Importance of self-consistency in relativistic continuum random-phase approximation calculations

A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed, where the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single-particle Green's function technique. The full consistency of the calculations is achieved that the same effective Lagrangian is adopted for the ground state and the excited states. The negative energy states in the Dirac sea are also included in the single-particle Green's function in the no-sea approximation. The currents from the vector meson and photon exchanges and the Coulomb interaction in RCRPA are treated exactly. The spin-orbit interaction is included naturally in the relativistic frame. Numerical results of the RCRPA are checked with the constrained relativistic mean-field theory. We study the effects of the inconsistency, particularly the currents and Coulomb interaction in various collective multipole excitations.

Effects on the proton production from explosions of hydrogen clusters subjected to intense femtosecond laser fields

The dependence of the maximum and average energies of protons, which were produced in the interaction of an intense laser pulse (similar to 1 x 10(16) W cm(-2), 65 fs) with hydrogen clusters in a gas jet backed up to 80 bar at liquid nitrogen temperature (similar to 80 K), on the backing pressure has been studied. The general trend of the proton energy dependence on the square of the average cluster radius, which is determined by a calibrated Rayleigh scattering measurement, is similar to that described by theory under the single size approximation. Calculations are made to fit the experimental results under a simplified model by taking into account both a log-normal cluster size distribution and the laser intensity attenuation in the interaction volume. A very good agreement between the experimental proton energy spectra and the calculations is obtained in the high- energy part of the proton energy distributions, but a discrepancy of the fits is revealed in the low-energy part at higher backing pressures which are associated with denser flows. A possible mechanism which would be responsible for this discrepancy is discussed. Finally, from the fits, a variation of the cluster size distributions was revealed to be dependent on the gas backing pressure as well as on the evolving time of the gas flow of clusters.

First-principles study on rutile TiO2 quantum dots

The electronic structure of rutile TiO2 quantum dots (QDs) are investigated via the first-principles band structure method. We first propose a model to passivate the rutile TiO2 surfaces for the local density approximation calculations. In this model pseudohydrogen atoms are used to passivate the surface dangling bonds, which remove the localized in-cap surface states in the TiO2 QDs. As the size of the QD decreases, the band gap evolves as E-g(dot) = E-g(bulk) + 73.70/d(1.93), where E-g(dot) and d are the band gap and diameter of the QD, and E-g(bulk) is the band gap of the bulk rutile TiO2. The valence band maximum and the conduction band minimum states of the QDs are distributed mostly in the interior of the QDs, and they well inherit the atomic characteristics of those states of the bulk rutile TiO2.

Numerical approximation improves well survey calculation

It is now possible to improve the precision of well survey calculations by order of magnitude with numerical approximation.

Although the most precise method of simulating and calculating a wellbore trajectory generally requires more calculation than other, less-accurate methods, the wider use of computers in oil fields now eliminates this as an obstacle.

The results of various calculations show that there is a deviation of more than 10 m among the different methods of calculation for a directional well of 3,000 m.¹ Consequently, it is important to improve the precision and reliability of survey calculation-the fundamental, necessary work of quantitatively monitoring and controlling wellbore trajectories.

The accuracy of Kirchhoff's approximation in describing the far field speckles produced by random self-affine fractal surfaces

Based on the rigorous formulation of integral equations for the propagations of light waves at the medium interface, we carry out the numerical solutions of the random light field scattered from self-affine fractal surface samples. The light intensities produced by the same surface samples are also calculated in Kirchhoff's approximation, and their comparisons with the corresponding rigorous results show directly the degree of the accuracy of the approximation. It is indicated that Kirchhoff's approximation is of good accuracy for random surfaces with small roughness value w and large roughness exponent alpha. For random surfaces with larger w and smaller alpha, the approximation results in considerable errors, and detailed calculations show that the inaccuracy comes from the simplification that the transmitted light field is proportional to the incident field and from the neglect of light field derivative at the interface.

Studies of magnetic interactions in Mn-doped β-Ga2O3 from first-principles calculations

The magnetic behavior of Mn-doped beta-Ga2O3 is Studied from first-principles calculations within the generalized gradient approximation method. Calculations show that ferromagnetic ordering is always favorable for configurations in which two Mn ions substitute either tetrahedral or octahedral sites, and the ferromagnetic ground state is also sometimes favorable for configurations where one Mn ion substitutes a tetrahedral site and another Mn ion substitutes an octahedral site. However, the configurations of the latter case are less stable than those of the former. (c) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Electronic structures and mechanical properties of uranium monocarbide from first-principles LDA plus U and GGA plus U calculations

The electronic structure, elastic constants, Poisson's ratio, and phonon dispersion curves of UC have been systematically investigated from the first-principles calculations by the projector-augmented-wave (PAW) method. In order to describe precisely the strong on-site Coulomb repulsion among the localized U 5f electrons, we adopt the local density approximation (LDA) + U and generalized gradient approximation (GGA) + U formalisms for the exchange correlation term. We systematically study how the electronic properties and elastic constants of UC are affected by the different choice of U as well as the exchange-correlation potential. We show that by choosing an appropriate Hubbard U parameter within the GGA + U approach, most of our calculated results are in good agreement with the experimental data. Therefore. the results obtained by the GGA + U with effective Hubbard parameter U chosen around 3 eV for UC are considered to be reasonable. (C) 2009 Elsevier B.V. All rights reserved.

Giant Zeeman splitting in manganese-doped ZnSe quantum spheres: Eight-band effective-mass calculations

We deduce the eight-band effective-mass Hamiltonian model for a manganese-doped ZnSe quantum sphere in the presence of the magnetic field, including the interaction between the conduction and valence bands, the spin-orbit coupling within the valence bands, the intrinsic spin Zeeman splitting, and the sp-d exchange interaction between the carriers and magnetic ion in the mean-field approximation. The size dependence of the electron and hole energy levels as well as the giant Zeeman splitting energies are studied theoretically. We find that the hole giant Zeeman splitting energies decrease with the increasing radius, smaller than that in the bulk material, and are different for different J(z) states, which are caused by the quantum confinement effect. Because the quantum sphere restrains the excited Landau states and exciton states, in the experiments we can observe directly the Zeeman splitting of basic states. At low magnetic field, the total Zeeman splitting energy increases linearly with the increasing magnetic field and saturates at modest field which is in agreement with recent experimental results. Comparing to the undoped case, the Zeeman splitting energy is 445 times larger which provides us with wide freedom to tailor the electronic structure of DMS nanocrystals for technological applications.

INTERVALLEY-GAMMA-CHI DEFORMATION POTENTIALS IN III-V ZINCBLENDE AND SI SEMICONDUCTORS BY AB-INITIO PSEUDOPOTENTIAL CALCULATIONS

Intervalley GAMMA - X deformation potential constants (IVDP's) have been calculated by first principle pseudopotential method for the III-V zincblende semiconductors AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs and InSb. As a prototype crystal we have also carried out calculations on Si. When comparing the calculated IVDP's of LA phonon for GaP, InP and InAs and LO phonon for AlAs, AlSb, GaAs, GaSb and InSb with a previous calculation by EPM in rigid approximation, good agreements are found. However, our ab initio pseudopotential results of LA phonon for AlAs, AlSb, GaAs, GaSb and InSb and LO phonon for GaP, InP and InAs are about one order of magnitude smaller than those obtained by EPM calculations, which indicate that the electron redistributions upon the phonon deformations may be important in affecting GAMMA - X intervalley shatterings for these phonon modes when the anions are being displaced. In our calculations the phonon modes of LA and LO at X point have been evaluated in frozen phonon approximation. We have obtained, at the same time, the LAX and LOX phonon frequencies for these materials from total energy calculations. The calculated phonon frequencies agree very well with experimental values for these semiconductors.

INTERVALLEY GAMMA-CHI DEFORMATION POTENTIALS IN III-V ZINCBLENDE SEMICONDUCTORS BY ABINITIO PSEUDOPOTENTIAL CALCULATIONS

Intervalley GAMMA-X deformation-potential constants (IVDP's) have been calculated by use of a first-principles pseudopotential method for the III-V zinc-blende semiconductors AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, and InSb. When the calculated IVDP's of LA phonons for GaP, InP, and InAs and of LO phonons for AlAs, AlSb, GaAs, GaSb, and InSb are compared with results of a previous calculation that used the empirical pseudopotential method (EPM) and a rigid-ion approximation, good agreement is found. However, our ab initio pseudopotential results on IVDP's of LA phonons for AlAs, AlSb, GaAs, GaSb, and InSb and of LO phonons for GaP, InP, and InAs are about one order of magnitude smaller than those obtained by use of EPM calculations, indicating that the electron redistribution accompanying crystal-lattice deformation has a significant effect on GAMMA-X intervalley scattering for these phonon modes when the anions are being displaced. In our calculations the LA- and LO-phonon modes at the X point have been evaluated in the frozen-phonon approximation. We have also obtained the LAX- and LOX-phonon frequencies for these materials from total-energy calculations, which agree very well with experimental values for these semiconductors. We have also calculated GAMMA-X hole-phonon scattering matrix elements for the top valence bands in these nine semiconductors, from which the GAMMA-X IVDP's of the top valence bands for the longitudinal phonons and transverse phonons are evaluated, respectively.

1ST PRINCIPLE CALCULATIONS OF QUASI-PARTICLE ENERGIES FOR BAND STRUCTURES OF SI AND GAAS

We have applied the Green function theory in GW approximation to calculate the quasiparticle energies for semiconductors Si and GaAs. Good agreements of the calculated excitation energies and fundamental energy gaps with the experimental band structures were achieved. We obtained the calculated fundamental gaps of Si and GaAs to be 1.22 and 1.42 eV in comparison to the experimental values of 1.17 and 1.52 eV, respectively. Ab initio pseudopotential method has been used to generate basis wavefunctions and charge densities for calculating dielectric matrix elements and electron self-energies.

1ST PRINCIPLES PSEUDOPOTENTIAL CALCULATIONS OF ZONE BOUNDARY PHONON FREQUENCIES OF III-V-ZINCBLENDE SEMICONDUCTORS

Longitudinal zone boundary X phonon frequencies have been calculated by a first principles pseudopotential method for III-V zincblende semiconductors AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs and InSb. The phonon frequencies have been evaluated from total energy calculations in the frozen phonon approximation. The calculated phonon frequencies agree very well with the experimental values.

1ST-PRINCIPLES CALCULATIONS FOR QUASI-PARTICLE ENERGIES OF GAP AND GAAS

We have applied the Green-function method in the GW approximation to calculate quasiparticle energies for the semiconductors GaP and GaAs. Good agreement between the calculated excitation energies and the experimental results was achieved. We obtained calculated direct band gaps of GaP and GaAs of 2.93 and 1.42 eV, respectively, in comparison with the experimental values of 2.90 and 1.52 eV, respectively. An ab initio pseudopotential method has been used to generate basis wave functions and charge densities for calculating the dielectric matrix elements and self-enegies. To evaluate the dynamical effects of the screened interaction, the generalized-plasma-pole model has been utilized to extend the dielectric matrix elements from static results to finite frequencies. We presen the calculated quasiparticle energies at various high-symmetry points of the Brillouin zone and compare them with the experimental results and other calculations.

1ST PRINCIPLE CALCULATIONS OF QUASI-PARTICLE ENERGIES FOR BAND STRUCTURES OF SEMICONDUCTORS

We successfully applied the Green function theory in GW approximation to calculate the quasiparticle energies for semiconductors Si and GaAs. Ab initio pseudopotential method was adopted to generate basis wavefunctions and charge densities for calculating dielectric matrix elements and electron self-energies. To evaluate dynamical effects of screened interaction, GPP model was utilized to extend dieletric matrix elements from static results to finite frequencies. We give a full account of the theoretical background and the technical details for the first principle pseudopotential calculations of quasiparticle energies in semiconductors and insulators. Careful analyses are given for the effective and accurate evaluations of dielectric matrix elements and quasiparticle self-energies by using the symmetry properties of basis wavefunctions and eigenenergies. Good agreements between the calculated excitation energies and fundamental energy gaps and the experimental band structures were achieved.

Isoscalar Giant Monopole Resonance in Relativistic Continuum Random Phase Approximation

The isoscalar giant monopole resonance (ISGMR) in nuclei is studied in the framework of a fully consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function technique. The negative energy states in the Dirac sea are also included in the single particle Green's function in the no-sea approximation. The single particle Green's function is calculated numerically by a proper product of the regular and irregular solutions of the Dirac equation. The strength distributions in the RCRPA calculations, the inverse energy-weighted sum rule m(-1) and the centroid energy of the ISGMR in Sn-120 and Pb-208 are analysed. Numerical results of the RCRPA are checked with the constrained relativistic mean field model and relativistic random phase approximation with a discretized spectrum in the continuum. Good agreement between them is achieved.