One-electron Contribution Research Articles

Radiative and photon-exchange corrections to new-physics contributions to energy levels in few-electron ions

The influence of hypothetical new interactions beyond the Standard Model on atomic spectra has attracted recent interest. In the present work, interelectronic photon-exchange corrections and radiative quantum electrodynamic corrections to the hypothetical contribution to the energy levels of few-electron ions from a new interaction are calculated. The $1s$, $2s$ and $2p_{1/2}$ ground states of H-like, Li-like and B-like ions are considered, as motivated by proposals to use isotope shift spectroscopy of few-electron ions in order to set stringent constraints on hypothetical new interactions. It is shown that, for light Li-like and B-like ions, photon-exchange corrections are comparable to or even larger, by up to several orders of magnitude, than the leading one-electron contribution from the new interaction, when the latter is mediated by heavy bosons.

Nuclear recoil effect on the g factor of highly charged Li-like ions

The nuclear recoil effect on the g factor of highly charged Li-like ions is evaluated in the range Z=10-92. The calculations are performed using the 1/Z perturbation theory. The one-electron recoil contribution is evaluated within the fully relativistic approach with the wave functions which account for the screening effects approximately. The two-electron recoil contributions of the first and higher orders in 1/Z are calculated within the Breit approximation using a four-component approach.

Nuclear recoil effect on the binding energies in highly charged He-like ions

The most precise to-date evaluation of the nuclear recoil effect on the n = 1 and n = 2 energy levels of He-like ions is presented in the range Z = 12–100. The one-electron recoil contribution is calculated within the framework of the rigorous quantum electrodynamics approach to first order in the electron-to-nucleus mass ratio m/M and to all orders in the parameter αZ. The two-electron m/M recoil term is calculated employing the 1/Z perturbation theory. The recoil contribution of the zeroth order in 1/Z is evaluated to all orders in αZ, while the 1/Z term is calculated using the Breit approximation. The recoil corrections of the second and higher orders in 1/Z are taken into account within the nonrelativistic approach. The obtained results are compared with the previous evaluation of this effect (Artemyev et al 2005 Phys. Rev. A 71 062104).

Anomalous Lattice Properties of Manganese Monosilicide: the Thermodynamic Approach

The temperature dependences of the thermal and elastic MnSi properties are analyzed within the limits of the self-consistent approach. The role of the anharmonicity of acoustic and optical lattice vibrations is analyzed. It is demonstrated that anomalously weak anharmonicity is characteristic for acoustic phonons. In particular, this explains the temperature dependence of the MnSi bulk compressive modulus. The one-electron contribution is estimated and the anomalous non-lattice contribution to the formation of the temperature dependences of heat capacity and volume thermal expansion coefficients.

Recoil Effect on the g Factor of Li-Like Ions.

The nuclear recoil effect on the g factor of Li-like ions is evaluated. The one-electron recoil contribution is treated within the framework of the rigorous QED approach to the first order in the electron-to-nucleus mass ratio m/M and to all orders in the parameter αZ. These calculations are performed in a range Z=3-92. The two-electron recoil term is calculated for low- and middle-Z ions within the Breit approximation using a four-component approach. The results for the two-electron recoil part obtained in the Letter strongly disagree with the previous calculations performed using an effective two-component Hamiltonian. The obtained value for the recoil effect is used to calculate the isotope shift of the g factor of Li-like ^{A}Ca^{17+} with A=40 and A=48 which was recently measured. It is found that the new theoretical value for the isotope shift is closer to the experimental one than the previously obtained value.

Point defects in aluminum: Single vacancy

The results of a first-principles calculation for the formation energy of a single vacancy in aluminum are reported. Solid-state scattering theory is modified to use localized Gaussian orbitals (instead of Wannier functions) and applied to evaluate the one-electron contribution. Energy bands and wavefunctions, obtained from a self-consistent LCGO band calculation, are used to evaluate the Green's function matrix. The defect potential consists of that due to the absence of a neutral atom, including the lattice relaxation. It is further made partially self-consistent by including the electronic dielectric function for screening.

G factor of Li-like ions with a nonzero nuclear spin

A relativistic theory of the g factor of Li-like ions with a nonzero nuclear spin is considered for the 1s 2 2s state. A correction to the atomic g factor for the magnetic-dipole hyperfine interaction is calculated including the one-electron contribution, as well as the contribution of interelectronic-interaction effects of the order of 1/Z. Along with corrections for the interelectronic interaction, quantum electrodynamic effects, nuclear recoil, and finite nuclear size, this correction allows high-precision theoretical values for the g factor of Li-like ions with a nonzero nuclear spin to be obtained. The results can be used for refining the nuclear magnetic moments from comparison with experimentally determined values of the g factor.

Effect of reconstruction-induced strain on the reflectance difference spectroscopy of GaAs (001) aroundE1andE1+Δ1transitions

We report measurements of reflectance difference (RD) spectra for $c(4\ifmmode\times\else\texttimes\fi{}4)$ and $(2\ifmmode\times\else\texttimes\fi{}4)$ reconstructed (001) surfaces of GaAs. Surface dimers induce an inhomogeneous orthorhombic strain field that penetrates several monolayers into the crystal. The thickness $d$ of this strained region is smaller than the penetration depth $L$ of the probing light, and an inhomogeneous anisotropy formalism can be used. The dielectric function of GaAs at room temperature can be described by a discrete (Lorentzian) excitonic line shape. For the contribution of the region near the surface to the optical response, the excitonic response should be at least partly quenched because of the electric field present near the surface. Thus, a one-electron contribution (logarithmic line shape) may have to be used to fit the RD spectra. By using an inhomogeneous perturbation formalism and a logarithmic line shape, we have been able to isolate the strain component induced by the dimers around ${E}_{1}$ and ${E}_{1}+{\ensuremath{\Delta}}_{1}$ critical points. We also inferred that the RD spectra include a component related to surface roughness.

Extraction of a one-electron absorption from the total one

To extract a one-electron contribution to the absorption, one should solve the problem of deconvolution of the measured X-ray absorption with the convolution kernel W(ω) taken directly from experimental XPS spectra or constructed empirically. An application of the Bayesian method to the deconvolution problem is considered. It is shown that the Fourier transform of the XAFS-function obtained after the deconvolution does not depend practically on the regularization parameter in a wide range of the latter. Therefore, there is no requirement for the uniqueness of the deconvoluted (any solution is suitable), and the Fourier transform of the one-electron XAFS-function can be found now. Moreover, the usage of the function W(ω) in constructing the atomic-like absorption is shown.

Adsorption of oxygen and hydrogen on a stepped BCC transition metal surface

The binding energy contour maps are calculated for an oxygen and a hydrogen adatom on an (m(110)*(011)) BCC transition metal surface. The chemisorption energy is split into a one-electron contribution treated in the tight-binding approximation, keeping all the atoms involved in the bonding neutral, and into a pairwise repulsive potential of the Born-Mayer type. One finds that the most stable adsorption sites are close to the ledge, but the perturbation due to the step on the profile of potential energy across the ledge is larger in the case of oxygen than in the case of hydrogen. Comparison of these results with a previous work (Jardin et al., 1985) shows that this perturbation is much smaller for both adsorbates than for transition adatoms.

Electronic structure of transition-atom impurities in GaP.

We describe the elements of the electronic structure and the chemical trends in cation-substitutional Cr, Mn, Fe, Co, Ni, Cu, and Zn impurities in GaP and Fe in InP. First, using the recently developed method of Fazzio, Caldas, and Zunger, we deconvolute the observed acceptor, donor, and intracenter d..-->..d( excitation energies into a one-electron mean-field contribution and a many-electron multiplet correction. Then, using the self-consistent quasiband crystal-field Green's-function method of Lindefelt and Zunger, we show that one-electron theory explains the magnitudes and the trends in the mean-field part of the observed transition energies (evaluated as differences in total energies). Many-electron contributions are found to be sizable, and are responsible for the nonmonotonic trends of the observed acceptor energies with the impurity's atomic number and a reduction in the Mott-Hubbard Coulomb energies. We discuss in detail the impurity-induced energy levels (gap states as well as resonances), the photoionization and intracenter excitations, the attenuation of the Mott-Hubbard Coulomb repulsion energies with the attendant plurality of charge states, the self-regulating response of the electron density to excitations, and the nature of the transition-atom--host chemical bond with its relationship to the structure of bulk 3d phosphides.

Magnetic and transport properties of Yb1−xTmxS

With a view to studying the behavior of diluted Tm in a nonmagnetic matrix, we have prepared single crystals of Yb1−xTmxS (0≤x≤0.25). The lattice constant a0 decreases abruptly as x approaches 0.14, which is interpreted as a valence transition of Tm towards 3+. For 50<T<300, χ follows a Curie–Weiss law. The calculated μeff seems to indicate a valence change from 0.7 for x=0.03 to ∼3 as x approaches 0.22, the change following that of a0. The magnetic moment per Tm increases with x (up to x=0.14) for fields up to 150 kOe. For x=0.03, ρ decreases from RT, shows a minimum at 85 K, and increases as −log T. The number of carriers calculated from RH does not correspond to a one-electron contribution per Tm atom for x=0.03, 0.08, and 0.17. The data suggest an intermediate valence of Tm for x<0.14.

Theory of hyperfine interactions in alkaline-earth ions isoelectronic with alkali-metal atoms:Mg+25ground state

Relativistic many-body perturbation theory has been used to investigate the hyperfine structure of the singly ionized magnesium ion. These investigations were carried out to explain the recent experimental data in the ground state $3^{2}S_{\frac{1}{2}}$ of ${\mathrm{Mg}}^{+}$ as well as to compare the hyperfine interaction results, both experimental and theoretical, in alkali-metal atoms with those in the corresponding isoelectronic alkaline-earth positive-ion series. The one-electron contribution to the hyperfine constant in $^{25}\mathrm{Mg}^{+}$ was found to be -553 MHz composed of the direct and exchange core-polarization contribution of -466 and -87 MHz, respectively, the many-electron correlation contribution being -48 MHz. The net theoretical hyperfine constant comes out to be -(602\ifmmode\pm\else\textpm\fi{}8) MHz, which agrees very well with the recent experimental value of -596.25 MHz obtained with the use of ion-storage techniques.

The role of the electrons-per-atom ratio in the structural stability of certain binary alloys

Reports on the structural phase stability of certain binary alloys of less simple metals. The results show that the one-electron contribution arising from the virtual crystal approximation dominates the structural prediction for some of the phases observed in these systems. The neutral object contribution describing the residual interaction of the pseudo-atoms simply reflects the concentration behaviour of the one-electron contribution. The calculations re-emphasise that the first non-vanishing reciprocal lattice vectors g and the diameter of the free electron Fermi sphere 2kF play a crucially important role in the structural energetics of the systems they consider.

Theory of hyperfine interactions in alkaline-earth ions isoelectronic with alkali-metal atoms —Ba+137

With the development of ion-storage techniques, it has become possible to study the hyperfine interactions of alkaline-earth positive ions which are isoelectronic with alkali-metal atoms. As part of a program to study the available experimental values of the hyperfine constants and the relative importance of various contributing mechanisms in these systems, we have investigated the singly ionized barium ion using relativistic many-body perturbation theory. The one-electron contribution to the hyperfine constant in $^{137}\mathrm{Ba}^{+}$ is found to be 3476 MHz composed of direct and exchange core-polarization contributions of 3055 and 421 MHz, respectively. The many-electron correlation contribution is found to be 727 MHz. The net calculated hyperfine constant of (4203\ifmmode\pm\else\textpm\fi{} 200) MHz agrees satisfactorily with the experimental value of 4018.2 MHz. The ratios of the exchange core-polarization and correlation contributions to the direct contribution are both found to be smaller than the corresponding ratios in the isoelectronic cesium atom. This can be ascribed to the lesser deformability of the core of ${\mathrm{Ba}}^{+}$ as compared to that of the neutral cesium atom.

Relativistic tight-binding calculation of core-valence transitions in Pt and Au

The results of a relativistic tight-binding energy-band model for Pt and Au, utilizing parameters derived from Smith's empirically adjusted combined interpolation scheme, are applied to calculate the one-electron contribution to various x-ray and energy-loss spectra involving $4f$ and $2p$ core states in these materials. These results show that the unoccupied holes in the Pt $5d$ bands have predominantly $j=\frac{5}{2}$ character (${h}_{\frac{5}{2}}$) such that the ($\frac{{h}_{\frac{5}{2}}}{{h}_{\frac{3}{2}}}$) ratio ranges from \ensuremath{\sim}3.5 within 0.5 eV of ${E}_{F}$ to \ensuremath{\sim}2.9 over the entire unoccupied conduction band. Taking into account dipole transition probabilities, the former ratio leads to a predicted line-strength ratio $\frac{{I}_{{N}_{7}}}{{I}_{{N}_{6}}}\ensuremath{\approx}2.9$ near threshold for excitations involving the $4f$$j=\frac{7}{2}({N}_{7})$ and $j=\frac{5}{2}({N}_{6})$ core levels in Pt. This result is in good agreement with the corresponding experimental ratios that are derived from electron energy-loss (2.5) and x-ray-absorption (2.3) spectra. Comparable agreement is obtained between the calculated and observed (electron-energy-loss) $\frac{{I}_{{N}_{7}}}{{I}_{{N}_{6}}}$ ratios in Au. The present results are applied to calculate the ${N}_{6}\ensuremath{-}{N}_{7}$ x-ray emission spectra in both Pt and Au and to interpret the ${L}_{2}\ensuremath{-}{L}_{3}$ absorption-edge data in Pt.

On the origin of the Hume-Rothery rules for phase stability in α and β brasses

The authors investigate the Blandin-Heine-Stroud-Ashcroft suggestion that the Hume-Rothery rules for the phase stability of alpha and beta brasses arise as a consequence of the rapid variation of the free electron density response function in the neighbourhood of 2KF. Using pseudopotential theory the authors show that the most structure-sensitive contribution to the free energy of a random binary alloy is the one-electron contribution arising from the virtual crystal bandstructure of neutral pseudo-atoms. The calculated difference in the one-electron contribution to the free energy between different crystal structures shows rapid variations at concentrations which are characterised by particular electron per atom ratios Z for which 2KF is equal to the first or second reciprocal lattice vector of the alloy.

Tensor interactions of conduction electrons in simple metals

Recent experiments by Lubzens, Shanabarger, and Schultz on aluminum have stimulated considerable theoretical works. In one of these, a tensor interaction between conduction electrons was proposed (Walker). We present here the first calculation of this interaction due to the spin–orbit contribution to the electron–phonon matrix element. Single orthogonalized plane waves (OPW) and realistic potentials are used. The spin–lattice relaxation due to the same mechanism is also computed. The tensor and spin–lattice contributions to conduction electron spin resonance (CESR) line width for Na and Al are compared with experiments. Although the calculations are crude, they demonstrate that the tensor interaction gives a contribution to the effective g tensor which is comparable in magnitude to the one-electron contribution and cannot be neglected.

Hyperfine interaction in excited states of sodium:Sstates

The direct and exchange-core-polarization (ECP) contributions to the hyperfine interaction in the excited states, $3s$ to $10s$, of the sodium atom are obtained from first-principles one-electron calculations. The exchange-core-polarization results indicate that this effect is a nearly constant fraction of the direct effect for all the excited states considered. Using the difference between experiment in the two states where data are available and the total theoretical one-electron contribution as a measure of the correlation effect, we find a significant decrease in the percentage importance of the correlation effect in going from the ground $3s$ to the excited $4s$ state. Physical explanations are offered for this behavior and the near constancy of the fractional ECP contribution.

Energy Transfer via Scattering of a Coherent Modulated Electron Beam

The total inelastic cross section for the scattering of a coherent modulated electron beam, viewed as a single quantum state, is calculated. In addition to the conventional one-electron contribution, there is a many-electron interference contribution which, under proper conditions, can lead to a greatly enhanced cross section. Furthermore, the interference term has the property of selectively exciting the target at a sharply defined frequency which is determined by the modulator. The possible relevance of this interference effect to the Schwarz-Hora experiment and potential applications, such as in electron microscopy, are discussed.