Green’s functions in quantum chemistry I. The Σ perturbation method

As an improvement over the Hartree-Fock approximation, we investigate a Green’s Function method—theΣ perturbation method—for molecular calculations. The method is applied to hydrogen molecule and to theπ-electron system of ethylene under PPP approximation. When the algebraic approximation is used, the energy obtained is better than that of the HF approach, but is not as good as that of the configuration-interaction method. The main advantage of this procedure is that it is devoid of the most serious defect of HF method, viz. incorrect dissociation limits.     

Partial structures and compressibilities of ions in fused potassium bromide

Treating the coulomb interaction between ion species as a perturbation on the Waisman-Lebowitz solution for direct correlation function within the hard core region, the total direct correlation function in K-space has been formulated, which gives a direct method of evaluating the partial structure factors between different ion species of the fused salts through the use of Pearson-Rushbrooke equations. The partial structure factors so obtained have been applied to evaluate the partial radial distribution functions of ion pairs. In addition, many other important associated functions such as the static correlations of total number, mass and charge densities have been computed by particular linear combination of partial structure factors. The charge neutrality relate the partial structure factors to the isothermal compressibility for the wavevectorK → 0 and hence the evaluation of the compressibilities of ions in fused KBr is possible, which agrees well with the observed value. As such the present method is very useful in investigating the structure of molten salts since only the parametersσ _ij , the distances of closest approach between ions andɛ, the effective dielectric constant (which can be estimated from the literature) are enough for this work.     

Search for low-mass exotic mesonic structures: II. Attempts to understand the results

Our previous paper, part I of the same study, shows the different experimental spectra used to draw a conclusion on the genuine existence of narrow, weakly excited mesonic structures having masses below and a little above the pion (M = 139.56 MeV) mass. This study [1] was instigated by the observation, in the Σ⁺ disintegration—Σ⁺ → pP ⁰, P ⁰ → μ⁻μ⁺ [2]—of a narrow range of dimuon masses. The authors make a conclusion on the existence of a neutral intermediate state P ₀ with a mass M = (214.3 ± 0.5) MeV. We present here some attempts to understand the possible nature of the structures observed in part I. The text was submitted by the authors in English.     

Application of density-functional perturbation theory to calculate nonlinear polarizabilities of helium-like systems

Density-based perturbation theory within the Hohenberg-Kohn (HK) formalism of density functional theory (DFT), developed recently by us, is employed to calculate hyperpolarizabilities of helium-like ions from their ground-state densities obtained from their respective Hylleraas wavefunctions. The only approximation made is that of the local density (LDA) for exchange and correlation. Use of densities — instead of wavefunctions — in density-based perturbation theory together with simple approximate energy functionals makes our calculations much simpler than those based on wavefunctions. They lead, however, to accurate results.     

Critical gravity in the Chern–Simons modified gravity

We perform the perturbation analysis of the Chern–Simons modified gravity around the AdS₄ spacetime (its curvature radius ℓ) to obtain the critical gravity. In general, we could not obtain an explicit form of perturbed Einstein equation which shows a massive graviton propagation clearly, but for the Kerr–Schild perturbation and Chern–Simons coupling θ=kx/y, we find the AdS wave as a single massive solution to the perturbed Einstein equation. Its mass squared is given by M ²=[−9+(2ℓ ²/k−1)²]/4ℓ ². At the critical point of M ²=0 (k=ℓ ²/2), the solution takes the log-form and the linearized excitation energies vanish.     

Dihyperons in chiral color dielectric model

The mass of the dibaryon having spin, parityJ ^π = 0⁺, isospinI = 0 and strangeness—2 is computed using chiral color dielectric model. The bare wave function is constructed as a product of two color-singlet three-quark clusters and then it is properly antisymmetrized by considering appropriate exchange operators for spin, flavor and color. Color magnetic energy due to gluon exchange, meson self energy and energy correction due to center of mass motion are computed. The calculation shows that the mass of the particle is 80 to 160 MeV less than twice λ mass.     

Energy efficiency of femtosecond laser ablation of refractory metals

We present the results of an experimental study of the ablation energy thresholds and ablated mass for a number of refractory metals (Ti, Zr, Nb, Mo) by femtosecond (τ _0.5 = 45–70 fs) exposed to laser pulses in the ultraviolet — near infrared range (λ = 266, 400, 800 nm) under atmospheric conditions and under vacuum (p ~ 10^–2 Pa). We have analyzed the ablation efficiency (mass yield per unit energy of the acting coherent radiation) and ablation energy thresholds vs. the laser pulse duration and photon energy.     

Erosion of the GaAs target under irradiation by a high-power pulsed ion beam

The results of examination of the GaAs-target erosion under irradiation by a high-power pulsed ion beam are reported. In the experiments, use was made of a high-power pulsed ion source with the following parameters: ion energy — 250 keV, target current density — 350 A/cm², pulse duration — 80 ns, target energy density — up to 7 J/cm². The target erosion coefficient and its dependence on the number of successive pulses are measured. It is found that the surface roughness parameter is increased with the number of successive beam pulses. A regular structure of surface relief is observed to form in the case where the number of pulses > 20–40. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 66–70, January, 2007.     

Self-assembled quantum dot semiconductor nanostructure modeling

The calculation of the electronic structure of a vertical multifold stack of self-assembled InAs/GaAs lens-shaped quantum dots is presented. The developed numerical method is based on a rigorous Hamiltonian formulation of an eight-band k.p perturbation accounting for the carrier kinetics and lattice-mismatch strain endured by the islands. The considered implementation is built upon a custom partition of the unit cell. The accompanying validation analysis—consisting of a comprehensive hierarchy of convergence criteria, qualitative, and quantitative test cases—unequivocally shows that the obtained results adhere to the prescribed zero dimensional physics.     

Superintegrability on N-dimensional spaces of constant curvature from so(N + 1) and its contractions

The Lie—Poisson algebra so(N + 1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the N-dimensional spherical, Euclidean, hyperbolic, Minkowskian, and (anti-)de Sitter spaces. We firstly present a Hamiltonian which is a superposition of an arbitrary central potential with N arbitrary centrifugal terms. Such a system is quasi-maximally superintegrable since this is endowed with 2N — 3 functionally independent constants of motion (plus the Hamiltonian). Secondly, we identify two maximally superintegrable Hamiltonians by choosing a specific central potential and finding at the same time the remaining integral. The former is the generalization of the Smorodinsky—Winternitz system to the above six spaces, while the latter is a generalization of the Kepler—Coulomb potential, for which the Laplace—Runge—Lenz N vector is also given. All the systems and constants of motion are explicitly expressed in a unified form in terms of ambient and polar coordinates as they are parametrized by two contraction parameters (curvature and signature of the metric). The text was submitted by the authors in English.     

Non-physical consequences of the muffin-tin-type intra-molecular potential

We demonstrate, using a simple model, that, in the frame of muffin-tin-like potential, non-physical peculiarities appear in molecular photoionization cross-sections that are a consequence of “jumps” in the potential and its first derivative at some radius. The magnitude of non-physical effects is of the same order as the physical oscillations in the cross-section of a diatomicmolecule. The role of the size of these “jumps” is illustrated by choosing three values for it. The results obtained are connected to the previously studied effect of non-analytic behavior as a function of r, the potential V(r) acting upon a particle on its photoionization cross-section. In reality, such potential has to be analytic in magnitude and have a first derivative function in r. The introduction of non-analytic features in model V(r) leads to non-physical features — oscillations, additional maxima, and so forth — in the corresponding cross-section.     

Some top-quark propertie s mea sured in $$p\bar p$$ colli sion s u sing CDF detector at √ s = 1.96 TeV (Review)

This review considers important properties of the top-quark. The top-quark decays before hadronization, and the spin information is directly transferred to the decay products. Therefore the structure of the weak interaction is investigated by measuring the helicity fractions, f, of the W boson—the top-quark decay product. Other investigations: search for the presence of V+A interaction, search for exotic top-quark charge — 4/3 and for t[`(t)]t\bar t — resonances—all of them, so far, were not found in the experiments — testifies against of going out of the Standard Model.     

Formation of a chaotic layer of nonlinear resonance by a two-frequency perturbation

A new effect [V. V. Vecheslavov, Zh. éksp. Teor. Fiz. 109, 2208 (1996) (JETP 82, 1190 (1996)]—the appearance of low-frequency secondary harmonics in the separatrix mapping of a system—is discussed in detail for the example of a pendulum with a two-frequency perturbation. It is shown that there exist regions of values of the perturbation parameters where these harmonics make the main contribution to the formation of the chaotic layer of the fundamental resonance. The results of analytical and numerical determinations of the amplitudes of the secondary harmonics are compared. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 989–994 (25 June 1996)     

Shiva diagrams for composite-boson many-body effects: how they work

The purpose of this paper is to show how the diagrammatic expansion in fermion exchanges of scalar products of N-composite-boson (“coboson”) states can be obtained in a practical way. The hard algebra on which this expansion is based, will be given in an independent publication. Due to the composite nature of the particles, the scalar products of N-coboson states do not reduce to a set of Kronecker symbols, as for elementary bosons, but contain subtle exchange terms between two or more cobosons. These terms originate from Pauli exclusion between the fermionic components of the particles. While our many-body theory for composite bosons leads to write these scalar products as complicated sums of products of “Pauli scatterings” between two cobosons, they in fact correspond to fermion exchanges between any number P of quantum particles, with 2 ≤P≤N. These P-body exchanges are nicely represented by the so-called “Shiva diagrams”, which are topologically different from Feynman diagrams, due to the intrinsic many-body nature of the Pauli exclusion from which they originate. These Shiva diagrams in fact constitute the novel part of our composite-exciton many-body theory which was up to now missing to get its full diagrammatic representation. Using them, we can now “see” through diagrams the physics of any quantity in which enters N interacting excitons — or more generally N composite bosons —, with fermion exchanges included in an exact — and transparent — way.     

Isospin breaking in <Emphasis Type="BoldItalic">K</Emphasis><Subscript><Emphasis Type="BoldItalic">l4</Emphasis></Subscript> decays

Data on K _e4 decays allow one to extract experimental information on the elastic π π scattering amplitude near threshold, and to confront the outcome of the analysis with predictions made in the framework of QCD. These predictions concern an isospin symmetric world, while experiments are carried out in the real world, where isospin-breaking effects—generated by electromagnetic interactions and by the mass difference of the up and down quarks—are always present. We discuss the corrections required to account for these, so that a meaningful comparison with the predictions becomes possible. In particular, we note that there is a spectacular isospin-breaking effect in K _e4 decays. Once it is taken into account, the previous discrepancy between NA48/2 data on K _e4 decays and the prediction of π π scattering lengths disappears.     

Direct methanol fuel cells: The influence of methanol on the reduction of oxygen over Pt/C catalysts with different particle sizes

Two Pt/C catalysts with different particle sizes (Pt/C: 2.5 nm, Pt/C-700Ar: 5.1 nm) were investigated by applying a half-cell configuration —rotating disk electrode (RDE) technique in H₂SO₄ aqueous solutions in the absence of or in the presence of methanol with different concentrations. Pt/C catalyst exhibited higher mass activity in H₂SO₄ aqueous solution without methanol and slightly lower mass activity in H₂SO₄ plus 0.1 mol/L CH₃OH in comparison with that of Pt/C-700Ar catalyst. On the contrary,single direct methanol fuel cell (DMFC) tests showed that Pt/C exhibited higheroxygen reduction reaction (ORR) activity and better cell performance, mainly due to the different kinds of electrolyte properties. Furthermore, it suggested that a better single DMFC performance could be obtained with a smaller particle size Pt-based cathode catalyst. Paper presented at the Patras Conference on Solid State Ionics — Transport Properties, Patras, Greece, Sept. 14 — 18, 2004.     

Electron impact excitation of hydrogen and helium in Coulomb-projected Born methods

Coulomb-projected Born methods for the theoretical study of electron impact excitation of hydrogen and helium are reviewed. The results obtained by using different forms of Coulomb-projected Born methods are compared with other theoretical and experimental results and analyzed. The inadequacy of the variable charge Coulomb-projected Born approximation (VCCPB)—the most recent form of the Coulomb-projected Born methods—in giving good results in processes where exchange is dominant is discussed in detail. The ‘modified’ VCCPB approximation obtained by modifying the VCCPB method to remove its shortcomings is also discussed and its application to electron impact excitation of 2³ s state of helium is studied.