Relativistic Green Research Articles

Relativistic central-field Green's functions for the Ratip package

From perturbation theory, Green’s functions are known for providing a simple and convenient access to the (complete) spectrum of atoms and ions. Having these functions available, they may help carry out perturbation expansions to any order beyond the first one. For most realistic potentials, however, the Green’s functions need to be calculated numerically since an analytic form is known only for free electrons or for their motion in a pure Coulomb field. Therefore, in order to facilitate the use of Green’s functions also for atoms and ions other than the hydrogen-like ions, here we provide an extension to the R ATIP program which supports the computation of relativistic (one-electron) Green’s functions in an—arbitrarily given—central-field potential V(r). Different computational modes have been implemented to define these effective potentials and to generate the radial Green’s functions for all bound-state energies E< 0. In addition, care has been taken to provide a user-friendly component of the RATIP package by utilizing features of the Fortran 90/95 standard such as data structures, allocatable arrays, or a module-oriented design. Program summary

Relativistic Green's function approach to parity-violating quasielastic electron scattering

A relativistic Green's function approach to parity-violating quasielastic electron scattering is presented. The components of the hadron tensor are expressed in terms of the single-particle Green's function, which is expanded in terms of the eigenfunctions of the non-Hermitian optical potential, in order to account for final state interactions without any loss of flux. Results for 12C, 16O, and 40Ca are presented and discussed. The effect of the strange quark contribution to the nuclear current is investigated.

Angular correlations in the two-photon decay of hydrogenlike ions: Relativistic Green’s-function approach

The angular correlations in the two-photon decay of hydrogenlike ions are studied within the framework of second-order perturbation theory, based on Dirac's equation. Particular attention has been paid to the effects which arise from the higher (nondipole) terms in the expansion of the electron-photon interaction. It is shown that the photon-photon angular correlation function, which is found symmetric with respect to the angle $\ensuremath{\theta}=90\ifmmode^\circ\else\textdegree\fi{}$ in the electric dipole approximation, becomes asymmetric because of the nondipole contributions, and that this effect is enhanced as the nuclear charge $Z$ increases. Detailed computations on the photon-photon angular distribution have been carried out for the $2{s}_{1∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ and $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transitions in neutral hydrogen (H) as well as for hydrogenlike xenon $({\mathrm{Xe}}^{53+})$ and uranium $({\mathrm{U}}^{91+})$ ions, and are compared with previous nonrelativistic results by Au [Phys. Rev. A 14, 531 (1976)]).

Relativistic Green's function approach to charged-current neutrino–nucleus quasielastic scattering

A relativistic Green's function approach to inclusive quasielastic charged-current neutrino–nucleus scattering is developed. The components of the hadron tensor are written in terms of the single-particle Green's function, which is expanded on the eigenfunctions of the nuclear optical potential, so that final state interactions are accounted for by means of a complex optical potential but without a loss of flux. Results for the ( ν μ , μ −) reaction on 16O and 12C target nuclei are presented and discussed.

Magnetic dichroism in valence-band photoemission from Co/Cu(001): Experiment and theory.

Ferromagnetic Co films on Cu(001) have been investigated both experimentally and theoretically by photoemission from valence bands with unpolarized 21.2 eV radiation. The measured spectra exhibit sizable magnetic dichroism and are well reproduced by their counterparts calculated by means of a fully relativistic Green's function method. Prominent intensity maxima can be attributed to direct bulk interband transitions. Magnetic dichroism with unpolarized light is explained by the interplay of exchange splitting with a spin-orbit-induced spin-polarization effect for off-normally incident p-polarized light. Experiment and calculations further give evidence that in Co films on Cu(001) prepared at elevated temperatures (400 K), Cu has diffused to the top of the film. \textcopyright{} 1996 The American Physical Society.

Collective excitations of the QED vacuum.

Using relativistic Green's-function techniques we examined single-electron excitations from the occupied Dirac sea in the presence of strong external fields. The energies of these excited states are determined taking into account the electron-electron interaction. We also evaluate relativistic transition strengths incorporating retardation, which represents a direct measure of correlation effects. The shifts in excitation energies are computed to be lower than 0.5%, while the correlated transition strengths never deviate by more than 10% from their bare values. A major conclusion is that we found no evidence for collectivity in the electron-positron field around heavy and superheavy nuclei.

THEORETICAL AND EXPERIMENTAL INVESTIGATION OF THE MAGNETIC X-RAY DICHROISM IN DILUTED AND CONCENTRATED TRANSITION METAL ALLOYS

By combining the Coherent Potential Approximation with the spin polarized relativistic Korringa-Kohn-Rostoker method of band structure calculation it got possible to describe the electronic structure of disordered magnetic alloys in a fully relativistic way. This new development allowed us to extend our theoretical description of the magnetic X-ray dichroism (MXD), which is based on the spin polarized relativistic Green's function formalism, to deal not only with pure and impurity systems but also with this interesting class of materials. We demonstrate this by calculations of K- and L-edge MXD spectra in the alloy systems FexCo1−x, CoxPt1−x and FexPt1−x, which are found in a very satisfying agreement with corresponding experimental data. In addition the relationship of the integrated MXD-spectra with the calculated spin magnetic moments is discussed in short.

Au-induced surface state on Pt(111) revealed by spin-resolved photoemission with linearly polarized light.

Photoelectrons ejected by normally incident linearly polarized He i radiation and emitted normal to epitaxial Au layers on Pt(111) are strongly spin polarized for both emission from the Pt substrate and the Au adsorbate up to 2.2 layers coverage. Relativistic Green's-function calculations reproduce the measured data and reveal the physical origin of the polarization for a monolayer Au coverage to be a Au-induced surface state. The spin polarization is significantly influenced by the underlying Pt bulk and is thus a sensitive measure of the Au adsorption site.

Calculation of Dipole Transition Matrix Elements in Crystals by the Relativistic Green's Function Method

AbstractAn analog of Green's theorem for the Dirac operator is obtained, which allows to reduce the integration over the outer part of the Wigner‐Seitz cell volume to that through the muffin‐tin sphere surface. Within the relativistic variant of the Green's function method, matrix elements of the velocity operator are computed in the veritable relativistic and c → ∞ cases. A comparison is made with the momentum matrix elements calculated by the nonrelativistic technique.

High-energy Delbruck scattering at large angles

An expression for the high-energy Delbruck amplitude at large scattering angles is derived. This expression is exact in the parameter Z alpha . The consideration is based on the use of the relativistic electron Green's function in a Coulomb field.

Nuclear matter problem in the relativistic Green's function approach.

In this paper we present the theory of nuclear matter in the framework of relativistic nuclear field theory utilizing the technique of relativistic many-body Green's functions. The analytic properties of the Green's functions and related quantities are given and used to obtain the final set of equations for the nuclear matter problem. In detail, we have investigated theoretically and numerically the so-called ..lambda../sup 00/ and ..lambda../sup 10/ approximations. For comparison we also calculated the relativistic Hartree-Fock and the Brueckner-Hartree-Fock approximation, respectively. For masses and coupling strengths we used (phenomenological) parameter sets given by the Bonn and Groningen group. The results of the ..lambda.. approximations are similar to the relativistic Brueckner treatment.

Spinor fields in an Einstein universe: Finite-temperature effects

The finite-temperature corrections to the vacuum energy density of scalar, neutrino, and photon fields in an Einstein universe are calculated by using the statistical-mode-sum technique with the aid of the Poisson summation formula. The theory of relativistic time-temperature Green's functions in static space-time is also considered and used to calculate the temperature correction to the neutrino-field vacuum energy density. Asymptotic limits of low and high temperature are discussed for each case.

Relativistic Green's-function method for solids and molecules

The relativistic multiple-scattering method (Green's-function method) for crystals and molecules is developed from the definition of the four-component wave function in the two regions. The secular equation is obtained by matching the wave functions at the two sides of the sphere surface separating the two regions. The secular equation is expanded in powers of $\frac{1}{{c}^{2}}$ so as to exhibit the mass and spin-orbit corrections. As an application of the method we present the results for the band structure of lead.

K · p parameters for HgSe based on a relativistic energy band calculation

AbstractFor HgSe the k · p parameters of Kane's theory have been derived from energy bands calculated by means of the relativistic Green's function (KKR) method. They compare reasonably with published experimental data.

Relativistic Green's-function approximation to the low-energy nucleon-nucleon interaction

From a unitary approximation to the nucleon-nucleon Green's function we derive the phase shifts for the Yukawa model and the nonlinear $\ensuremath{\sigma}$ model. The results agree with the experimental data except for the lowest waves: $^{1}S_{0}$, $^{3}S_{1}$, $^{3}P_{0}$ where, however, we get good scattering lengths.

Relativistic Green's-function electron-diffraction theory

A relativistic electron-diffraction theory is presented, which solves the Dirac equation by the Green's-function method and incorporates spin polarization. For muffin-tin potentials, the reflection coefficient of a beam scattered elastically from either unpolarized or polarized incident electrons is very similar to that of its nonrelativistic counterpart. The atomic properties are included in the relativistic phase shifts. The geometric structure constants are related to the nonrelativistic structure constants. The polarization of the scattered electrons is analyzed by the density matrix. The relation between this theory and the nonrelativistic one is discussed. The exact reflection coefficient is suitable for the calculation of diffraction intensities of low-energy incident electrons from heavy-atomic-crystal surfaces. A pseudokinematic theory, which may be useful for incident energies up to several keV, is obtained by taking the first-order approximation.

Energy Bands of Potassium Halides (Green's Function Method)

AbstractThe energy bands of KCl, KBr, and KI have been calculated using the relativistic Green's function (KKR) method. Besides the results of calculations with atomic potentials for KCl, KBr, and KI results for KI from ionic potentials with Kohn‐Sham and Slater exchange potentials are also compared. Special care is taken to interpret the excitonic structure of KI in terms of band separations. For this purpose extreme ultraviolet data are used to confirm the interpretation.

Relativistic Energy Bands of HgTe and HgSe

AbstractThe electronic band structures of HgTe and HgSe have been calculated using the relativistic Green's function method. The results are compared to reflectivity data. Particular care was taken to calculate the details of the band structure in the vicinity of the band gap. A valence band overlap is found which is in agreement with the estimate given by Vérié.

Electronic Structure of PbS, PbSe, and PbTe

AbstractThe electronic band structures of PbS, PbSe, and PbTe have been calculated using the relativistic Green's function method. The choice of a relativistic atomic potential for Pb and of nonrelativistic atomic potentials for S, Se, and Te inthe muffin‐tin spheres results in similar band models for the lead salts. Thus a nearly uniform interpretation of experimental data for these materials can be presented. A good agreement of calculated band separations with results from reflectivity, electroreflectance, and photoemission measurements is achieved.

Energy Bands of CsI (Green's Function Method)

AbstractEnergy bands of CsI in the s.c. and f.c.c. modification have been calculated using the full relativistic Green's function method. Results for ionic and atomic potentials are presented. The splitting of d‐like conduction bands, which is characteristically different in both crystal modifications, is explained by tight‐binding considerations. The binding energy of the Γ8− – Γ6+ excition turns out to be about 30% larger in f.c.c. than in s.c. CsI. The calculated band separations and deformation potentials for hydrostatic pressure are in good agreement with experimental results.