Relativistic Variant Research Articles

What Bergson should have said about special relativity

The debate between Einstein and Bergson is a salient episode in the history of modern physics and a telling example of the interaction between science and philosophy. This paper initially discusses five reasons why Bergson criticised Einstein for giving up absolute time. The most important one was Bergson’s commitment to an intuitionist, anti-Kantian metaphysics informed by common sense. Apart from that, he knew that the theory of special relativity permits “duration” (durée) in the form of the passage of proper time, to which Bergson referred as “real time”. Neither static eternalism (which excludes temporal passage) nor dynamic eternalism (which, like the former, claims the existence of the future) are acceptable from Bergson’s philosophical perspective, which acknowledges the role of temporal experience and everyday thinking in addition to science and metaphysics. He understood temporal passage as creation of new existence, anticipating what later became known as the growing block theory of time. The pointy relativistic variant of this theory, which divides the universe into blocks of growing past light cones, does justice to large parts of his philosophy, including the distinction between the actual and the virtual. Supporters of Bergson’s account of duration should adopt this theory of time.

ONCE AGAIN ABOUT THE PROBLEM “4/3”

It is shown that the problem "4/3" or the problem of electromagnetic mass has a strict solution only if the fields are instantaneous. This result is valid in both the classical and relativistic variants. The hypothesis of the existence of a physical ether is introduced, which allows us to explain the constancy of the speed of light in inertial reference systems and features of instantaneous action at a distance.

On a direct description of pseudorelativistic Nelson Hamiltonians

Abstract interior-boundary conditions allow for the direct description of the domain and the action of Hamiltonians for a certain class of ultraviolet-divergent models in quantum field theory. This method, which comes without the need for renormalization, was recently applied to the nonrelativistic Nelson model. Here, we demonstrate the flexibility of the novel approach by applying it to two relativistic variants of Nelson’s model. The existence of Hamiltonians for these models was shown using renormalization techniques by Eckmann [Commun. Math. Phys. 18, 247 (1970); J. Math. Phys. 15, 190 (1974)]. However, many important properties, such as the domain and the action of the Hamiltonian, were not known. We construct the Hamiltonians for such models via abstract boundary conditions, describing their action explicitly for the first time. In addition, we obtain a detailed characterization of their domain.

Relativistic quantum crystallography of diphenyl- and dicyanomercury. Theoretical structure factors and Hirshfeld atom refinement

Quantum crystallographic refinement of heavy-element-containing compounds is a challenge, because many physical effects have to be accounted for adequately. Here, the impact and magnitude of relativistic effects are compared with those of electron correlation, polarization through the environment, choice of basis set and treatment of thermal motion effects on the structure factors of diphenylmercury(II) [Hg(Ph)2] and dicyanomercury(II) [Hg(CN)2]. Furthermore, the individual atomic contributions to the structure factors are explored in detail (using Mulliken population analysis and the exponential decay of atomic displacement parameters) to compare the contributions of lighter atoms, especially hydrogen atoms, against mercury. Subsequently, relativistic Hirshfeld atom refinement (HAR) is validated against theoretical structure factors of Hg(Ph)2 and Hg(CN)2, starting from perturbed geometries, to test if the relativistic variant of HAR leads to multiple solutions. Generally, relativistic HAR is successful, leading to a perfect match with the reference geometries, but some limitations are pointed out.

Electron impact ionisation cross sections of cis- and trans-diamminedichloridoplatinum(II) and its hydrolysis products

ABSTRACTWe report total electron-impact ionisation cross sections (EICSs) of cisplatin, its hydrolysis products and transplatin in the energy range from threshold to 10 keV using the binary-encounter-Bethe (BEB) and its relativistic variant (RBEB), and the Deutsch-Märk (DM) methods. We find reasonable agreement between all three methods, and we also note that the RBEB and the BEB methods yield very similar (almost identical) results in the considered energy range. For cisplatin, the resulting EICSs yield cross section maxima of 22.09 × 10−20 m2 at 55.4 eV for the DM method and 18.67 × 10−20 m2 at 79.2 eV for the (R)BEB method(s). The EICSs of monoaquated cisplatin yield maxima of 12.54 × 10−20 m2 at 82.8 eV for the DM method and of 9.74 × 10−20 m2 at 106 eV for the (R)BEB method(s), diaquated cisplatin yields maxima of 7.56 × 10−20 m2 at 118.5 eV for the DM method and of 5.77 × 10−20 m2 at 136 eV for the (R)BEB method(s). Molecular geometry does not affect the resulting EICS significantly, which is also reflected in very similar EICSs of the cis- and trans-isomer. Limitations of the work as well as desirable future directions in the research area are discussed.

New quantum number for the many-electron Dirac-Coulomb Hamiltonian

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator $\mathcal{K}_+$, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator $\mathcal{K}$, the $\mathcal{K}^2_+$ has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that $\mathcal{K}_+$ is connected to $\mathcal{K}$ through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call $\mathcal{K}_+$ the generator of the many-electron TR symmetry. By diagonalizing the operator $\mathcal{K}^2_+$ in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with $\mathcal{K}^2_+$ has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree--Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.

The SS433 jet from subparsec to parsec scales

Context. Relativistic jets associated with compact objects, as in the X-ray binary SS433, are known to be multiscale because they spawn over many orders of magnitude in distance. Here we model the precessing SS433 jet and study its dynamics from 𝒪 (0.01) to 𝒪(1) parsec scales.Aims. We aim to solve the discrepancy between the observations on a 0.1 pc scale of SS433, where the jet is clearly precessing with an angle of 20°, and the larger scale observations where the jet of SS433 interacts with the associated supernova remnant W50, requiring a precessing angle of 10°. Methods. We use 3D special relativistic hydrodynamical simulations on a domain of a scale of 1 pc. We use the finite volume code MPI-AMRVAC, solving the relativistic variant of the Euler equations. To cover lengthscale variations from 𝒪(0.001) pc as the jet beam width up to the domain size, we take full advantage of code parallelization and its adaptive mesh refinement scheme.Results. We found that by means of a simple hydrodynamical process, the jet of SS433 can transit from a precessing jet with an angle of 20°, to a continuous hollow non-precessing jet with a smaller opening angle of about 10°. Successive windings of the precessing jet helix undergo gradual deceleration by ISM interaction, to ultimately merge in a hollow straight jet at distances where the ram pressure of individual jet elements match the ISM pressure at about 0.068 pc from the source.Conclusions. We solve the discrepancy with an elegant and simple model that does not require the jet of SS433 to undergo any temporal changes in jet injection dynamics, but does so as a consequence of a hydrodynamically enforced spatial recollimation. Our simulation thus serves to validate simpler model prescriptions for SS433 on large scales, where a continuous jet profile suffices.

Examining the heavy p-block with a pseudopotential-based composite method: Atomic and molecular applications of rp-ccCA

The relativistic pseudopotential variant of the correlation consistent composite approach (rp-ccCA) has been extended to lower p-block-containing molecules. The lower p-block is defined here as elements indium through iodine (In-I) and thallium through astatine (Tl-At). The accuracy of rp-ccCA has previously been established in a study of energetic properties of molecules containing 4p elements and thermodynamic data of 4d-containing molecules. In the current study, the atomic ionization potentials (IPs) and electron affinities (EAs) of In-I and Tl-At, as well as dissociation energies and enthalpies of formation of lower p-block mono-hydrides, mono-oxides, and dimers were determined with rp-ccCA. The compiled data set is referred to as the LP80 data set. The mean absolute deviation of the IPs and the EAs from the experimental data were 2.50 and 3.06 kcal mol(-1), respectively. Additionally, the total atomization energy for lead clusters (Pb(n), n = 2-6) was determined. For the lead clusters, a decrease in the total atomization energy was observed with the inclusion of spin-orbit coupling. The spin-orbit coupling of the molecules was determined with multireference configuration interaction, while scalar relativistic effects were accounted for within the pseudopotentials. The results obtained by rp-ccCA for the lower p-block support the utilization of the method in future studies where accurate energetic, spectroscopic, and thermodynamic data are necessary.

Communication: Explicitly correlated four-component relativistic second-order Møller-Plesset perturbation theory

We propose explicitly correlated Ansatz for four-component relativistic methods within the framework of the no-pair approximation. Kinetically balanced geminal basis is derived to satisfy the cusp conditions in the non-relativistic limit based on the Lévy-Leblend-like equation. Relativistic variants of strong-orthogonality projection operator (Ansätze 2α and 2β) suitable for practical calculations are introduced by exploiting the orthogonal complement of the large-component basis. A pilot implementation is performed for the second order Møller-Plesset perturbation theory.

Influence <i>β</i>-radioactive radiation on tissues of the organism

Research of interaction of β-radioactive radiation with biotissue of an organism is lead. It is shown, that during electrons moderation there is a brake electromagnetic radiation usually in an X-ray range. There are derivatives of the formulas in not relativistic and relativistic variant for a finding of dependence of a flux brake electromagnetic radiation from frequency, of charging number elements of a biotissue, of a parameter of efficiency braking of electrons, of initial intensity of a flux of electrons and initial energy of electrons, is given.

Excitation of orotron oscillations at the doubled frequency of a surface wave

We study theoretically an electron frequency self-multiplier in which a surface mode of a periodic system is self-excited at a low frequency for a comparatively low current. The electron bunches, which appear as a result of this, excite the volume mode of an open resonator at the doubled frequency (coherent Smith-Purcell radiation). The open-resonator scheme allows one to obtain the higher power and coherence degree of radiation compared with the presently popular frequency multiplication scheme with an open periodic system (diffraction grating). The weakly relativistic and relativistic variants of the multipliers with a two-mirror open resonator designed for obtaining a high-power coherent radiation in the short-wavelength part of the millimeter and submillimeter ranges are studied numerically. The developed approach can also be used for designing high-power frequency multipliers on the basis of an array of nonlinear solid-state elements.

Modeling of plasma fibers with radiative processes

A fully three dimensional Particle in Cell model of the plasma flber had been developed. The code is written in FORTRAN 95, implementation CVF (Compaq Visual Fortran) under Microsoft Visual Studio user interface. Five particle solvers and two fleld solvers are included in the model. The solvers have relativistic and non{relativistic variants. The model can deal both with periodical and non{periodical boundary conditions. Plasma flber and its surroundings are generated during the initiation process. Many parameters of the flber, such as temperatures of electrons and ions, electric and magnetic flelds, perturbations in the shape of the flber and of the charged particle positions can be in∞uenced by the input dialog. The PIC program package simulates the behavior of the flber, namely the evolution of the magnetic fleld structures and turbulences. The numerical solution of the particle motion and calculation of the electric and magnetic flelds is the core of the program package. There are many additional routines and collaborating program packages for computer diagnostics, graphical output and other calculations such as radiation, collisions with neutrals, etc. The mechanism of the surface turbulences generation in the plasma flber was successfully simulated with the PIC program package. One of the latest goals of the PIC package was clariflcation of the onset of turbulence structures on the plasma flbers surfaces. It was shown that the development of these structures can be caused by initial a radial perturbation of plasma concentration and charge density. The surface structures simulated by PIC package were observed experimentally in various z{pinch apparatuses.

Calculation of electric-field gradients based on higher-order generalized Douglas–Kroll transformations

In this paper, the calculation of electric-field-like properties based on higher-order Douglas-Kroll-Hess (DKH) transformations is discussed. The electric-field gradient calculated within the Hartree-Fock self-consistent field framework is used as a representative property. The properties are expressed as an analytic first derivative of the four-component Dirac energy and the nth-order DKH energy, respectively. The differences between a "forward" transformation of the relativistic energy or the "back transformation" of the wave function is discussed in some detail. Detailed test calculations were carried out on the electric-field gradient at the halogen nucleus in the series HX (X=F,Cl,Br,I,At) for which extensive reference data are available. The DKH method is shown to reproduce (spin-free) four-component Dirac-Fock results to an accuracy of better than 99% which is significantly closer than previous DKH studies. The calculations of both the Hamiltonian and the property operator are shown to be essentially converged after the second-order transformation, even for elements as heavy as At. In addition, we have obtained results within the density-functional framework using the DKHZ and zeroth-order regular approximation (ZORA) methods. The latter results included picture-change effects at the scalar relativistic variant of the ZORA-4 level and were shown to be in quantitative agreement with earlier results obtained by van Lenthe and Baerends. The picture-change effects are somewhat smaller for the ZORA method compared to DKH. For heavier elements significant differences in the field gradients predicted by the two methods were found. Based on comparison with four-component Dirac-Kohn-Sham calculations, the DKH results are more accurate. Compared to the spin-free Dirac-Kohn-Sham reference values, the ZORA-4 formalism did not improve the results of the ZORA calculations.

Exchange-correlation and QED effects from a density functional based level shift approach

Abstract Perturbation theory based on the auxiliary noninteracting Kohn–Sham Hamiltonian allows a systematic study of the exchange-correlation (xc) energy functional of nonrelativistic density functional theory. In particular, it serves as the starting point for the derivation of implicit (orbital-dependent) density functionals for the xc-functional. Within the framework of quantum electrodynamics, a relativistic variant of Kohn–Sham perturbation theory has been formulated in Phys. Rev. A 58 (1998) 964. In this approach, a coupling constant integration technique is used for the exact representation of the relativistic xc-functional. In the present contribution an alternative systematic approach to this functional is put forward, which is based on a density functional version of Sucher’s level shift formula. As in the case of the coupling constant integration form, an exact relation for the xc-functional can be established. This relation provides the basis for a perturbation expansion to second order, including all inherent radiative corrections. A detailed comparison with the coupling constant integration result verifies the equivalence of both approaches. Finally, the first order level shift is analyzed in order to identify the Lamb shift within the Kohn–Sham scheme.

Photoionization cross sections of O II, O III, O IV, and O V: BenchmarkingR-matrix theory and experiments

For crucial tests between theory and experiment, ab initio close-coupling calculations are carried out for photoionization of several oxygen ions: O II, O III, O IV, and O V. The relativistic fine-structure and resonance effects are studied using the $R$ matrix and its relativistic variant, the Breit-Pauli $R$-matrix (BPRM) approximations. Extremely detailed comparison is made with high-resolution experimental measurements carried out in three different setups: Advanced Light Source at Berkeley, synchrotron radiation experiment with a new modulator at University of Aarh\us, and synchrotron radiation experiment at University of Paris-Sud. The comparisons illustrate physical effects in photoionization such as (i) fine structure, (ii) resolution, and (iii) metastable components. Photoionization cross sections ${\ensuremath{\sigma}}_{PI}$ of the ground and a few low-lying excited states of these ions obtained in the experimental spectrum include combined features of these states. The general features of the measured ${\ensuremath{\sigma}}_{PI}$ were predicted in the earlier calculations in $LS$ coupling. However, due to higher-resolution achievement in the recent experiments, the theoretically calculated resonances need to be resolved with much finer energy mesh for precise comparison. In addition, prominent resonant features are observed in the measured spectra that can form from transitions allowed with relativistic fine structure, but not in $LS$ coupling. Present results include calculations from both $LS$ coupling and the relativistic BPRM method to decipher the features in photoionization spectra. ${\ensuremath{\sigma}}_{PI}$ are obtained for ground and metastable (i) $2{s}^{2}2{p}^{3}(^{4}S^{o},^{2}D^{o},^{2}P^{o})$ states of O II, (ii) $2{s}^{2}2{p}^{2}(^{3}P,^{1}D,^{1}S)$ and $2s2{p}^{3}(^{5}S^{o})$ states of O III, (iii) $2{s}^{2}2p(^{2}P_{J}^{o})$ and $2s2{p}^{2}(^{4}P_{J})$ levels of O IV, and (iv) $2{s}^{2}(^{1}S)$ and $2s2p(^{3}P^{o},^{1}P^{o})$ states of O V. Most of the computed theoretical resonance structures are seen experimentally, although there are some discrepancies. One of the main conclusions of the present study is that resonances in photoionization cross sections of the ground and metastable states can be a diagnostic of experimental beam composition, with potential applications to astrophysical and laboratory plasma environments.

A relativistic variant of the Wigner function

The conventional Wigner function is inappropriate in a quantum field theory setting because, as a quasiprobability density over phase space, it is not manifestly Lorentz-covariant. A manifestly relativistic variant is constructed as a quasiprobability density over trajectories instead of over phase space.

A two-component variant of the Douglas–Kroll relativistic linear combination of Gaussian-type orbitals density-functional method: Spin–orbit effects in atoms and diatomics

The scalar relativistic variant of the linear combination of Gaussian-type orbitals—fitting functions—density-functional (R-LCGTO-FF-DF) method is extended to a two-component scheme which permits a self-consistent treatment of the spin–orbit interaction. The method is based on the Douglas–Kroll transformation of the four-component Dirac–Kohn–Sham equation. The present implementation in the program PARAGAUSS neglects spin–orbit effects in the electron–electron interaction. This approximation is shown to be satisfactory as long as bonding is restricted to s, p, and d orbitals. The method is applied to the diatomics Au2, Bi2, Pb2, PbO, and TlH using both a local density (LDA) and a gradient-corrected approximation (GGA) of the exchange-correlation functional. At the LDA level, bond lengths and vibrational frequencies are reproduced with high accuracy. For the determination of binding energies the open-shell reference atoms Au, Tl, Pb, Bi have been treated by a jj coupling approach based on a self-consistent noncollinear spin density-functional scheme and with an intermediate coupling procedure. The atomic state energies obtained with the jj coupling scheme agree well with experiment, but they are somewhat too high due to the incomplete inclusion of static correlation. Binding energies of diatomics at the GGA level are considerably improved due to the inclusion of spin–orbit interaction. The jj derived values are somewhat overestimated (by about 10%) compared to experiment, and they compare slightly worse with experiment than results based on the intermediate coupling approximation.

Relativistic density-functional studies of naked and ligated gold clusters

Electronic structure investigations on a broad range of gold compounds, including naked and ligated gold clusters, are reviewed. The calculations have been carried out with a recently introduced relativistic variant of the linear combination of Gaussian-type orbitals density-functional (LCGTO-DF) method which affords all-electron investigations for very large systems. The accuracy of the method will be evaluated for the gold dimer. Then the electronic structure of the naked cluster Au{sub 55} is studied, both in I{sub h} and O{sub h} symmetry. Nonrelativistic and relativistic results obtained by the present method are compared to those of the much simpler jellium model. Since triphenylphosphine is among the most common ligands in gold chemistry a series of mononuclear gold phosphine compounds MeAuPR{sub 3} with increasingly complex ligands PR{sub 3}(R = H, Ch{sub 3}, C{sub 5}H{sub 6}) is discussed. The calculations reveal the success and the limitations of simpler phosphines often employed as model ligands in theoretical studies. Some aspects of the phosphine gold interaction in these simpler compounds carry over to the main group element centered gold clusters. Thereby one arrives at a rationalization of the particularly high stability of the carbon-centered octahedral cluster cation [(R{sub 3}PAu){sub 6}C]{sup 2+} as compared to the neighboringmore » isoelectronic boron and nitrogen-centered clusters.« less

Electronic structure of Ca 3AuN

The electronic structure of Ca 3AuN has been studied by the quasirelativistic and relativistic variants of the CNDO/1 method. The calculated valence molecular orbitals for two clusters of the composition {(Ca 3AuN) 9} 2 and {(Ca 3AuN) 9} 4 have been used to generate the density of state (DOS) functions. The projected Au ( d) DOS spans only the occupied levels so that the gold atoms behave like d 10 systems in this compound. The first excitation energy serves as a better estimate of the “energy gap” in this material.

Relativistic electron spectrum of ferromagnetic iron

The relativistic spin-polarized scheme of the electron spectrum calculation in crystal within the framework of the relativistic variant of the Korringa-Kohn-Rostoker method is realized. The technique proposed is used to calculate the electron bands and density of states of ferromagnetic iron. The crystallographic symmetry of the problem is investigated for the BCC lattice. The role of the exchange and spin-orbit interactions in forming the band structure of ferromagnetic iron are discussed.