Mean field methods for atomic and nuclear reactions: The link between time–dependent and time–independent approaches

Abstact: Three variants of mean field methods for atomic and nuclear reactions are compared with respect to both conception and applicability: The time–dependent Hartree–Fock method solves the equation of motion for a Hermitian density operator as initial value problem, with the colliding fragments in a continuum state of relative motion. With no specification of the final state, the method is restricted to inclusive reactions. The time–dependent mean field method, as developed by Kerman, Levit and Negele as well as by Reinhardt, calculates the density for specific transitions and thus applies to exclusive reactions. It uses the Hubbard–Stratonovich transformation to express the full time-development operator with two–body interactions as functional integral over one–body densities. In stationary phase approximation and with Slater determinants as initial and final states, it defines non–Hermitian, time–dependent mean field equations to be solved self–consistently as boundary value problem in time. The time–independent mean field method of Giraud and Nagarajan is based on a Schwinger–type variational principle for the resolvent. It leads to a set of inhomogeneous, non-Hermitian equations of Hartree–Fock type to be solved for given total energy. All information about initial and final channels is contained in the inhomogeneities, hence the method is designed for exclusive reactions. A direct link is established between the time–dependent and time–independent versions. Their relation is non–trivial due to the non–linear nature of mean field methods. Received: 7 January 1998 / Revised version: 20 April 1998     

Validated Spectroflurimetric Determination of Some H1 Receptor Antagonist Drugs in Pharmaceutical Preparations Through Charge Transfer Complexation

A validated simple, rapid, and selective spectrofluorimetric method was developed for the determination of some antihistaminic H₁ receptor antagonist drugs namely ebastine (EBS), cetirizine dihydrochloride (CTZ), and fexofenadine hydrochloride (FXD). The method is based on the reaction of the cited drugs with some Π acceptors namely p-chloranilic acid (CLA), tetracyanoethylene (TCNE), and 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ) to give highly fluorescent derivatives. The fluorescence intensity—concentration plots were rectilinear over the concentration ranges of 0.2–3.0, 0.2–2.5 and 0.15–2.0 μg/ml for EBS with CLA, DDQ, and TCNE respectively; 0.5–7.0, 0.5–6.0, and 0.2–4.0 μg/ml for CTZ with the previously mentioned reagents, and 0.2–3.5, 0.5–6.0, and 0.2–3.5 μg/ml for FXD. The factors affecting the formation of the reaction products were carefully studied and optimized. The method was applied for the determination of the studied drugs in their dosage forms. The results obtained were in good agreement with those obtained by the comparison methods. Reactions Stoichiometries of the complexes formed between the studied drugs and Π acceptors were defined by the Job’s method of the continuous variation and found in 1:1 in all cases.     

Hartree–Fock self-consistent field method for atoms with two open shells of identical symmetry

A generalization of the Roothaan–Bagus method (Roothaan–Hartree–Fock atomic theory) on atoms with open shells of identical symmetry is given. Using orbital exponents of Slater-type atomic orbitals optimized with high accuracy by methods for the minimization of the first and second orders, energy values for atoms with two open s-type shells are calculated within the limits of the Roothaan–Hartree–Fock atomic theory.     

Multiple (<Emphasis Type="Italic">G</Emphasis>′/<Emphasis Type="Italic">G</Emphasis>)-expansion method and its applications to nonlinear evolution equations in mathematical physics

In this paper, an extended multiple (G′/G)-expansion method is proposed to seek exact solutions of nonlinear evolution equations. The validity and advantages of the proposed method is illustrated by its applications to the Sharma–Tasso–Olver equation, the sixth-order Ramani equation, the generalized shallow water wave equation, the Caudrey–Dodd–Gibbon–Sawada–Kotera equation, the sixth-order Boussinesq equation and the Hirota–Satsuma equations. As a result, various complexiton solutions consisting of hyperbolic functions, trigonometric functions, rational functions and their mixture with parameters are obtained. When some parameters are taken as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solution. In addition, this method can also be used to deal with some high-dimensional and variable coefficients’ nonlinear evolution equations.     

Unrestricted symmetry-projected Hartree-Fock-Bogoliubov calculations for SD-shell nuclei

Abstact: The solution of the Hartree–Fock–Bogoliubov problem with restoration of the broken symmetries before the variation has been generalized for the use of totally unrestricted quasi–particle determinants. With this method doubly–even, doubly–odd and odd nuclei can be treated on the same footing. Comparison with the results of complete shell–model diagonalizations shows that already one–determinant representations yield a very good approximation to the exact solutions even in the middle of the 1s0d shell. The problem is especially suited for numerical implementation on parallel computers. First tests show a linear dependence of the inverse CPU time with the number of processors used. Received: 26 February 1998 / Revised version: 8 May 1998     

Nonlinearities in the reflection and transmission spectra of the photonic bandgap heterostructures with n–i–p–i crystals

Nonlinear optical properties of photonic crystal heterostructures with embedded n–i–p–i superlattices are investigated. Self-consistent calculations of the transmission and reflection spectra near the defect mode are performed using the transfer-matrix method and taking into account the gain saturation. Analysis of features and output characteristics is carried out for one-dimensional photonic crystal heterostructure amplifiers in the GaAs–GaInP system having at the central part an active “defect” from doubled GaAs n–i–p–i crystal layers. The gain saturation in the active layers in the vicinity of the defect changes the index contrast of the photonic structure and makes worse the emission at the defect mode. Spectral bistability effect, which can be exhibited in photonic crystal heterostructure amplifiers, is predicted and the hysteresis loop and other attending phenomena are described. The bistability behavior and modulation response efficiency demonstrate the potential possibilities of the photonic crystal heterostructures with n–i–p–i layers as high-speed optical amplifiers and switches.      

Determining the inelastic proton–proton cross section at the large hadron collider using minimum bias events

In this paper a new method is described for determining the non-diffractive part of the inelastic proton–proton cross section, at the LHC centre of mass energy of 14 TeV. The method is based on counting the number of inelastic proton–proton interactions in the collision regions. According to a preliminary investigation, this measurement will be best suited for the initial low luminosity phase of the LHC. Knowledge of the proton–proton luminosity is likely to dominate the measurement uncertainty. PACS 13.85.Hd     

Calibration of the solar radio spectrometer

This paper shows some improvements and new results of calibration of Chinese solar radio spectrometer by analyzing the daily calibration data recorded in the period of 1997–2007. First, the calibration coefficient is fitted for three bands (1.0–2.0 GHz, 2.6–3.8 GHz, 5.2–7.6 GHz) of the spectrometer by using the moving-average method confined by the property of the daily calibration data. By this calibration coefficient, the standard deviation of the calibration result was less than 10 sfu for 95% frequencies of 2.6–3.8 GHz band in 2003. This result is better than that calibrated with the constant coefficient. Second, the calibration coefficient is found in good correlation with local air temperature for most frequencies of 2.6–3.8 GHz band. Moreover, these results are helpful in the research of the quiet solar radio emission.     

Portable optical water-and-oil analyzer based on a mid-IR (1.6–2.4 μm) optron consisting of an LED array and a wideband photodiode

An optical method for measuring the water and oil content using mid-IR (1.6–2.4 μm) LEDs and a wideband photodiode is suggested for the first time. This method is developed based on the absorption spectra of pure water, dewatered oil, and water—oil emulsions (cut oil) with different content of water and uses 10 types of LEDs in the spectral range 1.6–2.4 μm. It is shown that pure water heavily absorbs the LED radiation in the spectral range 1.85–2.05 μm, oil absorbs in the range 1.67–1.87 μm, and the LED radiation with a maximum at 2.20 μm is equally weakly absorbed by water and oil. An optical cell of the water-and-oil analyzer is designed on the basis of a three-element diode array with radiation maxima at 1.65 (detection of oil), 1.94 (detection of water), and 2.2 μm (reference signal) wideband photodiode covering the spectral range 1.3–2.4 μm. A calibration curve is derived that represents the dependence of the water concentration in oil on the amplitude of the reduced signal obtained by processing three signals from the LEDs. This optical method of measuring the water content in oil underlies a portable analyzer making possible online measurements directly in an oil well.     

Simultaneous determination of aluminum (III) and iron (III) by first-derivative spectrophotometry in alloys

A highly sensitive and selective first-derivative spectrophotometric method has been developed for the determination of aluminum and iron in mixtures. The method is based on the formation of the binary complexes of aluminum and iron with Alizarin yellow R (AYR) 5-[4-nitrophenylazo]salicylic acid at pH 2.0 with molar absorptivity of 1.1∙10⁴ l⋅mol^–1⋅cm^–1. A zero-crossing technique is found suitable for the direct measurement of the first derivative value at the specified wavelength, so aluminum and iron were thus determined in the ranges 1.3–5.4 μg/ml and 1.1–8.3 μg/ml, respectively, in the presence of both components. The detection limits were found to be 1.4 ng/ml for aluminum and 2.8 ng/ml for iron. The relative standard deviations were in all cases less than 1.5%. The proposed method was successfully applied for the simultaneous determination of aluminum and iron in certified reference aluminum samples.     

Hawking Radiation of the Kerr–Newman Black Hole

Considering the unfixed background space-time and self-gravitational interaction, we review the Hawking radiation of the Kerr–Newman black hole by Hamilton–Jacobi method. The result shows the tunneling probability is related to the change of Bekenstein–Hawking entropy and the radiation spectrum deviates from the precisely thermal one, which is in accordance with Parikh and Wilczek’s result and gives another method to study the Hawking radiation of the black hole.     

Dispersion and nonlinear frequancy shift of natural waves in the Bose–Einstein condensate

Quantum mechanics equations for a system of the Bose particles are represented in the form of material field equations. A nonlinear equation for the macroscopic one-particle wave function is derived. Using the Krylov–Bogolyubov–Mitropol’skii method for equations in partial derivatives, nonlinear waves in the Bose–Einstein condensate are investigated. In the cubic approximation, dispersion relations for waves are derived and nonlinear frequency shift is calculated in the first- and third-order approximations for the interaction radius.     

Unrestricted symmetry-projected Hartree-Fock-Bogoliubov calculations for some PF-shell nuclei

Total binding energies and yrast energy spectra of three selected 1p0f–nuclei have been calculated using an unrestricted Hartree–Fock–Bogoliubov approach with symmetry–projection before the variation. The full 1p0f–shell has been used as single–particle basis and the semi–empirical FPD6 interaction as effective Hamiltonian. The results are compared to those of truncated shell–model calculations performed with the OXBASH code. In the middle of the 1p0f–shell the variational method yields energy gains up to 4.5 MeV and thus proves to be far superior than the conventional truncation methods at least if in the latter only up to about 13000 configurations for each spin–isospin combination are admitted. Received: 15 September 1999     

A New Derivation of the Quantum Navier–Stokes Equations in the Wigner–Fokker–Planck Approach

A quantum Navier–Stokes system for the particle, momentum, and energy densities is formally derived from the Wigner–Fokker–Planck equation using a moment method. The viscosity term depends on the particle density with a shear viscosity coefficient which equals the quantum diffusion coefficient of the Fokker–Planck collision operator. The main idea of the derivation is the use of a so-called osmotic momentum operator, which is the sum of the phase-space momentum and the gradient operator. In this way, a Chapman–Enskog expansion of the Wigner function, which typically leads to viscous approximations, is avoided. Moreover, we show that the osmotic momentum emerges from local gauge theory.     

Calculation of open p-shell atoms in the algebraic approach of the Hartree–Fock method

Highly precise calculations of analytical Hartree–Fock orbitals and energies have been performed within the limits of the Roothaan–Hartree–Fock atomic theory (Roothaan–Bagus method) for all open p-shell atoms of the Periodic Table. They were calculated in an algebraic approach using Slater-type atomic orbitals (AOs) as basis functions. Nonlinear parameters (orbital exponents) of AOs were optimized with exceptional accuracy by second-order methods. As a result, it was possible to satisfy exactly the virial relation (10^–14–10^–17) with calculated atomic term energies being close to the Hartree–Fock limit.     

Method to determine the interface’s fractal dimensions of metal-semiconductor electric contacts from their static instrumental characteristics

With the concept of fractal surfaces, the influence of the relief of the interface (roughness) and the heterogeneity of the potential barrier on the behavior of the current–voltage and capacity–voltage characteristics of the metal–semiconductor electric contacts with the Schottky barrier has been studied. The necessary and satisfactory conditions for the accurate relative measurements of the surface relief have been found with the mathematical apparatus of the Hausdorff–Besikovitsch fractional dimensionality 2 D _f3. It is shown that due to the fractal geometry the relative change of the real area of the interface of the metal–semiconductor contacts with the Schottky barrier is proportional to the ratio of their linear dimensions in the 4-D_f power. This is considerably slower than the change of the dimensions of the topological areas of their contact windows. The method to determine the fractal dimensionality of the real interface of the metal–semiconductor electric contacts with the Schottky barrier from the current–voltage and capacity–voltage characteristics has been developed.     

Simultaneous detection of dopamine and ascorbic acid in urine using the H-point standard addition method

A highly sensitive H-point standard addition method (HPSAM) was investigated for identification of dopamine and ascorbic acid in some synthetic and pharmaceutical samples in an aqueous medium at pH 9.2 using a universal buffer. The most suitable wavelengths for dopamine and ascorbic acid detection are 260:271 nm and 248:270 nm respectively. Recovery values are between 99.0–101 %. Also, the effect of most common interferents was studied. Detection ranges for dopamine and ascorbic acid are 2·10^–6–5·10^–5 M and 6·10^–6–3·10^–5 M respectively with an RSD range between 1.3 and 2.0 %. The method was used to determine both reagents in real and synthesized samples.     

Hawking Radiation from a Spherically Symmetric Static Black Hole

The massive particles’ Hawking radiation from a spherically symmetric static black hole is investigated with Parikh-Wilczek method, Hamilton–Jacobi method and Damour–Ruffini’s method. When energy conservation is considered, the same result can be concluded that the radiation spectrum is not precisely thermal. The corrected spectrum is consistent to the underlying unitary quantum theory, which can be used to explain the information loss paradox possibly.      

Variational method for determining the extraterrestrial constant for a solar ultraviolet spectrometer/ozonometer

A theoretical rationale is presented for a variational method for determining the extraterrestrial constant of a solar ultraviolet spectrophotometer for measuring total column ozone in the atmosphere. We have established the connection between this method and the familiar Langley method for calibration of extraterrestrial constants of solar spectrophotometers. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 2, pp. 291–297, March–April, 2009.     

Measurement of the thickness of thin polymer layers by infrared frustrated total internal reflection spectroscopy

A method is proposed for determining the thickness of thin (0.1–5.0 μm) polymer layers and coatings by means of infrared frustrated total internal reflection (FTIR) spectroscopy. This method is based on an analytic expression derived for the dependence of the intensities of absorption bands in IR FTIR spectra on the thickness of a polymer layer. The method is tested on model samples consisting of a thick film of polyethylene terephthalate with a layer of different thicknesses of polystyrene deposited on it. The advantage of this method is the ability to determine the thickness of thin polymer layers deposited on bulk or opaque polymer substrates. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 881–885, November–December, 2008.