Relativistic Local Density Approximation Research Articles

Electronic K x rays emitted from muonic atoms: An application of relativistic density-functional theory

We develop a method using relativistic density-functional theory with a self-interaction correction, which is simple and fast yet has reasonable accuracy. A comparison with measured $K\ensuremath{\alpha}$ lines and their hypersatellites of several atoms, from low $Z$ to high $Z$, reveals that the relativistic local density approximation is suitable for $K\ensuremath{\alpha}$ lines. In contrast, the relativistic local spin density approximation with a self-interaction correction is better for ${K}^{h}\ensuremath{\alpha}$ hypersatellites. Compared with the nonrelativistic density-functional theory, we found that the relativistic effect is significant (about 100 eV) even for middle-$Z$ atoms, such as Cu. The screening effects, from inner shell to outer shell, and the conduction band, are also discussed. The present paper provides all the transition lines of muonic atoms, which can be used to narrow down the possible transitions by comparing them with the measurements.

Slater approximation for Coulomb exchange effects in nuclear covariant density functional theory

The relativistic local density approximation (LDA) for the Coulomb exchange functional in nuclear systems is presented. This approximation is composed of the well-known Slater approximation in the non-relativistic scheme and the corrections due to the relativistic effects. Its validity in finite nuclei is examined by comparing with the exact treatment of the Coulomb exchange term in the relativistic Hartree-Fock-Bogoliubov theory. The relativistic effects are found to be important and the exact Coulomb exchange energies can be reproduced by the relativistic LDA within 5% demonstrated by the semi-magic Ca, Ni, Zr, Sn, and Pb isotopes from proton drip line to neutron drip line.

Nuclear effective charge factor originating from covariant density functional theory

Guiding by the relativistic local density approximation, we explore a phenomenological formula for the coupling strength of Coulomb field to take into account the Coulomb exchange term effectively in the relativistic Hartree approximation. Its validity in finite nuclei is examined by comparing with the exact treatment of the Coulomb exchange energies in the relativistic Hartree-Fock-Bogoliubov approach. It is found that the exact Coulomb exchange energies can be reproduced by employing the phenomenological formula with the relative deviations less than 1% for semi-magic Ca, Ni, Sn, and Pb isotopes. Furthermore, we check the applicability of the phenomenological formula for the effective interactions in the relativistic Hartree approach by investigating the binding energy differences of mirror nuclei.

Magnetic anisotropy ofR2Fe14B(R=Nd, Gd, Y): Density functional calculation by using the linear combination of pseudo-atomic-orbital method

The magnetocrystalline anisotropy energy (MAE) of rare-earth transition-metal intermetallics ${R}_{2}{\text{Fe}}_{14}\text{B}$ ($R=\text{Nd}$, Gd, Y) was calculated by using the linear combination of pseudo-atomic-orbital method. Electronic structures were calculated by using relativistic density functional theory with Hubbard-type on-site Coulomb potential $U$ for $f$ electrons in the $R$ sites. The calculated magnetic moments of ${\text{Y}}_{2}{\text{Fe}}_{14}\text{B}$ and ${\text{Gd}}_{2}{\text{Fe}}_{14}\text{B}$ are in agreement with the experimentally measured saturation moments of these compounds. The calculated MAEs of ${\text{Y}}_{2}{\text{Fe}}_{14}\text{B}$ and ${\text{Gd}}_{2}{\text{Fe}}_{14}\text{B}$ are also in agreement with the value measured at low temperature. Moreover, it was found that the shape of the charge density at the Nd sites is aspherical, which causes larger MAE of ${\text{Nd}}_{2}{\text{Fe}}_{14}\text{B}$ than that of ${\text{Gd}}_{2}{\text{Fe}}_{14}\text{B}$. However, the orbital moment of the $4f$ electrons at the Nd sites and the MAE of ${\text{Nd}}_{2}{\text{Fe}}_{14}\text{B}$ were underestimated within the scope of a relativistic local-density approximation plus $U$ with spherical average potential.

Analytical energy gradients in four-component relativistic density-functional theory

We report on the implementation and application of analytical energy gradients in four-component relativistic density-functional theory. Comparisons with numerical gradients for heavy diatomic molecules show good agreement. Results of geometry optimizations within the relativistic local-density approximation on heavy-element compounds are presented.

Dispersion of 5felectron states: Angle-resolved photoemission on ordered films of U metal

Ordered overlayers of U metal characterized by a hexagonal low-energy electron diffraction pattern were grown in situ by deposition of U metal onto a W(110) substrate and subsequent annealing. Angle-resolved photoemission reveals clearly dispersion of U $5f$-derived states. The experimental data are in excellent agreement with results of relativistic local density approximation band-structure calculations. The bandlike properties of the U $5f$ states stem from direct $f\ensuremath{-}f$ interaction rather than from $f\ensuremath{-}d$ hybridization as might be expected for $4f$-derived bands in Ce systems.

Approximate relativistic optimized potential method

Approximate semianalytical solutions of the integral equation for the relativistic optimized potential are constructed by extending a method recently proposed by Krieger, Li, and Iafrate Phys. Lett. A 146, 256 1990 to the relativistic regime. The quality of the approximation is tested in the longitudinal x-only limit where fully numerical solutions of the relativistic optimized effective potential integral equation are available for spherical atoms. The results obtained turn out to be in excellent agreement with the exact x-only values. The proposed method provides significant improvement over the conventional relativistic local density approximation and generalized gradient approximation schemes. S1050-2947 97 04912-3

Local-density-functional calculations of the energy of atoms

The total energies of atoms and with atomic number Z from 1 to 92 and singly charged cations with Z from 2 to 92 have been calculated to an accuracy of 1 \ensuremath{\mu}hartree within four variants of the Kohn-Sham local-density approximation (LDA). The approximations considered are the local-density approximation, the local-spin-density approximation, the relativistic local-density approximation, and the scalar-relativistic local-density approximation. The total energies for the LDA are found to be in 0.1% agreement with a large atomic number expansion from many-body theory for Z\ensuremath{\geqslant}40. A comparison to experiment is made for the ionization energies and spin-orbit splittings; also the total energies and eigenvalues of the various theories are compared among themselves.

Heavy-ion interactions in relativistic mean-field models

Abstract The interaction potential between spherical nuclei and the elastic scattering cross section are calculated within relativistic mean-field (linear and non-linear) models, using a generalized relativistic local density approximation. The nuclear densities are calculated self-consistently from the solution of the relativistic mean-field equations. It is found that both the linear and non-linear models predict the characteristic switching-over phenomenon of the heavy-ion nuclear potential, where the potential gets attraction with increasing energy up to some value where it reverses this behaviour. The non-linear NLC model predicts a deeper potential than the linear LW model. The elastic scattering cross section calculated within the non-linear NLC model is in better agreement with experiments than that calculated within the linear LW model.

Orbital and spin-orbit magnetic susceptibilities in face-centred cubic transition metals and noble metals

The uniform unenhanced orbital and spin-orbit susceptibilities, chi O and XSO, respectively, in Ni, Pd and Pt are evaluated by taking numerical extrapolations to q=0 of previous expressions for the wavenumber (q)-dependent orbital and spin-orbit susceptibilities, chi O(q) and chi SO(q), respectively. The wavefunctions and energies required in these calculations are obtained from self-consistent relativistic APW band calculations in the relativistic local-density approximation. From a study of trends in chi O and chi SO with the number of conduction electrons per atom ratio for FCC 3d, 4d and 5d metal series, chi O and chi SO in Rh, Ir, Cu, Ag and Au are estimated in the rigid-band assumption with reasonable corrections. For all these metals, the values of chi O+ chi SO show good agreement with empirical values. By using previously reported theoretical values of the enhanced spin susceptibility Ichi S, the total susceptibility chi =Ichi S+( chi o+ chi SO) is estimated and compared with observed results for these metals.

Orbital and spin-orbit magnetic susceptibilities in bcc transition metals: V, Nb and W

The uniform unenhanced orbital and spin-orbit susceptibilities in Nb and W are evaluated by using wavefunctions and energy values obtained from self-consistent relativistic APW band calculations in the relativistic local-density approximation. From the calculated value of the enhanced spin susceptibility the total susceptibility is estimated for Nb. The estimated value is very similar to the observed values. The dependence on the electron per atom ratio of the uniform unenhanced orbital and spin-orbit susceptibilities is calculated in the rigid band assumption and the results are compared with each other. The corresponding results obtained previously for V are also shown for comparison. Energy curves and density of states curves for V, Nb and W are presented.

Relativistic formulae for the wavevector-dependent magnetic susceptibilities and the numerical calculation of the orbital and spin-orbit magnetic susceptibilities in vanadium

From a relativistic treatment based on the Dirac equation, the wavevector-dependent magnetic susceptibility is expressed as the sum of three terms. Two of them, chi s(q) and chi o(q) (q being the wavevector), reduce to the well known expressions for the q-dependent spin and orbital susceptibilities, respectively, in the non-relativistic limit. The other term chi so(q) arises as a higher-order term and represents the q-dependent spin-orbit susceptibility. The uniform unenhanced orbital and spin-orbit susceptibilities chi o and chi so are derived as the q to 0 limit of chi o(q) and chi so(q), respectively. A self-consistent relativistic APW band-structure calculation is carried out in the relativistic local-density approximation for vanadium at the observed lattice constant 5.713 au. By making use of this result of the band calculation, chi o(q) and chi so(q) at small q are calculated and the values of chi o and chi so are obtained as 199.4 and -5.2*10-6 EMU mol-1, respectively. With a proper estimation of the enhanced spin susceptibility chi s', the total susceptibility chi =chi s'+chi so+ chi o and its volume dependence are estimated and the results are in reasonable agreement with the experimental results.

Space-like field in a relativistic local density approximation

We calculate the local space-like component of the relativistic nucleon-nucleus potential from nuclear matter results via a local density approximation. This component seems too small to remove the discrepancy between calculated and measured magnetic moments of nuclei.

Application of the relativistic local-density approximation to photoionization of the outer shells of neon, argon, krypton, and xenon

Parameters describing the low-energy photoionization of the outer shells of the rare gases Ne, Ar, Kr, and Xe have been calculated using a relativistic generalization of the time-dependent local-density approximation. The resulting photoionization cross sections, angular-distribution asymmetry parameters, and spin polarization parameters are presented here. The results are found to be in good agreement with those from the relativistic random-phase approximation (RRPA), even though the present theory is simpler, formally and computationally, than the latter. These results, and those of the RRPA, are generally in good agreement with experiment, illustrating the utility of the present approach to photoionization, especially for heavy atoms in which both relativistic and correlation effects are important.

The relativistic time-dependent local-density approximation

The relativistic time-dependent local-density approximation (RTDLDA), a time-dependent generalisation of the relativistic local-density approximation (RLDA), is presented in a form suitable for the description of electric multipole excitation of closed-shell atomic systems. The development of the theory from the relativistic density functional formalism is outlined. A discussion is given of the angular decomposition of the RLDA and RTDLDA equations to those for the radial wavefunctions. Results of applications of this theory to calculations of atomic photoionisation parameters for xenon and electric dipole susceptibilities for various heavy atoms are compared with predictions of other theories and with experimental measurements.

Polarizabilities of heavy closed-shell atoms from the relativistic local density approximation

Static polarizabilities of various closed-shell atoms are calculated using linear response theory in the relativistic local density approximation, with special attention to atoms of high nuclear charge. For atoms with closed outer np subshells the resulting values are found to be in good agreement with other determinations. For atoms with closed outer ns subshells the present values are considerably smaller than those from relativistic random-phase approximation calculations and in better agreement with recommended values.