All electron ab initio investigations of the electronic states of the FeC molecule

The low-lying electronic states of the molecule FeC have been investigated by performing all electron ab initio multi-configuration self-consistent-field (CASSCF) and multi reference configuration interaction (MRCI) calculations. The relativistic corrections for the one-electron Darwin contact term and the relativistic mass-velocity correction have been determined in perturbation calculations. The electronic structure of the FeC molecule is interpreted as antiferromagnetic couplings of the localized angular momenta of the ions and resulting in a triple bond in the valence bond sense. The electronic ground state is confirmed as being . The spectroscopic constants for the ground state and eleven excited states have been derived from the results of the MRCI calculations. The spectroscopic constants for the ground state have been determined as and ,and for the low-lying state as and . The values for the ground state agree well with the available experimental data. The FeC molecule is polar with charge transfer from Fe to C. The dipole moment has been determined as in the ground state and as 1.51 D in the state. From the results of the MRCI calculations the dissociation energy, , is determined as 2.79 eV, and D₀ as 2.74 eV. Received: 2 October 1998 / Received in final form: 30 March 1999     

Ab initio all-electron fully relativistic Dirac—Fock self-consistent field calculations for UCI6

Ab initio all-electron fully relativistic Dirac-Fock and non-relativistic Hartree-Fock self-consistent field (SCF) calculations are reported at four UCl bond distances, assuming octahedral UCl₆. The results are fitted to a polynomial, obtaining thereby the optimized values of the bond distance and the corresponding total electronic energy for the UCl₆. The nonrelativistic Hartree-Fock (HF) and Dirac-Fock (DF) SCF calculations predict UCl₆ to be bound, with a predicted dissociation (atomization) energy D _e of 11.88 eV and 17.89 eV, respectively. Relativistic effects lead to ~51% increment in the predicted atomization energy of UCl₆. The UCl bond lengths predicted for UCl₆ with the relativistic DF and non-relativistic HF wave-functions are 2.46 Å and 2.58 Å, respectively. Complete neglect in the SCF step of the two-electron [SS|SS] integrals involving the small components of the spinors (NOSS) in the DF SCF calculation for UCl₆ predicts a D _e of 18.25 eV and essentially the same bond length (2.48 Å) as that predicted with the full SCF procedure. Thus the small components contribute an antibinding relativistic effect of ~0.4 eV to the D _e of UCl₆ and have a negligible effect on the bond length. The calculations show that relativistic effects are significant for the bonding and the dissociation (atomization) energy of UCl₆, and that these may be treated accurately using Dirac's fully relativistic equation for an electron.     

Electron angular distributions in double photoionization: Use of effective Sommerfeld parameters

We present calculations of the fivefold differential cross-section (FDCS) for double photoionization of helium at excess energies of 6 and 20 eV above threshold. Our results are obtained using for the final double-continuum state a product of three Coulomb wave functions, with the Sommerfeld parameters modified to describe the strength of interaction of any two particles affected by the third particle. Our calculations are compared with recent absolute measurements by D?rner et al. (Phys. Rev. A 57, 1074 (1998)), both in coplanar and non-coplanar geometries. Very good agreement is obtained for the shape of the angular distributions, and differences in the absolute magnitude exist in comparison with the standard choice of Sommerfeld parameters. Received: 17 July 1998 / Received in final form and Accepted: 23 October 1998     

Comment Triton Binding Energy and Minimal Relativity

For relativistic three-body calculations, essentially two different approaches are in use: field theory and relativistic direct interactions. However, while results based upon relativistic field theory show an increase of the triton binding energy by about 0.3 MeV due to relativistic effects, calculations that claim to apply relativistic direct interactions obtain 0.3 MeV repulsion. In this paper, we discuss the origin of such a discrepancy. We show that the use of an invariant two-body amplitude increases the triton binding energy by about 0.3 MeV, consistent with the results from relativistic field theory. Furthermore, we point out that in calculations relying on the direct-interactions approach, indeed expansions are used, which may be a bad approximation and the reason for the discrepancy. Received November 4, 1996; revised January 15, 1998; accepted for publication January 19, 1998     

Exclusive charge exchange reaction pD↦n(pp) within the Bethe-Salpeter formalism

The exclusive charge exchange reaction pD↦n(pp) at intermediate and high energies is studied within the Bethe-Salpeter formalism. The final-state interaction in the detected pp pair at nearly zero excitation energy is described by the ¹ S ₀ component of the Bethe-Salpeter amplitude. Results of numerical calculations of polarization observables and differential cross-section persuade that, as in the non-relativistic case, this reaction i) can be utilized as a “relativistic deuteron polarimeter” and ii) delivers further information about the elementary nucleon-nucleon charge exchange amplitude. Received: 26 November 2002 / Accepted: 30 January 2003 / Published online: 29 April 2003     

Dynamical relativistic corrections to the leptonic decay width of heavy quarkonia

We calculate the dynamical relativistic corrections, originating from radiative one-gluon exchange, to the leptonic decay width of heavy quarkonia in the framework of a covariant formulation of light-front dynamics. Comparison with the non-relativistic calculations of the leptonic decay width of J = 1 charmonium and bottomonium S-ground states shows that relativistic corrections are large. Most importantly, the calculation of these dynamical relativistic corrections legitimate a perturbative expansion in , even in the charmonium sector. This is in contrast with the ongoing belief based on calculations in the non-relativistic limit. Consequences for the ability of several phenomenological potentials to describe these decays are described. Received: 6 December 2001 / Published online: 5 April 2002     

Testing Dirac-Brueckner models in collective flow of heavy-ion collisions

We investigate differential in-plane and out-of-plane flow observables in heavy-ion reactions at intermediate energies from 0.2-2 AGeV within the framework of relativistic BUU transport calculations. The mean field is based on microscopic Dirac-Brueckner-Hartree-Fock (DB) calculations. We apply two different sets of DB predictions, those of ter Haar and Malfliet and more recent ones from the Tübingen group, which are similar in general but differ in details. The latter DB calculations exclude spurious contributions from the negative-energy sector to the mean field which results in a slightly softer equation of state and a less repulsive momentum dependence of the nucleon-nucleus potential at high densities and high momenta. For the application to heavy-ion collisions in both cases non-equilibrium features of the phase space are taken into account on the level of the effective interaction. The systematic comparison to experimental data favours the less repulsive and softer model. Relative to non-relativistic approaches one obtains larger values of the effective nucleon mass. This produces a sufficient amount of repulsion to describe the differential flow data reasonably well. Received: 8 January 2001 / Accepted: 12 November 2001     

Energies and widths of triply excited states of lithiumlike oxygen and neon

Seven low-lying triply exited states of lithium-like oxygen and neon are calculated with the multichannel saddle-point and saddle-point complex-rotation methods. The term energies are given for these excited states, along with level shifts and partial Auger widths from dominant decay channels. The mass polarization effect and relativistic corrections are included. The radiative transition rates are also calculated. These results are compared with other theoretical data in the literature. Received: 25 May 1998 / Revised: 28 July 1998 / Accepted: 25 August 1998     

电子与原子、离子碰撞过程的相对论效应

在玻恩近似下,建立了高能电子与原子、离于非弹性碰撞过程的相对论性理论计算方法,并以类Li等电子系列为例,阐明了电子与原子、离子非弹性碰撞过程的相对论效应.它包括:1.靶原子的相对论效应,它随原子序数的增加而增大.低z靶(如Li)的相对论效应可以忽略;对Au~(+76)靶的2_3—3p跃迁,广义振子强度相对论性计算值比相应的非相对论性值小27.1%.2.入射电子的相对论效应,它随入射电子能量的增加而增大.对高能入射电子,在特殊角度,要考虑广义振子强度横场项对微分截面的影响.在极端相对论情况下,如入射电子动能 关键词：     

Unifying description of the optical properties of InN from first principles

The optical properties of hexagonal InN have been studied using the all-electron approach based on density functional theory (DFT). The full-potential augmented plane wave method is employed with two different exchange-correlation potentials, the Perdew–Wang (PW) and the Engel–Vosko (EV) approximations. In addition, both non-relativistic and relativistic approximations are considered. We found that the PW and relativistic approximations give a metallic ground state; whereas using the EV and non-relativistic approximations a semiconductor phase is obtained, opening the gap up to 0.83 eV. Besides, the calculated interband transitions of the complex dielectric function up to 13 eV show favourable agreement with the recent spectroscopic ellipsometry results.     

On the separability of relativistic electron propagators

In this contribution we examine the separability of relativistic electron propagators. Both, magnetic and non-magnetic systems are studied on the basis of the Kohn-Sham-Dirac equation. We find a Dirac-Green's function in excellent agreement with recent calculations utilizing the left and right-handed solutions to the Dirac equation. Starting from these Dirac-Green's functions we re-derive a rotation matrix formalism that was shown to result in separable scattering matrices in the non-relativistic case. It turns out, that spin-dependent scattering matrices can be formulated which are closely related to their non-relativistic counterparts. These matrices incorporate spin-flip and non spin-flip processes on an equal footing, but are irreducible to sums over composite rotation matrices. The latter result is a major drawback for numerical applications since electron scattering in terms of composite rotations had drawn a lot of attention recently. Received 1st July 1997     

Spherical averaged jellium model with norm-conserving pseudopotentials

The effect of non-local norm-conserving pseudo-potentials on the static and dynamic properties of Na_n and Li_n cluster with n=6,8 is investigated in the frame of self-consistent LDA calculations with spherically averaged ionic density (SAPS model). A comparison with previous calculations which use local pseudo-potentials as well with uniform averaged non-local pseudo-jellium calculation has been carried out. A better quantitative agreement with experiments has been found in the calculation of the photoresponse cross-section with respect to either simple jellium or pseudo-jellium model, even in very small clusters, where deviations from sphericity are not negligible. Received: 3 March 1998 / Received in final form and Accepted: 2 June 1998     

Transition probabilities of forbidden lines in Pb I

Multiconfiguration Dirac-Fock as well as semiempirical calculations of decay rates of forbidden transitions within the ground 6s ² 6p ² configuration of neutral lead are reported and compared with relativistic Hartree-Fock results as well as with available experimental data. Received: 15 July 1998 / Received in final form: 15 October 1998     

Lorentz Boosted Potential for a Two-Body System with Unequal Masses

We produce a Lorentz boosted two-body potential for particles of different mass that is phase equivalent to a given realistic non-relativistic two-body potential. The relativistic potential is related to the nonrelativistic potential using the Coester–Pieper–Serduke scheme, which ensures that the same scattering wave functions are obtained from the relativistic and non-relativistic potentials. This implies that the phase shifts are identical functions of the relative momentum. To construct the potential we use an iterative scheme that generalizes one that has been applied successfully to two-body systems with equal masses.     

Ab initio calculations of energy transfer and non-additivity in the He-Ne laser system

Ab initio calculations were performed for several suggested mechanisms of energy transfer between helium metastable particles and neon. Optimized geometries and excited-state energies were calculated for neon excited-state complexes and the convergence properties of the non-additive contributions to the interaction energies were examined. The most probable excitation-transfer mechanism was found to be based on an energy difference of 0.0674 eV between the triplet excited state of and the singlet excited state of . No theoretical evidence was found for the production of neon singlet excited-state complexes other than 20.0858 to 20.4875 eV by the considered two-, three- and four-body models of energy transfer processes. The energy curves of the reactions involving the excited-state complexes and are provided and compared with the previously reported experimental results on the reaction . The relation between the probability of energy transfer and laser activity is discussed. The non-additive contribution to the total interaction energy of the nominated intermediate complex was found to be negligible, pointing to the possibility of constructing model potentials and simulation of larger systems. Received: 15 December 1998 / Received in final form: 20 March 1999     

Self-consistent hartree description of finite nuclei in a relativistic quantum field theory

Relativistic Hartree equations for spherical nuclei are derived from a relativistic nuclear quantum field theory using a coordinate-space Green function approach. The renormalizable field theory lagrangian includes the interaction of nucleons with σ, ω, ρ and π mesons and the photon. The Hartree equations represent the “mean-field” approximation for a finite nuclear system. Coupling constants and the σ-meson mass are determined from the properties of nuclear matter and the rms charge radius in ⁴⁰Ca, and pionic contributions are absent for static, closed-shell nuclei. Calculated charge densities, neutron densities, rms radii, and single-nucleon energy levels throughout the periodic table are compared with data and with results of non-relativistic calculations. Relativistic Hartree results agree with experiment at a level comparable to that of the most sophisticated non-relativistic calculations to date. It is shown that the Lorentz covariance of the relativistic formalism leads naturally to density-dependent interactions between nucleons. Furthermore, non-relativistic reduction reveals non-central and non-local aspects inherent in the Hartree formalism. The success of this simple relativistic Hartree approach is attributed to these features of the interaction.     

Single-particle potential in a relativistic Hartree-Fock mean field approximation

A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucléon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucléons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor and of the fourth component of a Lorentz vector. A non-relativistic potential is derived which yields exactly the same single-particle energies and elastic scattering phase shifts as the relativistic Hartree-Fock potential. Analytical results are presented in the case of nuclear matter. A local density approximation is constructed which enables one to consider finite nuclei. The input parameters of the model can be chosen in such a way that the empirical saturation properties of nuclear matter are well reproduced. Good agreement is obtained between the calculated non-relativistic potential and the empirical value of the real part of the optical-model potential at low and at intermediate energy. At intermediate energy, the wine-bottle bottom shape which had previously been found for the potential in the framework of the relativistic Hartree approximation is maintained when the Fock contribution is included.     

Form-factor measurements on chromium with high-energy synchrotron radiation

Results of high-energy magnetic X-ray diffraction on pure antiferromagnetic chromium are presented. The temperature dependence of the propagation vector of the spin-density wave (SDW) and the strain-wave (SW) could be reproduced. The temperature dependence of the magnetic integrated intensity could be measured in the transversally as well as in the longitudinally polarised SDW phase. The magnetic form-factor has been determined in the transversally polarised SDW phase with five magnetic satellites. For the first time a spin-orbit separation has been performed by comparing X-ray to neutron data. The small orbital contribution to the magnetisation density turns out to be negligible, in agreement to our relativistic band-structure calculations. In addition, measurements of strain-wave reflections have been undertaken, and the results complement previous studies. Received 17 August 1998 and Received in final form 10 August 1999     

Intercombination transition rates in Al-like ions

N =3, intercombination transitions in Al-like ions of Au have been studied by time-resolved EUV spectroscopy of foil-excited ion beams. Wavelengths and lifetimes are compared to the available relativistic calculations. The theoretical data are found to be useful for guidance, but of clearly insufficient precision, in particular for the transition probabilities. Received: 23 February 1998 / Accepted: 5 March 1998