Study of the P1 approximation in an inverse scattering problem

We examine the validity of the P₁ approximation in determining the albedo and asymmetry factor of a scattering medium from the hemispherical transmittance data. For this purpose, an analytical expression of the hemispherical transmittance is derived with the P₁ approximation and then fitted to hemispherical transmittance data of a scattering medium using three methods. These include the asymptotic expansion method, the unconstrained least mean-squares method and the constrained least mean-squares method. We find that estimation of radiative properties with the P₁ approximation is effective only for high albedos. Only the constrained least mean-squares method yields physically resonable values for the radiative properties in all cases.     

Extension of the weak-line approximation and application to correlated-k methods

Global climate models require accurate and rapid computation of the radiative transfer through the atmosphere. Correlated-k methods are often used. One of the approximations used in correlated-k models is the weak-line approximation. We introduce an approximation T_γ which reduces to the weak-line limit when optical depths are small, and captures the deviation from the weak-line limit as the extinction deviates from the weak-line limit. This approximation is constructed to match the first two moments of the gamma distribution to the k-distribution of the transmission. We compare the errors of the weak-line approximation with T_γ in the context of a water vapor spectrum. The extension T_γ is more accurate and converges more rapidly than the weak-line approximation.     

A k-Space Analysis of MR Tagging

We present a k-space approximation that directly relates a pulse sequence to its residual pattern of z-directed magnetization M_z, in a manner akin to the k-space approximation for small tip-angle excitation. Our approximation is particularly useful for the analysis and design of tagging sequences, in which M_z is the important quantity—as opposed to the transverse magnetization components M_x and M_y considered in selective excitation. We demonstrate that our approximation provides new insights into tagging, can be used to design novel tag patterns, and, more generally, may be applied to selective presaturation sequences for purposes other than tagging.     

The validity of the average t-matrix approximation for low-energy electron diffraction from random alloys

We explore the validity of the average t-matrix approximation for the calculation of low-energy electron diffraction IV spectra from substitutionally disordered alloy surfaces. The accuracy of this approximation is assessed by comparison with the results of calculations for Ni_xPt_100−x(100) surfaces obtained using the more accurate coherent-potential approximation. We find excellent agreement the two approaches, demonstrating the validity of the average t-matrix approximation for interpreting low-energy electron diffraction from alloys. The physical origin of this agreement is discussed by reference to the scattering properties of the electrons in alloy surfaces.     

Structural properties of zinc-blende Ga<Subscript>x</Subscript>In<Subscript>1-x</Subscript>N: ab initio calculations

We present a theoretical study of the structural properties, namely lattice constant, bulk modulus and its pressure derivative of zinc-blende Ga_xIn_1-xN. The calculations are performed using first-principles calculations in the framework of the density-functional-theory within the local density approximation under the virtual crystal approximation. The computed values are in good agreement with the available experimental data. The composition dependence of the studied quantities is examined. Besides, the deviation of the alloy lattice constant from Vegard's law is evaluated.     

Theoretical investigations of structural, electronic and thermal properties of Ti2AlX(X=C,N)

We have carried out a first-principles total-energy calculations of the structural and the electronic properties for the series of H-phases compounds Ti₂AlC and Ti₂AlN. We have applied the full-potential linearized augmented plane waves (FP-LAPW) method based on the density functional theory (DFT) using the local-density approximation (LDA) and/or the generalized gradient approximation (GGA). The quasi-harmonic Debye model, using a set of total energy versus volume calculations obtained with the FP-LAPW method which is applied to study the thermal and vibrational effects. Temperature and pressure effects on the structural parameters, thermal expansions, heat capacities and Debye temperatures are determined from the non-equilibrium Gibbs functions.     

First-principles investigation of electronic and magnetic properties of some holmium pnictides under pressure

First-principles calculations of the structural, magnetic and elastic properties of Holmium pnictides compounds HoX (X = As, Sb, and P) in the rock-salt structure, as a function of pressure, have been performed using the Density Functional Theory (DFT). We have used two full-potential methods: full potential linearized augmented plane wave (FP-LAPW) implemented in WIEN2k code and full-potential local-orbital minimum-basis in FPLO code. The calculations are carried out within a framework of the generalized gradient approximation (GGA) and GGA+U (where U = 5 eV is the Hubbard correlation term). the total magnetic moments of HoAs, HoSb, and HoP using GGA approximation are 5.85, 6.35, and 5.70 µ_B respectively and using GGA+U are 5.803, 6.208, 5.634 µ_B respectively. We investigated the effect of pressure on the magnetic properties of these compounds, using GGA approximation. The total magnetic moment of HoP shows small variation at low pressure, but it decreases rapidly at high pressure to reach 3.87 µ_B at 50 GPa.     

Stark structure of the energy spectrum of the Am3+ ion in LaCl3

We have analyzed the structure of the energy spectrum of the Am³⁺ ion in LaCl₃ in the weak and intermediate configuration interaction approximation. We have established that in the intermediate configuration interaction approximation, the mean-square deviation of the calculated values of the Stark level energies from the experimental values is 53% smaller than in the weak configuration interaction approximation. We have determined the even and odd crystal field parameters and the covalency parameters. We conclude that based on analysis of the Stark structure of the energy spectrum, we can make quantitative estimates of the intensity characteristics. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 637–640, September–October, 2006.     

Calculation of the diffusion coefficient in acoustic turbulence

The first (Born) approximation commonly used to calculate the diffusion coefficient D_T of a passive scalar in acoustic turbulence is shown to be insufficient. Even for a small main parameter—the Mach number, M?1—the next approximation gives a larger contribution to D_T than does the first approximation, but negative in sign. We present a procedure for correctly calculating D_T based on the solution of a nonlinear DIA (direct interaction approximation) equation for the mean Green’s function of the problem. We include an additional term in the general formula for D_T that directly describes the compressibility of acoustic turbulence. This term has not been known previously and has been disregarded even in the Born approximation. A positive value was obtained for D_T=CM³u₀/p₀. The spectrum E(x) was assumed to be smooth at distances Δ x～M²?1.     

Transient Raman gain stimulated by a noise pump

We predict a strong transient Raman gain stimulated by a Gaussian noise field in dispersive media. Our theory is based on the method of successive approximations, the first of which is the Markovian approximation. It is shown that the transient behavior will take place near critical pump intensity both for “short” (τ_p > T₂) and “ultrashort” (τ_p < T₂) laser pulses (τ_p is the pump pulse duration, T₂ is the relaxation time of optical phonons). Solutions for average intensities of the Stokes wave and optical phonons are obtained for arbitrary form of the given pump pulse. We show that transient Raman gain allows to form a very steep leading edge of the Stokes pulse.The steady-state increments of the second approximation describe the effects of a strong noise field. We show that after the intensity of the pump has exceeded a value beyond which the framework of validity of the Markovian approximation does not hold anymore, the steady-state Raman gain is saturated.We give a review of experimental results and make estimations for conditions of observing transient scattering in the field of a noise pump. Methods of obtaining the powerful femtosecond pulses based on stimulated Raman scattering of broad-band excimer lasers and supercontinuum emission are suggested.     

Isomer shifts in Zr2Fe and Zr3Fe

The⁵⁷Fe isomer shifts in the crystalline compounds Zr₂Fe and Zr₃Fe are calculated. We use the standard first-principles linear-muffin-tin-orbital formalism in the atomic sphere approximation (LMTO-ASA) to obtain the electronic structure of the compounds. The electronic structure of pure Fe was also calculated with the same formalism, where the local spin density approximation for the exchange correlation term is used. We found that the calculated isomer shift values are in good agreement with the experimental values for Zr₂Fe and Zr₃Fe found in the literature.     

Radiative Quark <Emphasis Type="Italic">p</Emphasis><Subscript>⊥</Subscript>-Broadening in a Quark–Gluon Plasma beyond the Soft Gluon Approximation

We study the radiative correction to p_⊥-broadening of a fast quark in a quark–gluon plasma beyond the soft gluon approximation. We find that the radiative processes can suppress considerably p_⊥-broadening. This differs dramatically from previous calculations to logarithmic accuracy in the soft gluon approximation, predicting a considerable enhancement of p_⊥-broadening.     

A coordinate-space study of kowalski's three-term separable approximation for the fully off-shell two-nucleon T-matrix

Using elementary coordinate-space methods, we show that a three-term separable approximate fully off-shell T-matrix proposed by Kowalski can be reduced to a simpler expression. This T-matrix incorporates off-shell unitarity exactly, is exact half off the energy shell, and is free from the spurious poles that arise in the Noyes approximation. However, numerical tests employing the wave-function model of Picker, Redish, and Stephenson show that for realistic ¹S_o interactions, the Noyes approximation is more accurate than Kowalski's approximation except near the spurious pole at 250 MeV. We give a plausible explanation of this result.     

First-principle study of the structural,electronic, and thermodynamic properties of cuprous oxide under pressure

Cuprous oxide is selected as a promising material for photovoltaic applications. Density functional theory is used to study the structural, electronic, and thermodynamic properties of cuprous oxide by using the local density approximation and generalized-gradient approximation. The effect of pressure on the structural and electronic properties of Cu₂O is investigated. This study confirms and characterizes the existence of new phases. Hexagonal and tetragonal phases are not completely indentified. We focus on the phase transition of the cuprous oxide under hydrostatic pressure to tetragonal and hexagonal (CdI₂) structures. Variation of enthalpy with pressure is used to calculate the pressure of the phase transition.     

The singlet state in the Hubbard model with U=∞

We discuss, in connection with the problem of the ground state in the Hubbard model with U=∞, the normal (nonmagnetic) N-state of a system over the entire range of electron concentrations n≤1. It is found that in a one-particle approximation, e.g., in the generalized Hartree-Fock approximation, the energy ε ₀(n) of the N-state is lower than the energy ε _FM(n) of a saturated ferromagnetic state for all values of n. Using the random phase approximation we calculate the dynamical magnetic susceptibility and show that the N-state is stable for all values of n. A formally exact representation is derived for the mass operator of the one-particle electron Green’s function, and its expression in the self-consistent Born approximation is obtained. We discuss the first Born approximation and show that when correlations are taken into account, the attenuation vanishes on the Fermi surface and the electron distribution function at T=0 acquires a Migdal discontinuity, whose magnitude depends on n. The energy of the N-state in this approximation is still lower than ε _FM(n) for n<1. We show that the spin correlation functions are isotropic, which is a characteristic feature of the singlet states of the system. We calculate the spin correlation function for the nearest neighbors in the zeroth approximation as a function of n. Finally, we conclude that the singlet state of the system in the thermodynamic limit is the ground state. Zh. éksp. Teor. Fiz. 114, 2130–2144 (December 1998)     

Electronic Structure of RCo2 (R = Y, Nd, Ho, Er)

The results of electronic structure studies of the YCo₂ performed in the framework of the density functional theory (DFT) are reported. We have applied both local spin density approximation (LSDA) and generalized gradient approximation (GGA) for the treatment of exchange and correlation effects. We have found the stable paramagnetic ground state (a _min/a _exp = 0.962) using LSDA. In addition, we have investigated the influence of the local R-4f moments in RCo₂ (R = Nd, Ho, Er) on the ferrimagnetic solution using a self-interaction corrected LSDA method.     

High-pressure calculations of the elastic properties of ZnSx Se 1−x alloy in the virtual-crystal approximation

We report first-principles calculation results on the structural and elastic properties of ZnS _x Se_1?x alloy. The calculations done using density functional theory within the local density approximation and employing the virtual-crystal approximation. It is found that the lattice parameter, the phase transition pressure, and the elastic constants (and their derivative with respect to the pressure) follow a quadratic law in x.     

Structural,electronic and optical properties of cubic fluoroelpasolite Cs2NaYF6 by density functional theory

First-principles full-potential linearized augmented plane-wave method based on density functional theory is used to investigate the structural, electronic and optical properties of the cubic fluoroelpasolites Cs₂NaYF₆ within the local density approximation (LDA) and generalized gradient approximation (GGA) for potential exchange correlation. The modified Becke–Johnson (mBJ) potential approximation is also used for calculating the electronic and optical properties of the material. We have analyzed the structural parameters, total and partial densities of states, dielectric functions, absorption and reflectivity. The results show that the band structure of the fluoroelpasolites Cs₂NaYF₆ has an insulating behavior for the two directions of spin and as a result there is no net magnetic moment. A wide band gap of 9.6 eV is obtained with mBJ-GGA, which allows the application of this material as X-ray storage phosphor materials and scintillators.     

Ab initio investigation of the structural,elastic and electronic properties of the anti-perovskite TlNCa3

We have investigated the structural, elastic and electronic properties of the anti-perovskite TlNCa₃ using ab initio calculations within the generalized gradient approximation and the local density approximation for the exchange–correlation potential. The lattice constant, bulk modulus, elastic constants and their pressure dependence, energy band structures, density of states and charge density distribution are calculated and analyzed in comparison with the available experimental and theoretical data. The bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, Lamé’s coefficients, average sound velocity and Debye temperature are numerically estimated for ideal polycrystalline TlNCa₃ aggregates in the framework of the Voigt–Reuss–Hill approximation. This is the first theoretical prediction of the elastic constants and their related properties for TlNCa₃ that requires experimental confirmation.