Full Dirac Research Articles

Symmetric, Lorentz invariant NN amplitude: Yukawa representation.

Previous work on the general representation of NN scattering amplitudes in the full Dirac space of two nucleons is extended to allow a simple realization of the generalized Pauli principle. New kinematic covariants are found which are linearly independent and which have simple particle exchange symmetries. This permits a representation in which all invariant amplitudes are even or odd with respect to interchange of initial state four-momenta or interchange of final state four-momenta for on-mass-shell kinematics. When parity invariance, charge symmetry, and time-reversal invariance are taken into consideration, it is found that for each isospin state there are 56 independent amplitudes for off-mass-shell kinematics, 50 independent amplitudes for quasipotential kinematics, and 44 independent amplitudes for on-mass-shell kinematics. A relativistic meson exchange model is used to calculate the invariant amplitudes for on-mass-shell kinematics, and the resulting amplitudes are fit by sums of Yukawa terms. The analysis provides complete sets of Feynman invariant amplitudes for 200, 500, and 800 MeV NN scattering.

Fully relativistic band structure of SmTe

The authors report the results of a fully relativistic band-structure calculation made using the KKR method for SmTe with the NaCl structure in the low-pressure phase. The exchange parameter was obtained using the free-electron approximation scaled by the exchange parameter alpha . They have solved the full Dirac equation for the interior of the muffin-tin spheres and the energies were evaluated at several symmetry points and other general points in the 1/48 wedge of the FCC Brillouin zone. The energy band indicates a gap throughout the whole BZ with excited f-type bands located below the d-type conduction band, and the indirect band gap determined by the band structure for the Gamma to X direction to be 0.67 eV in good agreement with the experimental value of 0.63 eV.

Meson theoretical basis for Dirac impulse approximation.

Basic features of proton-nucleus optical potentials for use in the Dirac equation are discussed. The original form of the Dirac impulse approximation follows from using Fermi covariants (scalar, vector, tensor, pseudoscalar, and axial vector) to extend physical NN amplitudes into operators in the full Dirac space. Overly large scalar and vector optical potentials are shown to follow at low energy in this case due to forcing pion exchange contributions to be pseudoscalar. The pair contributions to proton-nucleus scattering are much too large at low energy. A variant of the impulse approximation is developed by replacing pseudoscalar covariants by pseudovector ones. Much reduced scalar and vector strengths are obtained at low energy in the pseudovector case. The pair contributions are similarly reduced to reasonable values. However, the large differences between optical potentials based on pseudoscalar and pseudovector covariants are not controlled by physical NN scattering data. These differences represent a basic ambiguity in NN amplitudes when the only constraint is positive energy scattering data. Using a complete and unambiguous set of NN Lorentz invariant amplitudes obtained from a relativistic one-meson-exchange model, the scalar and vector optical potential strengths are found to be reasonably constant over the range of 50 to 1000 MeV of proton energy. The meson theory results for nuclear matter are found to be comparable to those obtained when the pseudoscalar covariant is replaced by the pseudovector covariant in the original impulse approximation.

Particle-hole excitations in 16O in a relativistic field theory of nuclei

Low-lying negative parity excitations in 16O are studied in an RPA calculation based on a self-consistent, relativistic Hartree ground state. The particle-hole interaction is prescribed by the underlying meson-bary on field theory, with no additional parameters. Retardation in the meson propagators is neglected, but the full Dirac matrix structure is maintained. Reasonable excitation spectra are obtained.

KKR relativistic electronic structure for SMS

The authors report results of a relativistic ab initio band-structure calculation via the KKR method for the SmS compound with the NaCl structure in the low-pressure phase. The exchange potential was taken in the free-electron Slater approximation. They have solved the full Dirac equation in the interior of the 'muffin tin' spheres. The energies were evaluated at several symmetry points and other general points in the 1/48 wedge of the FCC Brillouin zone. The energy band obtained indicates a gap throughout the whole BZ. The most excited valence bands are f-like and energetically located immediately below the conduction band. The electronic structure is discussed in terms of the proposed models for the understanding of the unusual properties of this compound.

Wave equation of symmetry constrained Dirac particles

Starting from the energy-momentum vector relationship for two observers, a multivector wave equation, which we call the full Dirac equation, is derived. It is shown to correspond to a series of symmetry constrained Dirac Fields with basic, repetitive,SU(5) structure. The consequences of the symmetry restrictions for the definition of charge, hypercharge, color, charm, etc, are discussed together with a description of the associated gauge fields.

Relativistic norm-conserving pseudopotentials

The simple procedure to extract pseudopotentials from ab initio atomic calculations introduced by Hamann, Schl\"uter, and Chiang is extended to handle the case of heavy atoms. The solutions of the full core Dirac equation are used as references, following a recent suggestion by Kleinman. As an example, results for the atoms of group IV (C, Si, Ge, Sn, Pb) are presented.

Massless Dirac particles in supercritical Coulomb fields

We consider the Dirac equation for massless particles in an external Coulomb field of vanishingly small but finite size. We show that the onset of spontaneous pair creation is signaled by the occurrence of a pole in the complex energy plane; the pole argument is directly related to the point-Coulomb pair-creation probability. We also consider spontaneous pair creation in the framework of an approximate uncoupled Dirac equation, and we discuss its connection with the description of pair creation by means of the full Dirac equation.

Effective core potentials for fully relativistic Dirac–Fock calculations

A fully relativistic effective core potential method has been developed for use in the valence-only Dirac–Fock self-consistent-field calculations for atoms and molecules. The effective potentials are constructed so that the atomic valence-only Dirac–Fock calculations reproduce the energies and the outer region of the corresponding valence spinors obtained from the full Dirac–Fock SCF calculations.

Relativistic palladium electronic structure

We report here an “ab initio” relativistic KKR (1) electronic structure calculation for Pd metal in the fcc phase. The energies were evaluated in 89 points in the 1/48 wedge of the Brillouin Zone. The present results are in agreement with those obtained by Mueller et al (2) who treated the spin-orbit coupling as the principal relativistic effect. As it is explained below we have solved the full Dirac equation in the interior of the “muffin-tin” spheres. At the same time we have made use of the symmetry in order to reduce the calculation time. The relativistic version of the KKR method has proved to be a very efficient tool for investigating the band structure since energies are calculated by solving very small secular determinants.