Quasi-derivations and QD-algebroids

Axioms of Lie algebroid are discussed. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the C∞(M)-module ? of sections of a vector bundle E over a manifold M which satisfies [X, ? Y] = ? [X, Y] + A (X, ?)Y for all X, Y ε ?, ? ε C∞(M), and for certain A (X, ?) ε C∞(M)) is a Lie algebroid if rank (E) > 1, and is a local Lie algebra in the sense of Kirillov if E is a line bundle. Under a weak condition also the skew-symmetry of the bracket is relaxed.     

Search for strangeness changing neutral currents induced by neutrinos in gargamelle

A sample of 9930 neutrino neutral current interactions has been examined for single strange particle production. No signal in the channels νN → νγX and νN → ν|gS⁰X, where X means non-strange hadrons, has been found. This yields an upper limit of 5.4 × 10^?3 to a 90% confidence level on the ratio [(ν → νΓX) + (ν → νΣ⁰X)]/[ν → ν + anything]     

The Gell-Mann-Goldberger formula for long-range potential scattering

A derivation of the Gell-Mann-Goldberger (GG) formula and cut-off versions of this formula for the T-matrix involving long-range potentials is given. The derivation is based on the time-dependent and recently developed stationary formalisms for scattering via long-range potentials. A stationary S-operator expression for two-body Coulomb-like scattering is derived. Using the well-known expression for the off-energy-shell “T-matrix” for a pure Coulomb potential the energy-shell limit of this stationary expression is shown to yield the pure Coulomb scattering amplitude. A proof of the convergence of the perturbation series corresponding to the Gell-Mann-Goldberger formula for the two-body Coulomb-like T-matrix is given.     

Substitutional impurity in the graphene quantum dots

The process of formation of the localized defect states due to substitutional impurity in sp²-bonded graphene quantum dot is considered using a simple tight-binding-type calculation. We took into account the interaction of the quantum dot atoms surrounding the substitutional impurity from the second row of elements. To saturate the external dangling sp² orbitals of the carbon additionally 18 hydrogen atoms were introduced. The chemical formula of the quantum dot is H₁₈C₅₁X, where X is the symbol of substitutional atom. The position of the localized levels is determined relative to the host-atoms (C) ε_p energies. We focused on the effect of substitutional doping by the B, N and O on the eigenstate energies and on the total energy change of the graphene dots including for O the effect of lattice distorsion. We conclude that B, N, and O can form stable substitutional defects in graphene quantum dot.     

Prediction of double-pomeron cross sections from single-diffraction measurements

A particular case of a Mueller formula describing the absence of long-range two-particle correlations is used to predict double-pomeron cross sections from available data on single-diffraction dissociation. Although success of the formula in this application would immediately verify the double-pomeron hypothesis, the converse is not true because the formula may be invalidated by prominent low-energy resonances (such as the f₀) in the pomeron-pomeron total cross section. Low-statistics experiments at s = 200 and 400 GeV² are in order of magnitude agreement with the formula.     

Simple formulae for heavy ion subcoulomb transfer probabilities. Application to one and two-proton transfers in bismuth

A simple analytical formula is given to express the transition probability in a quasi-elastic transfer reaction. This formula is derived from the DWBA amplitude, using assumptions based on the fact that the main contribution to the DWBA integral comes from a narrow domain of distances of approach. Recoil effects are taken into account. This method is applied to calculate the excitation functions for one and two-proton transfer reactions induced in²⁰⁹Bi by heavy ions, below and near the barrier. The curves obtained are compared to the excitation functions measured for the production of residual²¹⁰Po and²¹¹At. The corresponding transfer reactions involve excitation energiesE ^* of the residue lying in the range 0–8 MeV. This excitation energy is taken as a free parameter in the calculation, and the valuesE _opt ^* which lead to the best agreement between the calculated and experimental curves are consistent with the classical values for the optimum reactionQ-values. Nuclear Reactions. Simplified transition probability for quasi-elastic transfer. Calculatedσ(E) ²⁰⁹Bi(X, Y)²¹⁰Po,²¹¹At,X=¹⁴N,¹⁶O,¹⁹F,⁴⁰Ar,⁴⁰Ca,⁵⁶Fe,⁶³Cu near threshold. Compared experimental data. Deduced optimum excitation energy.     

Effect of N-substitution in multinuclear complexes allows interplay between magnetic states and multistability investigated by Mössbauer spectroscopy

A series of pentadentate ligands N–X–⁵LH₂ (X?=?H, Methyl, Benzyl)?=?N–X–saldptn (4-X-N,N′-bis(1-hydroxy-2-benzylidene)-1,7-diamino-4-azaheptane) has been prepared by a Schiff base condensation between 1,7-diamino-4-X-azaheptane and salicylaldehyde. Complexation with Fe(III) yields a series of high-spin (S?=?5/2) complexes of [Fe^III(N–X–⁵L)Cl]. Such precursors were combined with [Mo(CN)₈]^4? and a series of blue nonanuclear cluster compounds [Mo^IV{(CN)Fe^III(N–X–⁵L)}₈]Cl₄ resulted. Such star-shaped nonanuclear compounds are high-spin systems at room temperature. On cooling to 10 K some of the iron(III) centers switched to the low-spin state as proven by Mössbauer spectra, i.e. multiple electronic transitions. Parts of the compounds perform a high-spin to high-spin transition. Under light irradiation the populations are altered slightly.     

New soft porous frameworks based on lambda-zirconium phosphate and aliphatic dicarboxylates: Synthesis and structural characterization

New dicarboxylate-functionalized pillared materials with a general formula of λ-ZrPO₄(OH)_1-x(OOC(CH₂)_nCOO)_x/2(dmso) (n=6, 8 and 10) have been prepared by post-synthesis modification of the inorganic layers of λ-zirconium phosphate (λ-ZrP), where the superficial Chloride monovalent anionic ligands of λ-layer are partially exchanged with the divalent anionic ligands of a series of long-chain aliphatic dicarboxylic acids, namely octanedioic acid, decanedioic acid and dodecanedioic acid. The synthesized materials are characterized by X-ray diffractometry, FT-IR spectrophotometry, elemental and thermogravimetric analyses. The X-ray diffraction patterns show that the obtained solid phases are pure. Furthermore, the interlayer distance of λ-ZrP systematically increases from 1.02 to 1.59 nm as a result of the incorporation of the mentioned acids inside the interlayer gallery.     

固溶体的位形配分函数

这篇短文分二节,第一节是将王德懋,许永焕及作者所合写的一篇论文中的求固溶体的配分函数的方法,应用到各种固溶体上。我们处理了二种不同晶体结构的情形,处理了有长程秩及无长程秩的情形,处理了只有最近邻作用而无其他邻作用的情形及既有最近邻作用又有次最近邻作用的情形。在各种不同情形下,这个方法都被证明是合用的。第二节是用同一方法讨论准化学公式。我们证明了在保留了这个方法中所谓结构常数中的最低一个时,准化学公式是成立的,不论固溶体中有多少种原子。其次,我们指出,在保留较高级的结构常数后,寻常的准化学公式应如何的改进。最后我们直接写下三个互为近邻的原子所构成的各种不同的集团的数目的准化学公式,讨论了与此相应的组合数,并指出这样的理论与我们的理论是不同的。     

Photoelectron spectra of bis-cyclopentadienyl metal dihalides

He(I) and HE(II) photoelectron spectra are reported for (η-C₅H₅)₂MX₂ (M = Ti; X = F, Cl, Br, I: M = Zr, Hf; X = Cl, Br: M = Ta; X = Cl, Br) and (η-MeC₅H₄)₂MX₂ (M = Nb, X = Cl: M = Mo; X = Cl, Br, I). A substantial variation is found in the ordering of the halogen and cyclopentadienyl ionizations, the order being dependent on the metal as well as on the halogen. The compounds may be divided into three classes, namely, those in which the electrons in cyclopentadienyl e₁ orbitals ionize at a lower energy than those occupying halogen pπ orbitals, those in which halogen pπ electrons have lower ionization energy than cyclopentadienyl e₁ electrons and those in which the corresponding electrons arise from extensively delocalized molecular orbitals with significant contributions from both these categories of fragment orbital.     

High energy fission and spallation systematics for trans-bismuth nuclei

A semi-empirical formula has been developed to estimate high energy (> 0.6 GeV) fission cross sections. This formula has then been used with a Rudstam-type spallation formula to estimate spallation yields for trans-lead nuclei.     

Refinement of a formula for decay after weak coherent excitation of a sphere

A new formula has been given recently by A.A. Svidzinsky and M.O. Scully to describe the temporal evolution of the excitation function in a large sphere satisfying the Markov condition after excitation by a single photon. This formula is based on a physically reasonable Ansatz from which differential equations are inferred for the undetermined radial functions in the Ansatz. The solution to these differential equations leads to the formula for β. Numerical calculations from this formula yield a value ∼10% for the maximum probability of occupancy of secondary excited states.In this paper, we refine the formula of Svidzinsky and Scully by allowing the radial functions in the Ansatz to depend on the angular index l of the spherical Bessel functions. By using the Debye formula for the asymptotic behavior of j_l(u) for large l as well as u, we obtain differential equations in each angular sector, similar to theirs but with a dependence on l. The solution to these equations yields our improved formula, from which we calculate 17.1% for the maximum probability of secondary excited states.     

A study of the VUV emission from highly ionized krypton in a theta pinch plasma

The ionization rates of Kr(IX), (X), (XI), and (XII) have been measured using a fast 60-kV-60kJ theta pinch as a plasma source. The line emission from each ion stage has been identified and the time evolution observed. A coupled set of rate equations was used along with time- and space-resolved measurements of the electron density and temperature to model the plasma light emission. The ionization rates of Kunze were adjusted by multiplying the rate for each ion stage with a constant until the peak intensity of the calculated emission agreed with the time of the observed peak intensity. The constants required for best fit were 2.5, 0.15, 3.0, and 2.0 for Kr(IX), (X), (XI), and (XII), respectively. Two successive ionization stages, Kr(X) and Kr(XI), have shown the same time dependence and possible reasons for this observation are discussed. During the course of modeling the light emission, we have also found that the rate for the excitation from the 3dⁿ to the 3p⁵3dⁿ⁺¹ level in Kr(X) (n=9) and Kr(XI) (n=8) is a factor of 5 lower than predicted by the van Regemorter excitation rate equation.     

Characterization of copper-exchanged Na-A,X and Y zeolites with X-ray photoelectron spectroscopy and transmission electron microscopy

Copper-exchanged sodium- A, X and Y zeolites have been characterized with X-ray photoelectron Spectroscopy (XPS), with supporting electron microscopy and X-ray diffraction measurements. Under reducing conditions (CO, H₂, 250–450° C), four distinct chemical states of copper have been identified. These are intrazeolite Cu(II), Cu(I) and 1 nm metal clusters, and externally segregated copper metal crystallites. We report spectroscopic data for both the Cu 2p_{$\text{3}\text{2}$} and Auger L₃M_4,5M_4,5 lines. Whereas Cu(II) and metallic copper crystallites have normal spectroscopic parameters, Cu(I) and 1 nm Cu clusters in the reduced zeolites lie in new areas of the two-dimensional chemical state plot.The reduction sequence of Cu(II), Cu(I), Cu clusters and Cu crystallites is different on the A zeolite compared with X and Y. One nm metal clusters are identified as an intermediate phase on the A with transmission electron microscopy (TEM) and XPS prior to external diffusion and crystallite formation. The ease of formation of the cluster intermediate in the A zeolite may be a consequence of the larger diffusion barrier imposed by the 0.42nm supercage aperture compared with the 0.74nm aperture in the X and Y zeolites.     

Femtosecond mid-IR pump-probe spectroscopy of photoinduced insulator to metal transition in dimer Mott insulator κ-(BEDT-TTF)2X

Ultrafast dynamics of the photoinduced insulator (I) to metal (M) transition were investigated using femtosecond mid-infrared pump-probe spectroscopy in two-dimensional organic Mott insulators [bis (ethylenedithio)]-tetrathiafulvalene (BEDT-TTF) salts κ-(BEDT-TTF)₂X (κ-(ET)₂X, where X denotes anion). In κ-(d-ET)₂Cu[N(CN)₂]Br, a metallic state was photogenerated using a phonon-mediated mechanism: the effective bandwidth increases through the photoinduced molecular rearrangement. The mechanism differs fundamentally from the previously reported photoinduced filling control in one-dimensional Mott insulators.     

A search for narrow resonances in the φφ system

Inclusive φφ production has been studied in π^?Be interactions at 85 GeV/c incident momentum, and a signal of 4327 φφ events was found in a sample of data recorded with the aim of studying the low mass φφ system. We estimate that ～ 75% of this signal can be attributed to the correlated production of two φ′s. A search for narrow enhancements leads to upper limits at the 99.7% confidence level for σ(X) × BR(X → φφ) varying from ? 562 nb/Be nucleus at a mass of 2.1 GeV/c² to ? 221 nb/Be nucleus at 3.1 GeV/c², where X represents a possible narrow state. These upper limits represent an increase in sensitivity by a factor 3 to 5 when compared to currently available data.     

Algebraic study of a class of relativistic wave equations

First-order relativistic wave equations are considered whose irreducible matrix coefficients satisfy the simplest (except for the Dirac algebra) unique mass condition, (β · p)³ = p²(β · p), which is also sufficient to guarantee causality in a minimally coupled external electromagnetic field. All of the associated representations of SL(2, ©) are classified and studied up to and including those which are the direct sum of four irreducible components, (n, m), with either n or m less than two. A large number of families of representations are found which permit the algebraic condition to be satisfied. These are tabulated according to whether a Hermitian choice for β⁰ is possible and their spin content is given. If a unique spin is described, then the only possible representations are

$\text{(1) (}\text{n}\text{,0) ⊕ (}\text{n}\text{? 1/2, 1/2)}$

$\text{(2) (}\text{n}\text{,0) ⊕ (}\text{n}\text{+ 1/2, 1/2)}$

$\text{(3) (}\text{n}\text{+ 1/2, 1/2) ⊕ (}\text{n}\text{,0) ⊕ (}\text{n}\text{? 1/2, 1/2)}$

$\text{(4) (1,0) ⊕ (1/2, 1/2) ⊕ (0,1)}$

and their conjugates. If, in addition, the representation is assumed to be self-conjugate, then only the Dirac and Petiau-Duffin-Kemmer equations survive.     

A nuclear mass formula based onSU(4) symmetry

It is argued that mass anomalies at the N≈Z line are associated with SU(4) isospin-spin symmetry. Drawing on these arguments, a Weizsäcker-type nuclear mass formula is investigated which has the eigenvalue of the quadratic Casimir operator of SU(4) as a Wigner term. This SU(4)-based mass formula yields a better agreement than the one with the usual Wigner term |N—Z|/A. In addition, the SU(4) eigenvalue expression adequately replaces the usual pairing term of the Weizsäcker formula giving a lower overall rms deviation than the latter.     

Semiempirical relation between λ and 2Δ/ktC of superconductors

A simple formula relating the electron-phonon coupling constant λ and 2Δ/kT_C is proposed. The formula allows one to estimate λ on the basis of experimental Δ and T_C.