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DOE OSTI2023

Spin polarization induced by magnetic field and the relativistic Barnett effect

First, I study the analogy between the magnetization of a material and the spin polarization of particles in a fluid. Using the relativistic version of the Barnett effect, i.e. the magnetization of a material induced by mechanical rotation, the spin polarization induced by thermal vorticity is obtained within a purely classical model, where spin is treated as an intrinsic magnetic moment and rotation is included as a non-inertial effect. I argue that since spin polarization induced by thermal vorticity can be obtained in a classical theory, it can not be dominated by quantum anomalies. Second, the spin polarization induced by magnetic field is obtained for a fluid at local thermal equilibrium using statistical quantum field theory. The obtained formula is valid beyond the weak field approximation and when contributions from the non-homogeneity of the magnetic field are small. The exact form of spin polarization is studied for a free Dirac field at global equilibrium, and, like magnetic susceptibility, it oscillates according to the de Haas - van Alphen effect. Finally, I briefly review how magnetic field contributes to the difference between the spin polarization of Λ and $\barΛ$ observed in heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Relativistic self-consistent G W : Exact two-component formalism with one-electron approximation for solids

We present a formulation of relativistic self-consistent GW for solids based on the exact two-component formalism with one-electron approximation (X2C1e) and nonrelativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and the interplay of relativistic effects with electron correlation without adjustable parameters. Our all-electron implementation is fully ab initio and does not require a pseudopotential constructed from atomic calculations. We examine the effect of the X2C1e approximation by comparison to the established four-component formalism and reach an excellent agreement. The simplicity of X2C1e enables the construction of higher order theories, such as embedding theories, on top of perturbative calculations.

36 MATERIALS SCIENCE↗

NASA NTRS1994

Relativistic and Correlation Effects in CuH, AgH and AuH: Comparison of Various Relativistic Methods

The effects of relativity on the bond lengths, dissociation energies, and harmonic vibrational frequencies of the 1Epsilon(+) electronic ground states of the group IB hydrides CuH, AgH and AuH have been evaluated with a variety of ab initio methods. These properties were investigated with moderately-sized basis sets at the self-consistent field Hartree Fock (SCF HF) level and with second-order Moller-Plesset (MP2) perturbation theory for electron correlation. Comparisons were made between all-electron results using the nonrelativistic Hamiltonian, perturbation theory (PT) at first-order with only the one-electron non-fine structure terms of the Breit-Pauli Hamiltonian, the spin-free Douglas-Kroll (DK) transformed Dirac Hamiltonian and the untransformed Dirac Hamiltonian, and results using two sets of relativistic effective core potentials (RECPs). The expected trends of bond length decrease, dissociation energy increase and harmonic frequency increase with both relativity and correlation are found. Both sets of RECPs are shown to give good results, if accompanied by a reasonable basis set. The DK method is demonstrated to be an inexpensive, reliable approximation to the DHF method.

Collins, Charlene L.↗

NASA NTRS1990

Auroral kilometric radiation - An example of relativistic wave-particle interaction in geoplasma

The earth's auroral kilometric radiation (AKR) is believed to be produced by the electron-cyclotron maser instability. This instability is the result of a wave-particle interaction in which relativistic effects are crucial. An explanation is given as to how these relativistic effects alter the shape of the resonance curve in velocity space and modify the R - X mode wave dispersion near the electron cyclotron frequency compared to the results obtained in the nonrelativistic limit and from cold-plasma theory. The properties of the cyclotron maser instability in a driven system are illustrated using two-dimensional electromagnetic particle simulations which incorporate a continual flow of primary energetic electrons along the magnetic field.

Pritchett, P. L.↗

DOE OSTI2023

Characterizing initial- and final-state effects of relativistic nuclear collisions

Here, the multiphase transport model (AMPT) is used to study the final-state effects on the symmetric correlations (SC), asymmetric correlations (ASC), normalized symmetric correlations (NSC), and normalized asymmetric correlations (NASC) in Au+Au collisions at 200 GeV. The correlators' sensitivity to nonflow effects associated with long- and short-range nonflow correlations are also discussed using the HIJING model. The results indicate that SC, ASC, NSC, and NASC can give accompanying constraints for initial- and final-state effects. In addition, conducting further detailed experimental measurements spanning a broad range of collision systems and beam energies will serve as an additional constraint for the theoretical models' calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1994

Relativistic tidal interaction of a white dwarf with a massive black hole

We compute encounters of a realistic white dwarf model with a massive black hole in the regime where relativistic effects are important, using a three-dimensional, finite-difference, Eulerian, piecewise parabolic method (PPM) hydrodynamical code. Both disruptive and nondisruptive encounters are considered. We identify and discuss relativistic effects important for the problem: relativistic shift of the pericenter distance, time delay, relativistic precession, and the tensorial structure of the tidal forces. In the nondisruptive case, stripping of matter takes place. In the surface layers of the surviving core, complicated hydrodynamical phenomena are revealed. In both disruptive and nondispruptive encounters, material flows out in the form of two thin, S-shaped, supersonic jets. Our results provide realistic initial conditions for the subsequent investigation of the dynamics of the debris in the field of the black hole. We evaluate the critical conditions for complete disruption of the white dwarf, and compare our results with the corresponding results for nonrelativistic encounters.

Frolov, V. P.↗

NASA NTRS2005

Reliable Spectroscopic Constants for CCH-, NH2- and Their Isotopomers from an Accurate Potential Energy Function

Accurate quartic force fields have been determined for the CCH- and NH2- molecular anions using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, CCSD(T). Very large one-particle basis sets have been used including diffuse functions and up through g-type functions. Correlation of the nitrogen and carbon core electrons has been included, as well as other "small" effects, such as the diagonal Born-Oppenheimer correction, and basis set extrapolation, and corrections for higher-order correlation effects and scalar relativistic effects. Fundamental vibrational frequencies have been computed using standard second-order perturbation theory as well as variational methods. Comparison with the available experimental data is presented and discussed. The implications of our research for the astronomical observation of molecular anions will be discussed.

Lee, Timothy J.↗

DOE OSTI2020

Relativistic configuration-interaction and many-body-perturbation-theory calculations of U i hyperfine constants

Neutral uranium (U i) is a very difficult atom for theoretical calculations due to a large number (six) of valence electrons, strong valence-valence and valence-core correlations, high density of states, and relativistic effects. Configuration-interaction many-body perturbation theory (CI-MBPT) can efficiently treat valence-core correlations and relativistic effects, but because the formalism was developed for a Dirac-Hartree-Fock (DHF) starting potential that does not contain valence electrons, quite large CI space is needed to compensate for the + 6 charge of such a potential. Much more efficient is the relativistic configuration-interaction (RCI) approach, which uses a relatively accurate starting DHF potential that includes some valence electrons to make the valence-electron Hamiltonian diagonally dominated for some states. Here we report calculations of U i hyperfine constants of several low-energy states using the RCI method with the starting potential that includes four f valence electrons. With this starting potential, it is possible to use the single-configuration approximation or small basis sets to obtain quite accurate results for hyperfine-structure constants. In fact, by scaling the nuclear magnetic moment, the agreement for five levels was within 5% and a new magnetic moment can be recommended, 0.43(2). When two states are mixed, it is difficult to predict the exact mixing fractions, so in this case we proposed a method in which the mixing fraction is found by optimization of one parameter in the MBPT correction to obtain correct g factors. The resulting hyperfine constants are significantly improved. Finally, the CI-MBPT approach was also tested, with some success for low-energy states, with the limited basis set. The methods investigated here can be further developed to include more extensive data sets to improve accuracy and can be applied to other atoms and for calculations of other properties, for example, relevant to fundamental symmetry tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1991

The gravitomagnetic interaction and its relationship to other relativistic gravitational effects

To better understand the relationship between the expected precession rates of an orbiting gyroscope (GP-B) and other observable consequences in the solar system of relativistic, post-Newtonian gravity, a phenomenological model was developed of post-Newtonian gravity which presupposes the very minimum possible concerning the nature and foundations of the gravitational interaction. Solar system observations, chiefly interplanetary ranging, fix all the parameters in the phenomenological model to various levels of precision. This permits prediction of gyroscope precession rates to better than 10 pct. accuracy. A number of new precession terms are calculated which would exist if gravity were not a metric field phenomenon, but this would clash with other empirical observations of post-Newtonian effects in gravity. It is shown that gravitomagnetism, the post-Newtonian gravitational corrections to the interactions between moving matter, plays a ubiquitous role in determining a wide variety of gravitational effects, including the precession of orbiting gyroscopes.

Nordtvedt, Kenneth↗

NASA NTRS1985

Theoretical transition probabilities between the lowest 2S, 2P and 2D states of Na, K, Rb and Cs

Theoretical transition probabilities between the lowest 2S, 2P and 2D states of the alkali atoms Na through Cs have been computed using near Hartree-Fock quality Slater basis sets. The important core-valence correlation effects are incorporated explicitly by a configuration-interaction procedure. For Cs, the calculations were repeated using a Gaussian basis set so that relativistic effects could be incorporated through an effective core potential procedure. The best calculated electric quadrupole Einstein coefficients are Na(196.3/s), K(103.6/s), Rb(72.4/s) and Cs(19.7/s). Core-valence effects become increasingly important down the column, and reduce the quadrupole transition strengths to about the same degree as for the 2P-2S and 2D-2P dipole-allowed transitions. Relativistic effects increase the quadrupole moment of Cs, but less so than in Ba, presumably because the alkali 2D states are more diffuse.

Langhoff, S. R.↗

NASA NTRS2008

Constraints on Black Hole Spin in a Sample of Broad Iron Line AGN

We present a uniform X-ray spectral analysis of nine type-1 active galactic nuclei (AGN) that have been previously found to harbor relativistically broadened iron emission lines. We show that the need for relativistic effects in the spectrum is robust even when one includes continuum "reflection" from the accretion disk. We then proceed to model these relativistic effects in order to constrain the spin of the supermassive black holes in these AGN. Our principal assumption, supported by recent simulations of geometrically-thin accretion disks, is that no iron line emission (or any associated Xray reflection features) can originate from the disk within the innermost stable circular orbit. Under this assumption, which tends to lead to constraints in the form of lower limits on the spin parameter, we obtain non-trivial spin constraints on five AGN. The spin parameters of these sources range from moderate (a approximates 0.6) to high (a > 0.96). Our results allow, for the first time, an observational constraint on the spin distribution function of local supermassive black holes. Parameterizing this as a power-law in dimensionless spin parameter (f(a) varies as absolute value of (a) exp zeta), we present the probability distribution for zeta implied by our results. Our results suggest 90% and 95% confidence limits of zeta > -0.09 and zeta > -0.3 respectively.

Brenneman, Laura W.↗

DOE OSTI2021

Efficient Four-Component Dirac–Coulomb–Gaunt Hartree–Fock in the Pauli Spinor Representation

Four-component Dirac Hartree--Fock is an accurate mean-field method for treating molecular systems where relativistic effects are important. However, the computational cost and complexity of the two-electron interaction makes this method less common, even though we can consider the Dirac Hartree--Fock Hamiltonian the ``ground truth" of electronic structure, barring explicit quantum-electrodynamical effects. Being able to calculate these effects is then vital to the design of lower scaling methods for accurate predictions in computational spectroscopy and properties of heavy element complexes that must include relativistic effects for even qualitative accuracy. In this work, we present a Pauli quaternion formalism of maximal component- and spin-separation for computing the Dirac-Coulomb-Gaunt Hartree-Fock ground state, with a minimal floating-point-operation count algorithm. Furthermore, this approach also allows one to explicitly separate different spin physics from the two-body interactions, such as spin-free, spin-orbit, and the spin-spin contributions. Additionally, we use this formalism to examine relativistic trends in the periodic table, and analyze the basis set dependence of atomic gold and gold dimer systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Relativistic collapse of the classical triple bond in the CBi − molecular ion

The conventional framework for chemical bonding between main-group elements involves separate σ and π orbitals to describe multiple bonds. However, relativistic effects mix these orbitals in molecules containing heavy elements through spin–orbit coupling, leaving the total angular-momentum projection (ω) as the only good quantum number. Direct experimental evidence that relativistic effects change the σ-π bonding framework has remained elusive. Here, we probe the carbon-bismuth triple bond in the CBi − anion using high-resolution cryogenic photoelectron spectroscopy, coupled with relativistic four-component Dirac-Coulomb coupled-cluster calculations. Furthermore, even though the CBi − anion is isovalent to the well-known CN − species, we demonstrate that the traditional σ + 2π triple-bond picture collapses into a pure π-like |ω| = 3/2 and two |ω| = 1/2 Kramers pairs containing substantial σ/π mixing.

Kahraman, Deniz [Brown University, Providence, RI ↗

NASA NTRS1991

All-electron molecular Dirac-Hartree-Fock calculations: Properties of the group IV monoxides GeO, SnO and PbO

Dirac-Hartree-Fock calculations have been carried out on the ground states of the group IV monoxides GeO, SnO and PbO. Geometries, dipole moments and infrared data are presented. For comparison, nonrelativistic, first-order perturbation and relativistic effective core potential calculations have also been carried out. Where appropriate the results are compared with the experimental data and previous calculations. Spin-orbit effects are of great importance for PbO, where first-order perturbation theory including only the mass-velocity and Darwin terms is inadequate to predict the relativistic corrections to the properties. The relativistic effective core potential results show a larger deviation from the all-electron values than for the hydrides, and confirm the conclusions drawn on the basis of the hydride calculations.

Dyall, Kenneth G.↗

NASA NTRS1993

All-electron molecular Dirac-Hartree-Fock calculations - Properties of the group IV monoxides GeO, SnO, and PbO

Dyall, Kenneth G.↗

NASA NTRS1980

The approximation of radiative effects in relativistic gravity - Gravitational radiation reaction and energy loss in nearly Newtonian systems

An argument is presented to determine the accuracy with which a solution of Einstein's field equations of gravitation must be approximated in order to describe the dominant effects of gravitational radiation emission from weak-field systems. Several previous calculations are compared in the light of this argument, and some apparent discrepancies among them are resolved. The majority of these calculations support the 'quadrupole formulae' for gravitational radiation energy loss and radiation reaction.

Walker, M.↗

NASA NTRS1981

Collisional excitation of electron Landau levels in strong magnetic fields

The cross sections for the excitation and deexcitation of the quantized transverse energy levels of an electron in a magnetic field are calculated for electron-proton and electron-electron collisions in light of the importance of the cross sections for studies of X-ray pulsar emission. First-order matrix elements are calculated using the Dirac theory of the electron, thus taking into account relativistic effects, which are believed to be important in accreting neutron stars. Results for the collisional excitation of ground state electrons by protons are presented which demonstrate the importance of proton recoil and relativistic effects, and it is shown that electron-electron excitations may contribute 10 to 20% of the excitation rate from electron-proton scattering in a Maxwellian plasma. Finally, calculations of the cross section for electron-proton small-angle scattering are presented which lead to relaxation rates for the electron velocity distribution which are modified by the magnetic field, and to a possible increase in the value of the Coulomb logarithm.

Langer, S. H.↗

NASA NTRS1993

Tidal disruptions by supermassive black holes - Hydrodynamic evolution of stars on a Schwarzschild background

We present a three-dimensional numerical study of tidal disruption of a main-sequence star by a supermassive black hole. The simulations include general relativistic effects which are important in this regime. We analyze stars in a marginally bound orbit around the black hole with pericentric separation of a few Schwarzschild radii. We show that during a close passage, as a result of relativistic effects analogous to the perihelion shift, the trajectories of the debris of the star fan out into a crescent-like shape centered on the black hole. We also discuss the increase of the central density of the star as it approaches pericentric distance, the fraction of the debris accreted by the hole, its accretion rate, the distribution of debris orbits bound to the hole, and the velocity of unbound ejected material. We compare these results with the disruption of the star by a Newtonian point mass.

Laguna, Pablo↗