Relativistic Hartree-Fock Calculations Research Articles

Relativistic interactions and realistic applications

A four-fermion coupling Lagrangian (relativistic Skyrme-type) interaction has been proposed for relativistic nuclear structure calculations. This interaction which has the merit of simplicity is from the outset tailored as an effective interaction for relativistic Hartree-Fock calculations. Various extensions of such a model are discussed and compared with Walecka's meson-nucleon mean field approach. We also present results of the calculation of nuclear ground state properties with an extended (density dependent) version of the four-fermion interaction in a relativistic Hartree-Fock approximation.

Wavelengths of neon-like 3p → 3s X-ray laser transitions

This paper presents the wavelengths of the neon-like 3p → 3s laser lines which have been observed in both lasing and nonlasing plasmas and compares the experimental wavelengths with relativistic multi-configuration Hartree-Fock calculations in order to estimate the wavelengths for these lines in all neon-like ions between S6+ and Xe44+. The seven 3p → 3s transitions which have been observed to lase in some neon-like ions are considered in this work.

Systematic relativistic Hartree-Fock calculation of deformed nuclei in s-d shell.

A systematic study of even-even deformed nuclei in [ital s]-[ital d] shell is performed in the QHD framework by using relativistic Hartree-Fock calculations. The exchange of [sigma], [omega], [rho], and [pi] mesons and photons are included, the parameters of the model (meson masses and coupling constants) adopted are from an earlier least-squares fit to finite nuclear ground-state properties. We compare to the results of a similar calculation using parameters adjusted to fit the nuclear matter saturation data. We found great improvement in the total binding energy, however the deformation pattern is essentially not changed; for closed subshell nuclei we still find that the ground state favors a spherical solution. A well-defined constant Fermi surface in the [ital s]-[ital d] shell is obtained which is consistent with the experiment observation. The results are also compared to the corresponding relativistic Hartree calculations.

Observations of doubly excited states in lithiumlike calcium.

We report observations of simultaneous electron excitation and electron capture in ion-atom collisions of 97-MeV ${\mathrm{Ca}}^{18+}$ and ${\mathrm{Ca}}^{19+}$ in an argon gas target. X-ray spectra at energies near 3.9 keV were collected using a high-resolution x-ray spectrometer. We have resolved transitions from doubly excited 1s2l2l' and 1s2l3l' states to singly excited 1${\mathit{s}}^{2}$2l' and 1${\mathit{s}}^{2}$3l' states in lithiumlike calcium. The observed transitions lie at energies close to the 1s2s-1s2p resonance transitions in heliumlike calcium. We compare the experimental wavelengths and intensities with relativistic Hartree-Fock calculations, and discuss the excitation mechanisms.

From nuclear matter to finite nuclei. I. Parametrization of the Dirac-Brueckner G matrix.

In this paper we develop various parametrizations of the nuclear matter Dirac-Brueckner G matrix, which are suitable for application in relativistic Hartree-Fock calculations of finite nuclei. The. relativistic one boson exchange model forms the basis of this effective interaction. The parameters, which are obtained from a least squares fit, explicitly depend on the density. We also require the interaction to reproduce the self-energies and the binding energy of nuclear matter very accurately. It is shown that for densities up to 1.5 times normal nuclear density the saturation curve virtually coincides with the original Dirac-Brueckner result and yields a good prediction of the nuclear matter compressibility.

Quantum hadrodynamics parametrization: A least-squares fit to nuclear ground-state properties.

We study the four meson masses and coupling constants used in quantum hadrodynamics by comparing the relativistic Hartree-Fock calculation with nuclear ground-state properties. Six parameters are determined by least-squares fit to experimental ground-state properties of five spherical nuclei $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$; these properties are total binding energies, charge radii, and surface thicknesses. This work is compared with an earlier relativistic Hartree least-squares fit. We find that by including exchange terms, the best-fit meson masses are within 3% of their physical values, which is not the case if only direct terms are used. Both calculations reproduce binding energies and radii with an average error around 1%. Hartree-Fock values for the nuclear surface thickness are a substantial improvement (around 15%); however, both calculations consistently produce too small a value.

Levels of the 4p4 configuration of Ge-like Kr V.

The spectrum of four-times-ionized krypton, Kr v, has been observed in the vuv region using a \ensuremath{\theta}-pinch as a light source. The 4s4${\mathit{p}}^{3\mathrm{\ensuremath{-}}}$4${\mathit{p}}^{4}$ transition array has been observed in this ion. This transition has not previously been observed in the Ge i isoelectronic sequence. Thirteen lines were classified that belong to this transition array. All levels of the 4${\mathit{p}}^{4}$ configuration were determined. The identifications are supported by relativistic Hartree-Fock calculations.

Ab-initio nonrelativistic and relativistic Hartree-Fock calculations for both closed- and open-shell molecules using GTO basis

Computer programs forab-initio Hartree-Fock and Dirac-Hartree-Fock calculations on closed- and open-shell atoms and molecules have been indigenously developed. Sample results of high quality are given for Li, Be, LiH and Be2. As a byproduct of these calculations the importance of considering relativistic effects in the investigation of the elusive bound-state structure of Be2 is clearly indicated.

Relativistic effects on the Compton profile of polycrystalline gold

The spherically averaged Compton profile (CP) for gold in calculated on the basis of the relativistic density-functional theory in the local-density approximation (LDA) with a warped muffin-tin potential. In the all-electron self-consistent procedure, the core levels are calculated by means of the Dirac operator while the valence levels are determined by a relativistic generalization of the modified augmented plane-wave (MAPW) method using the reduced 2*2 matrix Hamiltonian according to Foldy and Wouthuysen. The CPs of the core electrons are found to be in surprisingly good agreement with the orbital CPs of the relativistic Hartree-Fock calculation for atomic gold by Biggs et al. The relativistic corrections on the valence CP due to mass-velocity and the Darwin term are investigated separately and comparisons with non-relativistic calculations are made.

The Electron Momentum Distribution in Lead

Abstract Directional Compton profiles have been measured along the [100], [110] and [111] crystallographic axes in lead using 412 and 59.5 keV γ-radiation from 198 Au and 241 Am radioisotope sources, respectively. Both measurements are in mutual agreement and show a small anisotropy, which is just distinguishable within the statistical error. The spherically averaged data have been compared with the predictions of relativistic Hartree-Fock (RHF) and non-relativistic Hartree-Fock (HF) free atom calculations. As expected, the experiment clearly favours the RHF rather than the HF calculation.

Relativistic temperature-dependent Hartree-Fock calculation of spherical nuclei.

The temperature-dependent Hartree-Fock approach is extended to the relativistic quantum-field-theory framework; exchange of \ensuremath{\sigma}, \ensuremath{\omega}, \ensuremath{\rho}, and \ensuremath{\pi} mesons and photons are included. Application is made to two spherical nuclei, $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$. Temperature dependences of excitation energies, single-particle spectra, charge densities, and entropies are evaluated and compared to corresponding nonrelativistic calculations. We find a considerably larger thermal response for these nuclei when compared to the nonrelativistic results.

Energies of nickel-like 4d to 4p laser lines

Relativistic multi-configuration Hartree-Fock calculations have been carried out for the energies of the nickel-like 4d to 4p X-ray lines which are potential lasing lines. Measurements of a set of these transition energies have also been made. Predicted wavelengths, covering the range of atomic numbers from Z = 46-92, have been derived by adjusting the ab initio energies by experimentally derived empirical constants.

Relativistic compact effective potentials and efficient, shared-exponent basis sets for the third-, fourth-, and fifth-row atoms

Relativistic compact effective potentials (RCEP), which replace the atomic core electrons in molecular calculations, have been derived from numerical Dirac–Fock atomic wavefunctions using shape-consistent valence pseudo-orbitals and an optimizing procedure based on an energy-overlap functional. Potentials are presented for the third-, fourth-, and fifth-row atoms of the Periodic Table (excluding the lanthanide series). The efficiency of molecular calculations is enhanced by using compact Gaussian expansions (no more than three terms) to represent the radial components of the potentials, and energy-optimized, shared-exponent, contracted-Gaussian atomic orbital basis sets. Transferability of the potentials has been tested by comparing calculated atomic excitation energies and ionization potentials with values obtained from numerical relativistic Hartree–Fock calculations. For the alkali and alkaline earth atoms, core polarization potentials (CPP) have been derived which may be added to the RCEP to make possible accurate molecular calculations without explicitly including core-valence correlating configurations in the wavefunction. Keywords: model potentials, effective core potentials, transition metals, relativistic calculations.

Nucleon and isobar properties in a relativistic Hartree–Fock calculation with vector Richardson potential and various radial forms for scalar mass terms

Mean-field models of the nucleon (N) and the delta (Δ) are established with the two-quark vector Richardson potential along with various prescriptions for a running quark mass (single particle) in the Dirac–Hartree–Fock formalism. The N–Δ splitting is obtained from colour magnetic interaction and the results for gA and the magnetic moment are discussed. An effective density dependent one-body potential U(ρ) for quarks at a given density ρ inside the nucleon is derived. Asymptotic freedom and confinement properties are built-in in U(ρ) and the model dependence is restricted to the intermediate densities.

Spin polarization of electrons elastically scattered from krypton

Spin-polarization parameters S, T and U are calculated for electrons elastically scattered by krypton atoms at energies from 3-150 eV. The target atom is represented by a frozen core in a continuum relativistic Hartree-Fock calculation with dipole and quadrupole polarization corrections. Because these corrections are applied to the target electrons as well as to the scattered electron, all electrons experience the same interactions and the scattering wavefunction is automatically orthogonal to the target orbitals. Cut-off parameters in the model polarization potential are obtained from independent calculations. The exchange connected with the electrostatic and polarization interactions is calculated exactly for both large and small components of the scattered wavefunction. The spin polarization S is compared with available experimental and theoretical results.

Relativistic Hartree-Fock calculation of deformed nuclei.

Hartree-Fock calculations are performed for deformed nuclei {sup 20}Ne, {sup 24}Mg, and {sup 28}Si in the relativistic quantum-field-theory framework, the exchange of {sigma}, {omega}, {rho}, and {pi} mesons and photons are included, the coupling constants are adopted from relativistic Hartree-Fock nuclear-matter calculation. Compared to the Hartree results, binding energies are improved by around 8%; however, no appreciable improvement on the quadrupole moments is observed.

Photoexcitation of the inner 3d electron in As i

The photoabsorption spectrum that is due to the inner 3d-subshell excitation of atomic arsenic was photographed in the 400–200-Å region, using the flash-pyrolysis technique. With the help of relativistic Hartree–Fock calculations and least-squares fitting programs, 19 lines were ascribed to transitions from the ground state to the 3d94s24p4 configuration and 20 lines to transitions to the 3d94s24p3np (n = 4–8) configurations. Two series limits were estimated as 403 600 cm−1 (50.0 eV) and 410 600 cm−1 (50.9 eV).

Renormalized relativistic Hartree Fock models with skyrme type interactions

A manifestly nonrenormalizable effective Lagrangian with four fermion coupling is proposed for relativistic Hartree Fock calculations. A consistent scheme for the inclusion of the Dirac sea is described in detail. It is briefly compared with other field theoretic models commonly used in nuclear physics.

Low-energy elastic scattering of positrons on argon.

Elastic scattering of positrons from argon has been calculated for incident-positron energies of up to 300 eV. The target atom is represented by a frozen core in a continuum relativistic Hartree-Fock calculation with dipole- and quadrupole-polarization corrections. The cutoff parameter ${r}_{0}$ is fitted to reproduce measured values of the scattering length. Scattering lengths near -4 a.u. give good agreement of the calculations with recent measurements of total, differential, and momentum-transfer cross sections below 3 eV. Relativistic and positron-polarization effects are found to be much smaller than for electrons. The relativistic effects are dominated by the relativistic contraction of the target atom.

Ab initio Hartree-Fock band structures of different lead surfaces using effective potentials

The energy band structures of single layered Pb(100)-, Pb(110)- and Pb(111)-surfaces are calculated using the ab initio Hartree-Fock formalism with non-local exchange. The core electrons are replaced by effective core potentials generated from relativistic Hartree-Fock calculations. We show that the method gives a promising way how to treat surfaces containing heavy atoms on the Hartree-Fock level. Additionally, in the case of Pb(100) we have investigated a three layered system. We have found a stabilization by 0.758 eV per atom with respect to the single layer.