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     

Consequences of the center–of–mass correction in nuclear mean–field models

We study the influence of the scheme for the correction for spurious center–of–mass motion on the fit of effective interactions for self–consistent nuclear mean–field calculations. We find that interactions with very simple center–of–mass correction have significantly larger surface coefficients than interactions for which the center–of–mass correction was calculated for the actual many–body state during the fit. The reason for that is that the effective interaction has to counteract the wrong trends with nucleon number of all simplified schemes for center–of–mass correction which puts a wrong trend with mass number into the effective interaction itself. The effect becomes clearly visible when looking at the deformation energy of largely deformed systems, e.g. superdeformed states or fission barriers of heavy nuclei. Received: 6 September 1999     

The geometry of the higher dimensional black hole thermodynamics in Einstein–Gauss–Bonnet theory

In this paper, we have studied the geometry of the five-dimensional black hole solutions in (a) Einstein–Yang–Mills–Gauss–Bonnet theory and (b) Einstein–Maxwell–Gauss–Bonnet theory with a cosmological constant for spherically symmetric space time. Formulating the Ruppeiner metric, we have examined the possible phase transition for both the metrics. It is found that depending on some restrictions phase transition is possible for the black holes. Also for Λ = 0 in Einstein–Gauss–Bonnet black hole, the Ruppeiner metric becomes flat and hence the black hole becomes a stable one.     

The Nambu–Jona–Lasinio model of light nuclei

The Nambu–Jona–Lasinio model of the deuteron suggested by Nambu and Jona–Lasinio (Phys. Rev. 124 (1961) 246) is formulated from the first principles of QCD. The deuteron appears as a neutron–proton collective excitation, i.e. a Cooper np–pair, induced by a phenomenological local four–nucleon interaction in the nuclear phase of QCD. The model describes the deuteron coupled to itself, nucleons and other particles through one–nucleon loop exchanges providing a minimal transfer of nucleon flavours from initial to final nuclear states and accounting for contributions of nucleon–loop anomalies which are completely determined by one–nucleon loop diagrams. The dominance of contributions of nucleon–loop anomalies to effective Lagrangians of low–energy nuclear interactions is justified in the large N _C expansion, where N _C is the number of quark colours. Received: 10 March 2000     

Hg-coordination studies of oligopeptides containing cysteine,histidine and tyrosine by 199mHg-TDPAC

In order to study the interaction of histidine- and tyrosine-containing peptide chains with Hg(II), the nuclear quadrupole interaction (NQI) of ^199mHg in the Hg complexes of the oligopeptides Alanyl–Alanyl–Histidyl–Alanyl–Alanine-amid (AAHAA–NH₂) and Alanyl–Alanyl–Tyrosyl–Alanyl–Alanine-amid (AAYAA–NH₂) was determined by time differential perturbed angular correlation and is compared with previous data on Alanyl–Alanyl–Cysteyl–Alanyl–Alanyl (AACAA–OH). The ^199mHg–NQIs depend on the oligopeptide to Hg(II) stoichiometry and indicate that two-fold and four-fold coordinations occur for the bound Hg(II). This revised version was published online in August 2006 with corrections to the Cover Date.     

The components of the \gamma^* \gamma^* cross section

We extend our previous treatment of the p cross section based on Gribov's hypothesis to the case of photon–photon scattering. With the aid of two parameters, determined from the experimental data, we separate the interactions into two categories corresponding to short (“soft”) and long (“hard”) distance processes. The photon–photon cross section thus receives contributions from three sectors, soft–soft, hard–hard and hard–soft. The additive quark model is used to describe the soft–soft sector, pQCD the hard–hard sector, while the hard–soft sector is determined by relating it to the system. We calculate and display the behaviour of the total photon–photon cross section and its various components and polarizations for different values of energy and virtuality of the two photons, and discuss the significance of our results. Received: 12 January 2000 / Published online: 6 April 2000     

Indentation analysis of nano-particle using nano-contact mechanics models during nano-manipulation based on atomic force microscopy

Atomic force microscopy is applied to measure intermolecular forces and mechanical properties of materials, nano-particle manipulation, surface scanning and imaging with atomic accuracy in the nano-world. During nano-manipulation process, contact forces cause indentation in contact area between nano-particle and tip/substrate which is considerable at nano-scale and affects the nano-manipulation process. Several nano-contact mechanics models such as Hertz, Derjaguin–Muller–Toporov (DMT), Johnson–Kendall–Roberts–Sperling (JKRS), Burnham–Colton–Pollock (BCP), Maugis–Dugdale (MD), Carpick–Ogletree–Salmeron (COS), Pietrement–Troyon (PT), and Sun et al. have been applied as the continuum mechanics approaches at nano-scale. In this article, indentation depth and contact radius between tip and substrate with nano-particle for both spherical and conical tip shape during nano-manipulation process are analyzed and compared by applying theoretical, semiempirical, and empirical nano-contact mechanics models. The effects of adhesion force, as the main contrast point in different nano-contact mechanics models, on nano-manipulation analysis is investigated for different contact radius, and the critical point is discussed for mentioned models.     

Characterization of probe lasers for thin-film optical measurements

The peak-power-density stability and beam-wander precision of a probe laser are important factors affecting the inspection results in precise thin-film optical measurements. These factors are also key to evaluating a probe laser for in-line long-time operation of precise thin-film optical measurements. The peak-power density and beam wander of liner helium–neon (He–Ne) lasers, random He–Ne lasers, and diode lasers as functions of time are investigated experimentally using a beam profiler. It is found that the linear polarized He–Ne laser is considered to be a promising candidate for a probe laser employed in precise thin-film optical measurements due to better peak-power-density stability and beam-wander precision. Both the peak-power-density stability and beam-wander precision of He–Ne lasers are usually better than that of diode lasers, but an adequate warm-up of He–Ne laser for 30 min is required before thin-film optical measurements are made. After 12 h operation, the linear polarized He–Ne laser is suitable for precise thin-film optical measurements because both the peak-power-density stability and the beam-wander precision reach the minimum level. A cost-effective system composed of two linear polarized He–Ne lasers for long-term operation is proposed. This system can operate for around 0.5–1.2 years in precise thin-film optical measurements under the normal operating life of a He–Ne laser by switching the probe laser every 18 h.     

Source Identity and Kernel Functions for Elliptic Calogero–Sutherland Type Systems

Kernel functions related to quantum many-body systems of Calogero–Sutherland type are discussed, in particular for the elliptic case. The main result is an elliptic generalization of an identity due to Sen that is a source for many such kernel functions. Applications are given, including simple exact eigenfunctions and corresponding eigenvalues of Chalykh–Feigin–Veselov–Sergeev-type deformations of the elliptic Calogero–Sutherland model for special parameter values.     

Fractional Pais–Uhlenbeck Oscillator

In this paper we study the fractional Lagrangian of Pais–Uhlenbeck oscillator. We obtained the fractional Euler–Lagrangian equation of the system and then we studied the obtained Euler–Lagrangian equation numerically. The numerical study is based on the so-called Grünwald–Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grünwald–Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman–Liouville fractional derivative is equivalent to the Grünwald–Letnikov derivative for a wide class of the functions.     

Spontaneous polarization and piezoelectric effects on intraband relaxation time in a wurtzite GaN/AlGaN quantum well

Spontaneous (SP) and piezoelectric (PZ) polarization effects on the intraband relaxation time for a wurtzite (WZ) GaN/AlGaN quantum well (QW) are investigated theoretically as functions of the sheet carrier density and well thickness. The self-consistent (SC) model with the SP and PZ polarizations shows that linewidths for carrier–carrier and carrier–phonon scatterings are significantly reduced compared to those for the flat-band (FB) model without SP and PZ polarization. In particular, line-widths for the e–h and h–e scatterings are reduced by about two orders of magnitude at a sheet carrier density as low as 2×10¹² cm^-2 compared to the case of the FB model. This is attributed to the decrease of the matrix element due to the spatial separation between electron and hole wave functions. In the case of the e–e and h–h scatterings, the reduction of linewidths is mainly attributed to the decrease of the scattering matrix element due to the increase of the inverse screening length. Linewidths for e–h and h–e scatterings gradually increase with the sheet carrier density since the screening field increases, while linewidths for the other scatterings are almost independent of the sheet carrier density. The SC model also shows that linewidths for the carrier–carrier and carrier–phonon scatterings are nearly, constant irrespective of well thickness except for e–h and h–e scatterings. In the case of e–h and h–e scatterings, linewidths greatly decrease with the well width because of the increase of the spatial separation of wave functions. Received in final version: 13 July 2000 / Accepted: 13 July 2000 / Published online: 16 August 2000     

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.      

Manganese(III)-promoted reactions for formation of carbon–heteroatom bonds

Manganese(III) reagent is an important one- electron oxidant for initiation of free-radical reactions and formation of carbon–carbon bonds. The reactions are usually carried out under mild conditions, have high regio- and stereo-selectivities, and good functional group tolerance. Summarized in this article are the developments of manganese (III)-based reactions for the formation of carbon–heteroatom bonds including carbon–oxygen, carbon–phosphorus, carbon–sulfur, and carbon–nitrogen bonds, and their applications for the synthesis of related heterocyclic systems.     

A Class of Counterexamples to Jeans' Theorem for the Vlasov–Einstein System

The Vlasov–Poisson and Vlasov–Einstein systems model the motion of a self gravitating system such as a galaxy. The Vlasov–Poisson system is nonrelativistic. Jeans' theorem states that every spherically symmetric solution of the Vlasov–Poisson system that is independent of time may be expressed as a function of the two invariants, energy and angular momentum. This paper shows this is not the case for the Vlasov–Einstein system. Received: 2 November 1998 / Accepted: 24 December 1998     

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     

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.     

Quark mixing in the standard model and space rotations

The rotation matrix and the Cabibbo–Kobayashi–Maskawa (CKM) matrix are discussed. The CKM matrix is viewed as the rotation matrix in Euler angles with pitch–roll–yaw convention for the angles and as the angle–axis representation of the rotation matrix. A comparison of the exponential parameterisation of the CKM matrix with the matrix exponent generator of the space rotations is made. How to account for the CP violating phase in CKM and the O(3) rotation matrix in the angle–axis form is discussed in the context of such a view of the mixing matrix. The generation of the new parameterisations of the CKM matrix in an exponential form with distinguished CP violating part is demonstrated.     

Optical and structural analysis of plasma-treated and annealed Al–Sb bilayer thin films

Aluminum–antimony (Al–Sb) seems to be a promising semiconducting material for high-temperature application especially for transistors and P–N junction diodes and is a highly coefficient solar material. No attempt has been made to study the bilayer diffusion properties of Al–Sb thin film by plasma exposure. In this paper, the characterization of plasma-exposed Al–Sb bilayer thin films is presented. Thin films were coated by thermal vapor coating technique, and after coating, the sample was annealed and exposed with plasma. Results were obtained from optical band gap data and X-ray diffraction for treated and untreated Al–Sb thin films, and these results were compared with annealed Al–Sb thin films.     

Geometrothermodynamics of five dimensional black holes in Einstein–Gauss–Bonnet theory

We investigate the thermodynamic properties of 5D static and spherically symmetric black holes in (i) Einstein–Maxwell–Gauss–Bonnet theory, (ii) Einstein–Maxwell–Gauss–Bonnet theory with negative cosmological constant, and in (iii) Einstein–Yang–Mills–Gauss–Bonnet theory. To formulate the thermodynamics of these black holes we use the Bekenstein–Hawking entropy relation and, alternatively, a modified entropy formula which follows from the first law of thermodynamics of black holes. The results of both approaches are not equivalent. Using the formalism of geometrothermodynamics, we introduce in the manifold of equilibrium states a Legendre invariant metric for each black hole and for each thermodynamic approach, and show that the thermodynamic curvature diverges at those points where the temperature vanishes and the heat capacity diverges.     

Study of optical properties and molecular structure of plasma polymerized diethylene glycol dimethyl ether

This paper deals with plasma polymerization processes of diethylene glycol dimethyl ether. Plasmas were produced at 150 mtorr in the range of 10 W to 40 W of RF power. Films were grown on silicon and quartz substrates. Molecular structure of plasma polymerized films and their optical properties were analyzed by Fourier transform infrared spectroscopy (FTIR) and ultraviolet-visible spectroscopy. The IR spectra show C–H stretching at 3000–2900 cm^-1, C=O stretching at 1730–1650 cm^-1, C–H bending at 1440–1380 cm^-1, C–O and C–O–C stretching at 1200–1000 cm^-1. The concentrations of C–H, C–O and C–O–C were investigated for different values of RF power. It can be seen that the C–H concentration increases from 0.55 to 1.0 au (arbitrary unit) with the increase of RF power from 10 to 40 W. The concentration of C–O and C–O–C decreases from 1.0 to 0.5 au in the same range of RF power. The refraction index increased from 1.47 to 1.61 with the increase of RF power. The optical gap calculated from absorption coefficient decreased from 5.15 to 3.35 eV with the increase of power. Due to its optical and hydrophilic characteristics these films can be applied, for instance, as glass lens coatings for ophthalmic applications.