Relativistic Approach Research Articles

Effect of Fluid Composition on a Jet Breaking out of a Cocoon in Gamma-Ray Bursts: A Relativistic de Laval Nozzle Treatment

In this paper we carry out a semi-analytic general relativistic study of a Gamma-Ray Bursts (GRB) jet that is breaking out of a cocoon or stellar envelope. We solve hydrodynamic equations with the relativistic equation of state that takes care of fluid composition. In short GRBs, a general relativistic approach is required to account for curved spacetime in strong gravity. The piercing of the jet through the cocoon resembles a de Laval nozzle and the jet may go through recollimation shock transitions. We show that the possibility of shock transition and the shock properties are sensitive to the matter composition and the cocoon strength. Obtained Lorentz factors in thermally driven jets comfortably reach few ×10.

Screening effects in the electron bremsstrahlung from heavy ions

A fully relativistic approach is presented for the calculation of the bremsstrahlung emitted by an electron scattered off an ionic target. The ionic target is described as a combination of a nuclear electrostatic potential and a screening potential induced by the electronic cloud of the ion. The approach allows us to investigate the influence of the target electrons on the properties of the emitted radiation. We calculate the double differential cross section and Stokes parameters of the bremsstrahlung of an electron scattered off uranium ions in different charge states, ranging from bare to neutral uranium. Results on the high-energy endpoint of the electron bremsstrahlung from Li-like uranium ions ${\mathrm{U}}^{89+}$ are compared to the recent experimental data. For this process, it is found that taking into account the screening effect leads to a change of the cross section on the level of 14%, which can, in principle, be seen in present-day experiments.

Electromagnetic and gravitational form factors of Δ resonance in a covariant quark-diquark approach

In this work, the electromagnetic and gravitational form factors of a spin-$3/2$ particle, $\mathrm{\ensuremath{\Delta}}$ resonance, are simultaneously calculated with the help of a relativistic covariant quark-diquark approach. The two kinds of form factors are separately extracted from the matrix elements of the electromagnetic current and of the energy-momentum tensor of the system. Our numerical results show that the approach can reproduce the electromagnetic monopole, dipole, quadrupole, and octupole form factors well compared to the lattice calculations. Our obtained electromagnetic moments are also comparable with some other approaches. Moreover, the obtained gravitational form factors, which give the mechanical properties of the system (like the mass and spin distributions) are also given for the $\mathrm{\ensuremath{\Delta}}$ isobar. In addition, some discussions of the sign and the interpretation of the $D$ term are given.

A chiral mean-field equation-of-state in UrQMD: effects on the heavy ion compression stage

It is shown that the initial compression in central heavy ion collisions at beam energies of E_{mathrm {lab}}=1-10A GeV depends dominantly on the underlying equation of state and only marginally on the model used for the dynamical description. To do so, a procedure to incorporate any equation of state in the UrQMD transport model is introduced. In particular we compare the baryon density, temperature and pressure evolution as well as produced entropy in a relativistic ideal hydrodynamics approach and the UrQMD transport model, where the same equation of state is used in both approaches. Not only is the compression similar if the same equation of state is used in either dynamical model, but it also strongly depends on the actual equation of state. These results indicate that the equation of state can be studied with observables which are sensitive to the initial compression phase and maximum compression achieved in heavy ion collisions at these beam energies.

Comparison of different relativistic models applied to dense nuclear matter

We explore three different classes of relativistic approaches applied to the description of dense nuclear matter: a Walecka-type relativistic mean field model (RMF), an extension including an effective chiral potential (RMF-C) and a further extension with a chiral potential and confinement effects (RMF-CC). The parameters of the latter are controlled by fundamental properties such as the chiral potential, Lattice-QCD predictions, the quark sub-structure, as well as empirical properties at nuclear matter saturation. While these models are calibrated to the same properties at saturation density, they differ in their predictions as the density increases. We take care of parameter uncertainties and propagate them to our predictions for symmetric nuclear matter by employing Bayesian statistics. We show that RMF and RMF-C share common features as the density increases, while RMF-CC behaves differently. For instance, the scalar field at $6n_\textrm{sat}$ reaches $\sim 20$ MeV for RMF-CC while it is larger than $\sim 70$ MeV for RMF and RMF-C. Interestingly, we also show that, by fixing the $\rho$ coupling constant from the quark structure of the nucleon, these three models reproduce only half of the empirical symmetry energy.

Ab Initio Composite Approaches for Heavy Element Energetics: Ionization Potentials for the Actinide Series of Elements.

The first, second, and third gas-phase ionization potentials have been determined for the actinide series of elements using an ab initio composite scalar and fully relativistic approach, employing the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) and Dirac Hartree-Fock (DHF) methods, extrapolated to the complete basis set (CBS) limit. The impact of electron correlation and basis set choice within this framework are examined. Additionally, the first three ionization potentials were obtained using an ab initio heavy element correlation-consistent Composite Approach (here referred to as α-ccCA). This is the first utilization of a ccCA for actinide species.

Polarization effects, shape resonances and bound states in low energy positron elastic scattering by Zinc and Cadmium vapours

Low energy elastic positron scattering from Zn and Cd atoms was studied using model correlation potential. Special attention is given to the study of polarization effects through the incorporation of quadrupole polarizabilities and hyperpolarizabilities in the scattering potential. Resonant p-wave shape structures are found for both systems. Results show that these become sharper and move to lower energies as the level of polarization of the potential is increased. Resonance was suppressed in Cd when the second hyperpolarizability γ was taken greater than 46000 a.u. and true p-wave bound states were formed. Comparison to previous calculations and dependence of the results with the scheme adopted to match the correlation and polarization components of the potential is discussed. We find that the elastic cross sections and the resonant effects do not depend on the specific form of the correlation potential but strongly depend on the polarization parameters and the matching point determined by the crossing between the correlation and polarization components of the potential. The value for the dipole–dipole–quadrupole polarizability B for Cd was specifically calculated using the relativistic coupled-cluster approach and is reported for the first time in this work.

Many Body Current Density from Foldy–Wouthuysen Transformation of the Dirac–Coulomb Hamiltonian

This paper analyzes how special relativity changes the equation for the many-body-induced current density starting from the Foldy–Wouthuysen diagonalization of the Dirac–Coulomb Hamiltonian. This current density differs from that obtained with the Gordon decomposition due to the presence of a spin-orbit coupling contribution not considered before for many-body molecular systems. This contribution diverges on atomic nuclei due to the nature of the point charges considered in the nonrelativistic approach, demonstrating that conventionally used nonrelativistic methods are not suitable for dealing with spin effects such as spin-orbit coupling or effects smaller than α2, with α the fine structure constant, and that a fully relativistic approach with a finite charge should be used. Despite the singularity, the spin-orbit coupling current becomes an important contribution to the total current in open-shell systems with high-spin multiplicity and a high atomic number in the nuclear proximity. On long ranges, this contribution is overcome by the Coulomb potential and the derived electric field which decays very quickly for small distances from nuclear charges. An evaluation of this spin-orbit current has been performed in the linear response approach at the HF/DFT level of theory.

Landau parameters and entrainment matrix of cold stellar matter: effect of the symmetry energy and strong magnetic fields

Nuclear matter properties based on a relativistic approach suitable for the description of multi-component systems are calculated. We use a set of nuclear relativistic mean-field models that satisfy acceptable nuclear matter properties and neutron star observations. The effects of the density dependence of the symmetry energy and of the Landau quantization due to the presence of a strong external magnetic field are discussed. Properties such as the proton fraction, the Landau mass, Landau parameters and entrainment matrix, the adiabatic index and speed of sound are calculated for cold β-equilibrium matter. A large dispersion on the calculated properties is obtained at two to three times saturation density ρ0 . The proton Landau mass can be as low as one third of the vacuum nucleon mass at 2-3 ρ0 . Similar effects are obtained for the Landau parameters, in particular, the ones involving protons, where the relative dispersion of F0 pp and F1 pp is as high as 30% to 50% at 2-3 ρ0 . These parameters are particularly sensitive to the symmetry energy. The effect of the magnetic field on the nuclear properties is small for fields as high as 1018G except for a small range of densities just above the crust-core transition. Tables with the EoS, and the parameters, are provided in the supplementary data section.

Do Kentucky Kami Drink Bourbon? Exploring Parallel Glocalization in Global Shinto Offerings

Scholars of Japanese religion have recently drawn attention to the global repositioning, “greening”, and international popularization of Shinto. However, research on Shinto ritual practice and material religion continues to focus predominantly on cases located within the borders of the Japanese state. This article explores the globalization of Shinto through transnational practitioners’ strategic glocalization of everyday ritual practices outside of Japan. Drawing upon digital ethnographic fieldwork conducted in online Shinto communities, I examine three case studies centering on traditional ritual offerings made at the domestic altar (kamidana): rice, sake, and sakaki branches. I investigate how transnational Shinto communities hold in tension a multiplicity of particularistic understandings of Shinto locality and authenticity when it comes to domestic ritual practice. While relativistic approaches to glocalization locate the sacred and authentic in an archetypical or idealized form of Japanese tradition rooted in its environment, creolization and transformation valorize the particularities of one’s personal surroundings and circumstances. Examining these strategies alongside recent and historical cases in Shinto ritual at shrines within Japan, I propose that attending to processes of “parallel glocalization” helps to illuminate the quasi-fictive notion of the religious “homeland” and close the perceived gap in authenticity between ritual practices at home and abroad.

Benchmarking calculations of wavelengths and transition rates with spectroscopic accuracy for W xlviii through W lvi tungsten ions

Atomic properties of $n=3$ levels for ${\mathrm{W}}^{47+}\ensuremath{-}{\mathrm{W}}^{55+}$ ions ($Z=74$) are systematically calculated using two different and independent methods, namely, the second-order many-body perturbation theory and the multiconfiguration Dirac-Hartree-Fock method combined with the relativistic configuration interaction approach. Wavelengths and transition rates for electric- and magnetic-dipole transitions involving the $n=3$ levels of ${\mathrm{W}}^{47+}\ensuremath{-}{\mathrm{W}}^{55+}$ are calculated. In addition, we discuss in detail the importance of the valence and core-valence electron correlations, the Breit interaction, the higher-order frequency-dependent retardation correction, and the leading quantum electrodynamical corrections for transition wavelengths. Spectroscopic accuracy is achieved for the present calculated wavelengths, and most of them agree with experimental values within $0.05%$. Our calculated wavelengths, combined with collisional radiative model simulations, are used to identify the yet unidentified 25 observed lines in the extremely complex spectrum between $27\phantom{\rule{0.16em}{0ex}}\AA{}$ and $34\phantom{\rule{0.16em}{0ex}}\AA{}$ measured by Lennartsson $et\phantom{\rule{4pt}{0ex}}al.$ [Phys. Rev. A 87, 062505 (2013)]. We provide additional data for 472 strong electric-dipole transitions in the wavelength range of 17--50 \AA{}, and 185 strong magnetic-dipole transitions between $36\phantom{\rule{0.16em}{0ex}}\AA{}$ and $4384\phantom{\rule{0.16em}{0ex}}\AA{}$, with a line intensity greater than $1\phantom{\rule{0.16em}{0ex}}\mathrm{photon}/\mathrm{s}$. These can provide benchmark data for future experiments and theoretical calculations.

Benchmark Study on the Calculation of 119Sn NMR Chemical Shifts.

A new benchmark set termed SnS51 for assessing quantum chemical methods for the computation of 119Sn NMR chemical shifts is presented. It covers 51 unique 119Sn NMR chemical shifts for a selection of 50 tin compounds with diverse bonding motifs and ligands. The experimental reference data are in the spectral range of ±2500 ppm measured in seven different solvents. Fifteen common density functional approximations, two scalar- and one spin-orbit relativistic approach are assessed based on conformer ensembles generated using the CREST/CENSO scheme and state-of-the-art semiempirical (GFN2-xTB), force field (GFN-FF), and composite DFT methods (r2SCAN-3c). Based on the results of this study, the spin-orbit relativistic method combinations of SO-ZORA with PBE0 or revPBE functionals are generally recommended. Both yield mean absolute deviations from experimental data below 100 ppm and excellent linear regression determination coefficients of ≤0.99. If spin-orbit calculations are not affordable, the use of SR-ZORA with B3LYP or X2C with ωB97X or M06 may be considered to obtain qualitative predictions if no severe spin-orbit effects, for example, due to heavy nuclei containing ligands, are expected. An empirical linear scaling correction is demonstrated to be applicable for further improvement, and respective empirical parameters are given. Conformational effects on chemical shifts are studied in detail but are mostly found to be small. However, in specific cases when the ligand sphere differs substantially between conformers, chemical shifts can change by up to several hundred ppm.

Theoretical evaluation of excitation cross section and fluorescence polarization of a solid-density Si plasma

In this article, a fully relativistic approach is proposed to precisely predict the electronic structures, spectral properties, cross sections, and degrees of linear polarization of light emitted after excitation of plasma-embedded ions by electron impact, taking into account the plasma shielding effects on the atomic structures and collision dynamics, in addition to the contributions of Breit interaction and quantum electrodynamics effects. The scheme employs the effective shielding potential deduced from a solution of Poisson equation, based on the self-consistent field ion-sphere simulations to explain the interactions among the charged particles, where the perturbation correlation Dirac–Coulomb Hamiltonian is constructed. The simple and understandable form makes it a good substitute for complex self-consistent field calculation. As an illustrative example, a comparative investigation regarding the influences of different plasma temperature and density parameters on the level energies, transition rates, integrated total/magnetic sublevel cross sections, and linear polarizations of the radiation following electron-impact excitation of Si XIII (a solid-density Si plasma) is carried out. Numerical results show that the plasma density effect can significantly affect the atomic structures and collision cross sections, yet has limited influence on the polarization characteristics. A comparison of our calculations with other results, when available, is made. The advanced approach presented here not only opens a novel window for exploring the atomic dynamics processes in hot and/or dense plasmas, but also provides important information about polarization of the line emission. This study is beneficial for the high energy density physics, laser-produced plasmas, and astrophysical applications.

Calculations of electron-impact excitation and dielectronic recombination rate coefficients of highly charged silicon ions

The rate coefficients for dielectronic recombination and electron-impact excitation processes with H-like to Be-like silicon ions (${\mathrm{Si}}^{13+}\text{\ensuremath{-}}{\mathrm{Si}}^{10+}$) are calculated using relativistic distorted-wave approach. The prominent $▵n=1$ and the weaker $▵n=2$ and 3 dielectronic recombination (DR) resonances with $K$-shell excitations are presented, and compared with the existing DR experimental rate coefficients of ${\mathrm{Si}}^{13+}, {\mathrm{Si}}^{12+}$, and ${\mathrm{Si}}^{11+}$ ions, it is found that the theoretical DR rate coefficients are in very good agreement with the experimental results. With the same approach, the direct and resonant electron-impact excitation (EIE) cross sections associated with $1s\ensuremath{-}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}$ core excitations are calculated for the ground states of ${\mathrm{Si}}^{13+}\text{\ensuremath{-}}{\mathrm{Si}}^{10+}$ ions and found in excellent agreement with the available experiment. Finally, we present the synthesized DR and EIE rate coefficients for the sum of all detected $(13+\ensuremath{\sim}10+)$ charge states of Si and these agree well with the experimental results.

Appearance of a peak in the symmetry energy at N=126 for the Pb isotopic chain within the relativistic energy density functional approach

The newly derived relativistic energy density functional [\textcolor{blue}{ Phys. Rev. C \textbf{103}, 024305 (2021)}], which stems from the effective field theory motivated relativistic mean-field (E-RMF) is employed to establish the appearance of peak/kink in the symmetry energy over the isotopic chain of Pb-nuclei. The coherent density fluctuation model parametrization procedure for finite nuclei is adopted here to obtain the relativistic energy density functional at local density. The relativistic energy density functional from E-RMFT takes precedence over the Br\"uckner energy density functional as it accurately predicts the empirical saturation density and binding energy per nucleon $E/A$, so-called 'Coester Band Problem'. Interestingly, using the relativistic energy density functional, it is possible to predict the peak at $N=126$ for recently developed G3 and widely used NL3 parameter sets, which is not observed for Br\"uckener's functional in-spite of using the E-RMF density. From the present analysis, the newly fitted energy density functional is found to be minutely sensitive to the choice of the parameter sets employed.

Screening vs. gevolution: In chase of a perfect cosmological simulation code

We compare two competing relativistic approaches to the N-body simulation of the Universe large-scale structure. To this end, employing the corresponding alternative computer codes (“gevolution” and “screening”), we conduct a series of cosmological simulations in boxes of different sizes and calculate the power spectra of the scalar perturbation Φ, the frame-dragging vector potential B and the difference between scalar modes χ=Φ−Ψ. We demonstrate that the corresponding power spectra are in very good agreement between the compared schemes. For example, the relative difference of the power spectra for Φ is 0.04% maximum. Since the perturbed Einstein equations have much simpler form in the screening approach, the simulation with this code consumes less computational time, saving almost 40% of CPU hours.

Systematic application of the M3Y NN forces for describing the capture process in heavy-ion collisions involving deformed target nuclei

We present results of a systematic study of the capture process through the barrier penetration model. The nucleus-nucleus interaction potential is calculated using the double-folding model (DFM) with the M3Y Paris $\mathit{NN}$ forces. The nucleon densities entering the model are generated from the experimental three-parameter Fermi charge densities. The DFM has been extended to the case of deformed target nuclei. It is shown that the density-dependent M3Y $\mathit{NN}$ forces with the finite range exchange part can be mimicked successfully by the zero-range density-independent forces. The latter option significantly reduces the required computer time. For the nucleon densities and target nuclei deformations, we employ the values from the commonly used data bases. Thus, we do not vary any parameters to reach a better agreement with the data. The resulting cross sections are compared with data for 20 reactions with the product of the charge numbers ${Z}_{P}{Z}_{T}$ ranging from 216 up to 2576. We discuss the opinion met in the literature that the M3Y $\mathit{NN}$ forces provide a poorer description of the capture cross sections in heavy-ion collisions in comparison to the $\mathit{NN}$ forces coming from the relativistic mean-field approach. Our calculations show that the M3Y $\mathit{NN}$ forces give an agreement with the data which is not perfect yet is not worse than the one resulting from the relativistic mean-field approach $\mathit{NN}$ forces.

Thermodynamics Modeling for Actinide Monocarbides and Mononitrides from First Principles

The high-temperature thermodynamical properties for the actinide monocarbides and mononitrides ThC, ThN, UC, UN, PuC, and PuN are calculated from first-principles electronic-structure theory. The electronic structure is modeled with density-functional theory (DFT) and is fully relativistic, including the spin-orbit interaction. Furthermore, the DFT is extended to account for orbital–orbital interactions, by means of a parameter-free orbital-polarization (OP) technique, that has proven to be essential for the 5f electrons in plutonium. Strong anharmonicity and the temperature dependence of the lattice vibrations are captured with the self-consistent ab initio lattice dynamics (SCAILD) method. The calculated free energies and heat capacities are compared to published results from quasi-harmonic (QH) theory, and experiments, where available. For the uranium and plutonium compounds, we make use of CALPHAD assessments to help evaluate the theory. Generally, our anharmonic relativistic approach compares well with both CALPHAD and experiments. For the thorium compounds, our theory is in good accord with QH modeling of the free energy at lower temperatures but for the heat capacity the comparison is less favorable.

Structural evolution and shape transition in even-even Hf-isotopes within the relativistic mean-field approach

In this theoretical study, we calculate the ground state parameters like binding energy, charge radii, neutron skin-thickness, chemical potentials, quadrupole deformation parameter, neutron separation energy, and single-particle energy for Hf isotopes of mass 170 ⩽ A ⩽ 220. The potential energy surface in parallel with the Fermi energy as a function of the quadrupole deformation parameter is estimated to determine the ground state configuration. The Relativistic Hartree-Bogoliubov approach with density-dependent DD-ME2 and the relativistic mean-field formalism with the popular NL3 and NL3⁎ parameter sets are used for the present analysis. The study involves a constant gap BCS approach within NL3, & NL3⁎ and Bogoliubov transformation within DD-ME2 parameter sets to examine the effect of pairing correlations. The calculated bulk quantities are reasonably good agreement with available experimental data, the finite range droplet model predictions, and the Weizsäcker-Skyrme mass formula. We find the signature of shell/sub-shell closure at N = 126 for all the parameter sets, which indicates the stability of 198Hf in the neutron drip-line region of the Hf-isotopes.

Relativistic extended uncertainty principle from spacetime curvature

The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work that is recovered in the nonrelativistic limit. Applying the $3+1$ splitting in accordance with the ADM formalism, we find the relativistic physical momentum operator and compute its standard deviation for wave functions confined to a geodesic ball on a spacelike hypersurface. Its radius can then be understood as a measure of position uncertainty. Under the assumption of small position uncertainties in comparison to background curvature length scales, we obtain the corresponding corrections to the uncertainty relation in flat space. Those depend on the Ricci scalar of the effective spatial metric, the particle is moving on, and, if there are nonvanishing time-space components of the spacetime metric, there are gradients of the shift vector and the lapse function. Interestingly, this result is applicable not only to massive but also to massless particles. Over all, this is not a covariant, yet a consistently general relativistic approach. We further speculate on a possible covariant extension.