr−1, , and ∼1 pc, respectively.

Preface for the special issue, ‘Second quantum revolution: foundational questions’

Recent outstanding theoretical and experimental successes in quantum physics are considered by many to be forging a second quantum revolution . These successes clearly indicate that important quantum technological improvements are on the way. However, many important foundational issues in quantum theory have not yet been clearly resolved, e.g. the quantum measurement problem, the justification of the application of the quantum formalism for macroscopic systems, the possibility of going beyond quantum theory, quantum non-locality, the relativistic treatment of entanglement and an indisputable understanding of the …

CMB anisotropies from patchy reionisation and diffuse Sunyaev-Zel'dovich effects

Anisotropies in the Cosmic Microwave Background (CMB) can be induced during the later stages of cosmic evolution, and in particular during and after the Epoch of Reionisation. Inhomogeneities in the ionised fraction, but also in the baryon density, in the velocity fields and in the gravitational potentials are expected to generate correlated CMB perturbations. We present a complete relativistic treatment of all these effects, up to second order in perturbation theory, that we solve using the numerical Boltzmann code {\\SONG}. The physical origin and relevance of all second order terms are carefully discussed. In addition to collisional and gravitational contributions, we identify the diffuse analogue of the blurring and kinetic Sunyaev-Zel'dovich (SZ) effects. Our approach naturally includes the correlations between the imprint from patchy reionisation and the diffuse SZ effects thereby allowing us to derive reliable estimates of the induced temperature and polarisation CMB angular power spectra. In particular, we show that the B-modes generated at intermediate length-scales (ℓ ≃ 100) have the same amplitude as the B-modes coming from primordial gravitational waves with a tensor-to-scalar ratio r=10−4.

Relativistic Light Sails

One proposed method for spacecraft to reach nearby stars is by accelerating sails using either solar radiation pressure or directed energy. This idea constitutes the thesis behind the Breakthrough Starshot project, which aims to accelerate a gram-mass spacecraft up to one-fifth the speed of light toward Proxima Centauri. For such a case, the combination of the sail's low mass and relativistic velocity renders previous treatments incorrect at the 10% level, including that of Einstein himself in his seminal 1905 paper introducing special relativity. To address this, we present formulae for a sail's acceleration, first in response to a single photon and then extended to an ensemble. We show how the sail's motion in response to an ensemble of incident photons is equivalent to that of a single photon of energy equal to that of the ensemble. We use this principle of ensemble equivalence for both perfect and imperfect mirrors, enabling a simple analytic prediction of the sail's velocity curve. Using our results and adopting putative parameters for Starshot, we estimate that previous relativistic treatments underestimate the spacecraft's terminal velocity by ∼10% for the same incident energy. Additionally, we use a simple model to predict the sail's temperature and diffraction beam losses during the laser firing period; this allows us to estimate that, for firing times of a few minutes and operating temperatures below 300°C (573 K), Starshot will require a sail that absorbs less than one in 260,000 photons.

Dirac–Fock photoionization parameters for HAXPES applications

Presented here are the photoionization cross sections and parameters of the photoelectron angular distribution for atomic subshells with binding energies lower than 1.5 keV of all elements with 1≤Z≤100 in the photon energy range 1.5–10 keV. The calculations were performed in an effort to provide handy theoretical data for experimental studies by hard X-ray photoelectron spectroscopy (HAXPES). We used the relativistic treatment of atomic photoeffect and the Dirac–Fock method with proper consideration of the electron exchange for computing the electron wave functions. The photoionization cross sections were determined including all multipoles of the radiative field while the photoelectron angular distribution parameters were obtained within the quadrupole approximation. The effect of the hole resulting in the atomic subshell after photoionization was taken into account by the use of the frozen orbital model.

Nuclear magnetic shielding in boronlike ions

The relativistic treatment of the nuclear magnetic shielding effect in boronlike ions is presented. The leading-order contribution of the magnetic-dipole hyperfine interaction is calculated. Along with the standard second-order perturbation theory expression, the solutions of the Dirac equation in the presence of magnetic field are employed. All methods are found to be in agreement with each other and with the previous calculations for hydrogenlike and lithiumlike ions. The effective screening potential is used to account approximately for the interelectronic interaction.

General relativistic calculations for white dwarfs

The mass-radius relations for white dwarfs are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff (TOV) equations for hydrostatic equilibrium assuming the electron gas to be non-interacting. We find that the Newtonian limiting mass of is modified to in the general relativistic case for (and ) white dwarfs. Using the same general relativistic treatment, the critical mass for white dwarfs is obtained as . In addition, departure from the ideal degenerate equation of state (EoS) is accounted for by considering Salpeter’s EoS along with the TOV equation, yielding slightly lower values for the critical masses, namely for , for and for white dwarfs. We also compare the critical densities for gravitational instability with the neutronization threshold densities to find that and white dwarfs are stable against neutronization with the critical values of and , respectively. However, the critical masses for , , , , and white dwarfs are lower due to neutronization. Corresponding to their central densities for neutronization thresholds, we obtain their maximum stable masses due to neutronization by solving the TOV equation coupled with the Salpeter EoS.

Relativistic radiative transfer and relativistic spherical flows: Relation between the mass-loss rate and terminal speed

Abstract Radiatively driven relativistic spherical flows are numerically investigated under the fully special relativistic treatment and relativistic radiative transfer. We first solve the relativistic radiative transfer equation for spherically symmetric outflows iteratively, using a trial velocity distribution, and obtain specific intensities as well as moment quantities, and the Eddington factor. Using the obtained comoving flux, we next solve the relativistic equation of motion, and obtain the refined velocity distribution, the mass-loss rate being determined as an eigenvalue. Until both the intensity and velocity distributions converge, we repeat these double iteration processes. We found that the flows are quickly accelerated near to the central lumious core to reach the terminal speed. The Eddington factor has a complicated behavior, depending on the optical depth and flow speed. We further found that a relation between the flow terminal speed βout normalized by the speed of light and the mass-loss rate $\dot{m}$ normalized by the critical one is roughly approximated as $\dot{m} \propto \tau _* \beta _{\rm out}^{-5/2}$, where τ* is a typical optical depth of the flow, whereas we can analytically derive the relation of $\dot{m} \propto \tau _* \beta _{\rm out}^{-2}$ using a back-of-the-envelope calculation in the nonrelativistic case.

Relativistic ionization dynamics for a hydrogen atom exposed to superintense XUV laser pulses

We present a theoretical study of the ionization dynamics of a hydrogen atom exposed to attosecond laser pulses in the extreme ultra violet region at very high intensities. The pulses are such that the electron is expected to reach relativistic velocities, thus necessitating a fully relativistic treatment. We solve the time dependent Dirac equation and compare its predictions with those of the corresponding non-relativistic Schr{\"o}dinger equation. We find that as the electron is expected to reach about 20% of the speed of light, relativistic corrections introduces a finite yet small decrease in the probability of ionizing the atom.

Ringed Accretion Disks: Evolution of Double Toroidal Configurations

Abstract We investigate ringed accretion disks composed of two tori (rings) orbiting on the equatorial plane of a central supermassive Kerr black hole. We discuss the emergence of the instability phases of each ring of the macro-configuration (ringed disk) according to the Paczynski violation of mechanical equilibrium. In the full general relativistic treatment, we consider the effects of the geometry of the Kerr spacetimes relevant to the characterization of the evolution of these configurations. The discussion of ring stability in different spacetimes enables us to identify particular classes of central Kerr attractors depending on their dimensionless spin. As a result of this analysis, we set constraints on the evolutionary schemes of the ringed disks relative to the torus morphology and on their rotation relative to the central black hole and to each other. The dynamics of the unstable phases of this system is significant for the high-energy phenomena related to accretion onto supermassive black holes in active galactic nuclei and the extremely energetic phenomena in quasars, which could be observed in their X-ray emission.

Cosmological evolution of a complex scalar field with repulsive or attractive self-interaction

We study the cosmological evolution of a complex scalar field with a self-interaction potential $V(|\varphi|^2)$, possibly describing self-gravitating Bose-Einstein condensates, using a fully general relativistic treatment. We generalize the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field approximation developed in our previous paper. We establish the general equations governing the evolution of a spatially homogeneous complex scalar field in an expanding background. We show how they can be simplified in the fast oscillation regime and derive the equation of state of the scalar field in parametric form for an arbitrary potential. We explicitly consider the case of a quartic potential with repulsive or attractive self-interaction and determine the phase diagram of the scalar field. We show that the transition between the weakly self-interacting regime and the strongly self-interacting regime depends on how the scattering length of the bosons compares with their effective Schwarzschild radius. We also constrain the parameters of the scalar field from astrophysical and cosmological observations. Numerical applications are made for ultralight bosons without self-interaction (fuzzy dark matter), for bosons with repulsive self-interaction, and for bosons with attractive self-interaction (QCD axions and ultralight axions).

Relativistic Treatment of Massive Klein-Gordon Particle by Modified Generalized Hulthen Potential

Relativistic Treatment of Massive Klein-Gordon Particle by Modified Generalized Hulthen Potential

Effect of asymmetric spin–orbit coupling on the electronic structure properties of noncentrosymmetric superconductor

We report a theoretical investigation of the electronic structure properties of weakly correlated electronic noncentrosymmetric superconductor ( K). The first-principle calculations have been performed using the full potential linearised-muffin-thin-orbital method and including both scalar relativistic and fully relativistic (FR) treatments. We detect distinct differences between the data obtained from the two applied approaches. In particular, the bands along the , and separate and Fermi surfaces become highly anisotropic in FR calculations. The observed differences are ascribed to a strong effect of the asymmetric spin–orbit coupling with a splitting energy of order of –100 meV. Furthermore, we unveil that the valence bands originating from the Fe-3d orbitals essentially compose peak-structured profile in density of states (DOS) with a sharp peak situated at 0.65 eV below . The latter feature reflects the presence of a Van Hove type singularity. The main contribution to DOS at the Fermi level , however, comes equally from the Th-6d and Fe-3d electronic orbitals. The calculated value = 16.7 eV/f.u results in theoretical Sommerfeld coefficient = 39.31 mJ/mol K and electron–phonon coupling parameter = 0.34. The theoretical electronic structure properties of are discussed in comparison with those of other noncentrosymmetric superconductors.

Experimental Study of Three-Nucleon Dynamics in the Dp Breakup Collisions Using the WASA Detector

Until recently, all calculations of breakup observables were carried out in a non-relativistic regime. The relativistic treatment of the breakup reaction in 3 N system is quite a new achievement. The detailed study of various aspects of few-nucleon system dynamics in medium energy region, with a particular emphasis on investigation of relativistic effects and their interplay with three nucleon force (3NF) becomes feasible with increasing available energy in the three nucleon system. Therefore an experiment to investigate the ^1H(d, pp)n breakup cross section using a deuteron beam of 300, 340, 380 and 400 MeV and the WASA detector has been performed at COSY-Jülich. The almost 4pi geometry of the WASA detector gives an unique possibility to study variety of kinematic configurations, which reveal different sensitivity to aspects of dynamics of the three nucleon system. The main steps of the analysis, including energy calibration, PID, normalization and efficiency studies, and their impact on the final accuracy of the result, are discussed.

Classical and Relativistic Models for Time Duration of Gamma-Ray Bursts

A classical model based on a power law assumption for the radius-time relationship in the expansion of a Supernova (SN) allows to derive an analytical expression for the flow of mechanical kinetic energy and the time duration of Gamma-ray burst (GRB). A random process based on the ratio of two truncated lognormal distributions for luminosity and luminosity distance allows to derive the statistical distribution for time duration of GRBs. The high velocities involved in the first phase of expansion of a SN requires a relativistic treatment. The circumstellar medium is assumed to follow a density profile of Plummer type with eta=6. A series solution for the relativistic flow of kinetic energy allows to derive in a numerical way the duration time for GRBs. Here we analyse two cosmologies: the standard cosmology and the plasma cosmology.

Computational study of the anticancer drug cisplatin

Systems containing platinum (Pt) are more challenging for reliable computations, because Pt has 78 electrons and requires relativistic treatment. However, to reduce computational demands, most previous researchers used effective core potentials. In this investigation, we perform numerous computations on the cisplatin molecule with ab initio methods and density functional theory, some of which involve all electron and zero-order relativistic approximation. Tentative conclusions on the reliability of various methods are drawn from comparison of our results with previous calculations and available experimental data. Vibrational and electronic spectra are calculated and compared with previous studies and available experimental data.

Relativistic radiative transfer in relativistic spherical flows

Abstract Relativistic radiative transfer in relativistic spherical flows is numerically examined under the fully special relativistic treatment. We first derive relativistic formal solutions for the relativistic radiative transfer equation in relativistic spherical flows. We then iteratively solve the relativistic radiative transfer equation, using an impact parameter method/tangent ray method, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities, and the Eddington factor. We consider several cases; a scattering wind with a luminous central core, an isothermal wind without a core, a scattering accretion on to a luminous core, and an adiabatic accretion on to a dark core. In the typical wind case with a luminous core, the emergent intensity is enhanced at the center due to the Doppler boost, while it reduces at the outskirts due to the transverse Doppler effect. In contrast to the plane-parallel case, the behavior of the Eddington factor is rather complicated in each case, since the Eddington factor depends on the optical depth, the flow velocity, and other parameters.

Relativistic (SR-ZORA) quantum theory of atoms in molecules properties.

The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density-functional theory at both the nonrelativistic level and using the scalar relativistic zeroth-order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc.

Post-Newtonian evolution of massive black hole triplets in galactic nuclei – I. Numerical implementation and tests

Massive black-hole binaries (MBHBs) are thought to be the main source of gravitational waves (GWs) in the low-frequency domain surveyed by ongoing and forthcoming Pulsar Timing Array campaigns and future space-borne missions, such as {\it eLISA}. However, many low-redshift MBHBs in realistic astrophysical environments may not reach separations small enough to allow significant GW emission, but rather stall on (sub)pc-scale orbits. This "last-parsec problem" can be eased by the appearance of a third massive black hole (MBH) -- the "intruder" -- whose action can force, under certain conditions, the inner MBHB on a very eccentric orbit, hence allowing intense GW emission eventually leading to coalescence. A detailed assessment of the process, ultimately driven by the induced Kozai-Lidov oscillations of the MBHB orbit, requires a general relativistic treatment and the inclusion of external factors, such as the Newtonian precession of the intruder orbit in the galactic potential and its hardening by scattering off background stars. In order to tackle this problem, we developed a three-body Post-Newtonian (PN) code framed in a realistic galactic potential, including both non-dissipative 1PN and 2PN terms, and dissipative terms such as 2.5PN effects, orbital hardening of the outer binary, and the effect of the dynamical friction on the early stages of the intruder dynamics. In this first paper of a series devoted at studing the dynamics of MBH triplets from a cosmological perspective, we describe, test and validate our code.