Numerical calculation of soft-X ray transition probability for the muffin-tin potential

The matrix elements of the coordinate, the momentum and the gradient of the potential were used to calculate the optical transition probability between the valence and core states, obtained for the muffin-tin model of the crystal potential. It has been found that gradV is the most suitable form for the numerical calculation while the other forms can yield substantial errors for both transition and simple metals when the core energy amounts few Rydbergs and the amplitude of the core function reaches at the muffin-tin radius 10^–3-10^–2 of its maximum value.     

Methods for calculation of ir intensities in polyatomic molecules: A comparative study

Various methods for calculating intensities in ir spectra of polyatomic molecules are reviewed against the current theory of small vibrations of polyatomic molecules. The valence optical theory based on the representation of the molecular dipole moment as the sum of dipole moments of bonds has been shown to be erroneous. Of the two calculation procedures which use no assumptions on the molecular dipole moment, the Mayants-Averbukh method is shown to have certain advantages over the polar tensor method.     

Perturbation-theory calculation of line intensities for transitions in multiply ionized atoms

A semiempirical method is proposed for taking into account the spin-orbit interaction in calculating line intensities for transitions in atoms and molecules. Use of the method is demonstrated for SX and CaXIV ions.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 84–89, December, 1969.     

The energy dependence of photoelectron peak intensities,Part I: Experimental methods

With the increasing popularity of synchrotron radiation as a tunable photon source for photoemission spectroscopy, the significance of photoelectron peak variation with photon energy is becoming apparent. This variation is due to a number of intrinsic factors (excitation cross section, photon and electron reflection and refraction, inelastic processes, etc.) as well as instrumental factors (monochromator transmission and spectral purity, electron analyzer transmission and resolution, etc.). In this paper we develop methods for factoring out these contributions with the goal of determining the excitation cross section from a peak area measurement. Parts II and III will deal with a range of cross section measurements, and the use of relative peak area information to determine stoichiometry vs. probe depth.     

Diffraction by a corrugated interface of media: The influence of the corrugation shape and losses in the medium on total transformation regimes

We study regimes of total reflection of a plane wave to the diffraction lobe in the case where the wave is incident on a corrugated metal surface or a corrugated interface of two dielectric media. The purpose is to analyze the influence of both the corrugation shape and losses in the medium on the characteristics of the regimes of total reflection to the diffraction lobe. We consider a number of corrugation profiles differing from the sinusoid by the resonance-region width and the presence of additional elements, namely, (i) the profiles having pair resonance regions with scale of the order of the wavelength, for which qualitatively new diffraction regimes compared with those observed for the sinusoidal interface can be realized due to interaction of waves, and (ii) the profiles comprising small-scale deviations, which can be a model of actual gratings. To study the influence of losses in the problem of scattering from a corrugated interface of dielectrics, the dielectric permittivity is assumed complex. We compare the obtained results with data for a sinusoidal profile and loss-free media. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 5, pp. 391–405, May 2006.     

A quantitative study of diffracted X-ray intensities from type I natural diamond crystals by high resolution X-ray diffractometry and comparison with nearly perfect silicon single crystals

Results of accurate measurements of peak and integrated intensities of , 111 and 333 reflections of natural diamonds of type I and nearly perfect silicon single crystals are reported. Highly monochromated and collimated MoK _{α 1} exploring beam was used. A quadrupole crystal X-ray diffractometer was employed in (+, −, +) and (+, −, +, −) settings. (111) platelets of diamond and silicon crystals with thicknesses of about 1 mm were selected. High resolution diffraction curves, stationary and traverse topographs were recorded. Diffraction curve half widths of diamond and silicon crystals were in the range: 45–200 arc sec and a few arc sec respectively. The experimental values of integrated intensitiesρ for diamond crystals were found to lie between the theoretical values for ideally perfect and ideally imperfect crystals. Experimental values ofρ for silicon were closer to the “perfect crystal” values. This is consistent with the results of diffractometric and topographic evaluation. The peak intensities of all reflections were higher for diamond crystals in comparison to the silicon crystals. The ratioI _C/I _Si lies in the range 1.3 (111 reflection) to 10.5 and (333) reflections. This is anomalous and cannot be accounted for by considering the degree of perfection, structure factor and difference in absorption coefficient.     

New method for calculation of intensities of X-rays and thermal neutrons scattered dynamically in defected single crystals

We propose a new method for calculating intensities of X-rays and thermal neutrons, dynamically scattered in defected single crystals by comparing the dynamical theory of Bragg diffraction of X-rays and thermal neutrons in perfect single crystals with the theory of their small-angle scattering.     

Model potential for calculation of multiphoton processes in diatomic molecules

The model potential, analogous to the Fues atomic potential is suggested for analytical calculation of the perturbation theory matrix elements, defining interaction of molecule with electromagnetic field. The explicit expressions for the Green and wave functions of the molecular optical electron are received.     

Two-loop calculation of the effective potential for the Wess-Zumino model

The effective potential for the supersymmetric Wess-Zumino model is computed off-shell to two loops. A renormalization procedure which preserves positivity of the kinetic terms in the effective action is implemented. Supersymmetry is not broken to this order.     

Numerical calculation of trapped magnetic field for square multiple bulk superconductors

In this work, the trapped magnetic field was calculated for square bulk superconductors using the sand-pile model and Biot–Savart law. The numerical simulation of the trapped magnetic field was performed varying the sample dimensions, distance between the sample surface and observation point. In addition the magnetic field characteristics of superconducting bulk arrangement in an array was determined. The trapped magnetic field was found to be depending on the sample dimensions and distance between the sample and observation point. It is observed that, when the distance from the surface is larger, the value of the trapped magnetic field decreases, but the variation of the trapped magnetic field becomes small due to averaging the distribution of the trapped magnetic field.     

Compression of frequency-modulated pulses using helically corrugated waveguides and its potential for generating multigigawatt rf radiation

A new method to generate ultrahigh-power microwave pulses compatible with mildly relativistic electron sources is proposed. This method involves a novel microwave compressor in the form of a metal helically corrugated waveguide, which can enhance the power of frequency-modulated nanosecond pulses up to the multigigawatt level. The results of the proof-of-principle experiments at kilowatt power levels are in good agreement with theory.     

势场中粒子行为的量子计算与模拟

从量子力学的基本原理出发,采用指数差分方法,利用Matlab,模拟了入射不同势场后的粒子密度分布情况.结果表明,改变势场分布及粒子入射方式,粒子密度分布会产生显著变化.该模拟适用面广,可应用于不同的物理问题.     

On the calculation of the transition matrix for an arbitrary potential

In this paper the calculation of the elements of the transition operator in the angular momentum representation is carried out. It is shown that these matrix elements can be expressed in terms of surface integrals over the surrounded surface in the usual case of scattering of a plane wave by an arbitrary short range potential as well as in the case of scattering of a spherical wave by a surrounding potential field.     

Numerical calculation of the fidelity for the Kondo and the Friedel-Anderson impurities

The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N _eff of states. A plot of ln(F) versus N ∝ ln(N _eff ) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F) – ln(N _eff ) plot for the Kondo impurity diverges for large N _eff . On the other hand, the corresponding plot for the symmetric FA impurity saturates for large N _eff when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime.     

Numerical calculation of Kerr spectra for Co/Pt magnetic multilayered films

The Kerr spectra as function of wavelength, incident angle and layer number are calculated with 4×4 matrix method. It is found that the calculated results are in good agreement with experimental ones for [Co (0.3 nm)/Pt (0.4 nm)]×43/glass (1.21 mm) and [Co (0.4 nm)/Pt (1.1 nm)]×53/glass (1 mm). In addition, for [Co (0.3 nm)/Pt (0.4 nm)]×43/glass (1.21 mm), it shows a maximum Kerr rotation at N = 10. For [Co (0.4 nm)/Pt (1.1 nm)]×53/glass (1 mm), the calculated Kerr rotation as a function of incident angle reveals maximum when the incident angle is 89°.     

Numerical calculation of the entanglement entropy for scalar field in dilaton spacetimes

Using coupled harmonic oscillators model, we numerical analyze the entanglement entropy of massless scalar field in Gafinkle–Horowitz–Strominger (GHS) dilaton spacetime and Gibbons–Maeda (GM) dilaton spacetime. By numerical fitting, we find that the entanglement entropy of the dilaton black holes receive contribution from dilaton charge and is proportional to the area of the event horizon. It is interesting to note that the results of numerical fitting are coincide with ones obtained by using brick wall method and Euclidean path integral approach.     

Integral intensities of absorption bands of silicon tetrafluoride in the gas phase and cryogenic solutions: Experiment and calculation

The spectral characteristics of the SiF₄ molecule in the range 3100–700 cm^?1, including the absorption range of the band ν₃, are studied in the gas phase at P = 0.4–7 bar and in solutions in liquefied Ar and Kr. In the cryogenic solutions, the relative intensities of the vibrational bands, including the bands of the isotopically substituted molecules, are determined. The absorption coefficients of the combination bands 2ν₃, ν₃ + ν₁, ν₃ + ν₄, and 3ν₄ are measured in the solution in Kr. In the gas phase of the one-component system at an elevated pressure of SiF₄, the integrated absorption coefficient of the absorption band ν₃ of the ²⁸SiF₄ molecule was measured to be A(ν₃) = 700 ± 30 km/mol. Within the limits of experimental error, this absorption coefficient is consistent with estimates obtained from independent measurements and virtually coincides with the coefficient A(ν₃) = 691 km/mol calculated in this study by the quantum-chemical method MP2(full) with the basis set cc-pVQZ.     

Isolation and quantization of the two degrees of freedom of the electromagnetic potential for any gauge

The true dynamical degrees of freedom (TDDF) of the electromagnetic potential are found for any gauge. They are the components of the Fourier transform of the electromagnetic potential on a two-dimensional spacelike plane orthogonal to the lightlike momentum vector for k² = 0 and vanish for k² ≠ 0. Gauge invariance is related to the (two-parameter) indeterminacy of this spacelike plane and the arbitrariness of the component of the electromagnetic potential along the momentum vector. By direct quantization of the TDDF for any gauge (compatible with the equations of motion), some of the well-known problems of the usual treatments are avoided. For instance, the constraint div E = 0 is a c-number (agrees with the commutation relations) without choosing a gauge, there appears no need for an indefinite metric in the space of state amplitudes, the commutators for creation and annihilation operators of every component of the electromagnetic potential (timelike, longitudinal, and transverse) have the same sign, and the energy of the electromagnetic field is positive for any gauge. When gauges are chosen, the results of the literature are recovered. In our treatment, gauge fixation and quantization commute.     

A matrix method for the calculation of nonlocal exchange potential and spin-orbit coupling in the first-principles calculation method

Adequate treatment of exchange interaction and inclusion of spin-orbit coupling are important in obtaining reliable electronic structures of semiconductors and magnetic materials. Here, a matrix method has been derived to calculate nonlocal exchange potential and spin-orbit coupling within a muffin-tin-orbital based first-principles calculation method. Good agreement between calculated and experimental band gaps for various zinc-blende and wurtzite semiconductors demonstrated that direct calculation of nonlocal exchange potential is feasible. This method may be an improvement over the currently used LSDA  +  U or LSDA  +  GGA  +  U method, which uses an adjustable U parameter, for wide-band-gap semiconductors and magnetic materials. In this method, the use of an extended Hamiltonian matrix, which contains off-diagonal matrix elements between up- and down-spin states due to spin-orbit coupling, enables mutual adjustment of the occupation of up- and down-spin states through atomic orbitals. In contrast, in the conventional spin-polarized calculation method up- and down-spin sub-matrices are diagonalized separately. The calculated spin-orbit splitting for the triplet states at the Γ point for GaAs and ZnS are in good agreement with experimental data.