Mean amplitudes of vibration in some tetrahedral tetrahalogeno complexes

The Cyvin method, utilizing symmetry coordinates, has been employed here to compute the mean-square amplitude quantities, generalized mean-square amplitudes (mean-square parallel amplitudes, mean-square perpendicular amplitudes and mean cross products) and mean amplitudes of vibration for the bonded as well as non-bonded atom pairs at the temperaturesT=298°K andT=500°K for the tetrahedral tetrahalogeno complexes of zinc, cadmium, gallium, indium, thallium and arsenic. The non-linear behaviour of the mean amplitudes of vibration in terms of the electronegativities of the central atoms has been discussed, followed by a discussion on the replacement of peripheral atoms.     

Configurational-conformational statistics of stereoirregular poly(methyl methacrylate)s

The mean-square radius of gyration of poly(methyl methacrylate) (PMMA) with Bemoullian statistics was theoretically investigated utilizing the method of periodic condition. The dependent curve of the characteristic ratio of mean-square end-to-end distance on periodic microstructure length increases monotonously with the length and goes gradually to its asymptotic value for atactic PMMA chains (P _m = 0.5). Conformational energies E _α ～1.3 kcal mol^?1 and E _β ～-0.6 kcal mol^?1 of the two-state scheme are acceptable, from which the derived meansquare end-to-end distance and mean-square radius of gyration conform to the experimental data. The ratio ?S²?/χ of atactic PMMA (P _m = 0.2) as a function of the degree of polymerization χ first increases with increasing chain length, then passes through a maximum at χ = 30, and finally decreases to its asymptotic value, which is in reasonable agreement with the experimental measurements reported elsewhere. The ratio ?S²?/χ as a function of stereochemical composition indicates that theoretical and experimental data are in accord for isotactic and atactic PMMA, but small-angle neutron scattering (SANS) measurements are higher than the calculated values for syndiotactic PMMA.     

Ab-initio theoretical analysis of thermal expansivity,thermal vibrations and melting of thorium

The thermal expansivity and mean-square thermal vibrational amplitudes were determined as a function of temperature for thorium from first principles total energy calculations using the full potential linearized augmented plane wave (FP-LAPW) method. The coefficient of thermal expansion determined from variation of theoretical potential energy with interatomic separation is ～1.427 × 10^?5 K^?1 as compared to an experimental value of 1.23 × 10^?5 K^?1. The mean-square thermal vibrational amplitudes determined as a function of temperature from the theoretically calculated volume-dependent Debye temperature agree well with experimental data derived form neutron diffraction measurements. The melting temperature of thorium, determined theoretically from the mean-square thermal vibrations and the Lindemann rule for melting, is 2234 K, as compared to the reported experimental value of 2021 K.     

A re-examination of the I.R. spectrum of dinitrogen trioxide

Assuming a planar geometry of C _s symmetry and using a Urey-Bradley potential field, the force constants of dinitrogen trioxide have been re-determined within the formalism of Wilson's G-F matrix method. The outcome of the present investigation suggests a new set of force constants some of which are drastically (～ 50 per cent) different than those previously reported. Furthermore, since the i.r. frequencies used in the present investigation were obtained both in the solid state and at low temperatures, the mean amplitudes of thermal vibrations of both ¹⁴N₂O₃ and ¹⁵N₂O₃ are given at 77°k. Finally, it is suggested that more isotopic i.r. data is necessary to ascertain unequivocably the geometry of dinitrogen trioxide.     

Trapping of random walks on the line

Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability ton steps is O(( ₂n)^–1/3), where =–ln(1–c), andc is the trap concentration. (2) The short time form for the survival probability is found to be exp[–a(c)n ^1/2], wherea(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go liken ^2/3for largen. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn. One such model is studied.     

On The Contribution of the P and D Partial-Wave States to the Binding Energy of the Triton in the Bethe-Salpeter-Faddeev Approach

The influence of the partial-wave states with nonzero orbital moment of the nucleon pair on the binding energy of the triton T(nnp) in the relativistic case is considered. The relativistic generalization of the Faddeev equation in the Bethe-Salpeter formalism is applied. Two-nucleon t matrix is obtained from the Bethe-Salpeter equation with separable kernel of nucleon-nucleon interaction of the rank one. The kernel form factors are the relativistic type of the Yamaguchi functions. The following two-nucleon partial-wave states are considered: ¹S₀, ³S₁, ³D₁, ³P₀, ¹P₁, ³P₁. The system of the integral equations are solved by using the iteration method. The binding energy of the triton and three-nucleon amplitudes are found. The contribution of the P and D states to the binding energy of triton is given.

     

Helicity amplitudes and crossing relations for one-photon exchange antiproton proton reactions

Antiproton proton annihilation reactions allow unique access to the moduli and phases of nucleon electromagnetic form factors in the time-like region. We present the helicity amplitudes for the unequal-mass single-photon reaction pˉ → l ⁺ l ^- in the s channel including the lepton mass. The relative signs of these amplitudes are determined using simple invariance properties. Helicity amplitudes for one-photon exchange annihilation reaction pˉ → Bˉ are also given, where B is any spin-one-half particle with structure. Crossing relations between the ep → ep scattering and the pˉ → l ⁺ l ^- annihilation channels are discussed and the crossing matrix for the helicity amplitudes is given. This matrix may be used to verify known expressions for the space-like helicity amplitudes due to one-photon exchange.     

Topological Open Strings on Orbifolds

We use the remodeling approach to the B-model topological string in terms of recursion relations to study open string amplitudes at orbifold points. To this end, we clarify modular properties of the open amplitudes and rewrite them in a form that makes their transformation properties under the modular group manifest. We exemplify this procedure for the \mathbb C³/\mathbb Z₃{{\mathbb C}^3/{\mathbb Z}_3} orbifold point of local \mathbb P²{{\mathbb P}^2}, where we present results for topological string amplitudes for genus zero and up to three holes, and for the one-holed torus. These amplitudes can be understood as generating functions for either open orbifold Gromov–Witten invariants of \mathbb C³/\mathbb Z₃{{\mathbb C}^3/{\mathbb Z}_3}, or correlation functions in the orbifold CFT involving insertions of both bulk and boundary operators.     

Angular correlation for nuclear muon capture

Formulae for the capture rates, gamma-neutrino correlations, and angular distributions of recoil in muon capture processes J_i J_f by an unpolarized nucleus for J_i ≦ 3 and J_f ≦ 5/2, with and without change of parity of nuclear levels, are given explicitely in terms of the multipole amplitudes. Relation of helicity amplitudes for muonic atom decay to the multipole amplitudes and to amplitudes introduced by other authors is presented. The derivation is based on kinematics only, and the formulae are strictly valid for the muon capture by any nuclei. The formulae are convenient for model calculations of partial transitions with realistic nuclear and muon wave functions and for the phenomenological analysis of a weak interaction.     

Force Constants,Coriolis Coupling Constants,and Mean Amplitudes of Vibration of InCl6 3-

Abstract

The general quadratic force constants, coriolis coupling constants and mean amplitudes of vibration have been evaluated for InCl₆ ^3- using recent vibrational data. The results are employed to study the trend of variation in the isoelectronic sequences e.g. InCl₆ ^3-, SnCl₆ ^2- and SbCl₆ ^?.

In the present communication we report the force constants, coriolis coupling constants and mean amplitudes of vibration for InCl₆ ^3- which have not been reported so far. The results are used to study the trend of variation of the molecular parameters in the isoelectronic sequence e.g. InCl₆ ^3-, SnCl₆ ^2- and SbCl₆ ^?. The fundamental frequencies of InCl₆ ^3-, employed in this computation, have been reported on the basis of octahedral symmetry, from infrared and Raman Spectral Studies¹.     

G-, F-, and ∊-Matrices for XY4Z Molecules of C4V Symmetry

XY₄ Z molecules or ions with a square-pyramid structure (C_4v) are relatively rare. This explains the infrequency of investigations of their vibrational spectra, with analysis in normal coordinates and computation of the mean-square amplitudes of vibration.     

Mössbauer study of the Bi-system superconductor at low temperature

Mossbauer measurements were performed in the temperature range from 77 to 300K. Temperature-dependent⁵⁷Fe Mossbauer recoil-free fraction in high-T_c superconducting phase of Bi-system display cvidence of a softening in lattice vibrations, which appears at T<150K as a precursor effect to the onset of superconductivity. The mean-square displacement (Inf) and the mean-square velocity (IS) of Fe³⁺ ion are both characterized by Debyc temperature O_D=320K within higher temperature range.     

Charge radii and shape transitions in short-lived Hg,Au and Pt isotopes

The hyperfine structure and the isotope shift of very neutron-deficient Au and Pt isotopes have been determined at the on-line isotope separator ISOLDE/CERN by resonance ionization mass spectroscopy combined with pulsed-laser induced desorption of the implanted radioactive sample. The changes of the mean-square charge radii were determined for the isotopes¹⁸⁴Au (T_1/2=53 s) and¹⁸³Au (T_1/2=42 s) as well as for 15 isotopes of platinum in the range between¹⁹⁸Pt (stable) and¹⁸³Pt (T_1/2=6.5 min). The strong deformation of¹⁸⁵Au (|β₂|≃0.25) persits down to¹⁸³Au. In¹⁸³Pt nearly the same value of |β₂| is reached but the deformation is build up rather smoothly in contrast to the neighbouring isotopes of gold and mercury. The magnetic moment of¹⁸³Pt was found to be μ₁=+0.51(3)μ _N .     

Magnetic defect structure of iron-rich Fe x O

Mössbauer spectra were recorded at 80 and 4.2 K for Fe _x O (x> 0.95) samples that had been synthesized at 1000 C and pressures up to 10 GPa. The spectra, which consist predominantly of six broadened lines, were fit to three magnetic components: bulk Fe²⁺, defect cluster Fe²⁺ and defect cluster Fe³⁺. Mean hyperfine parameter values for bulk Fe²⁺ were calculated using second-order perturbation theory, and correlations between fluctuations were determined from the mean-square linewidths. Implications for the magnetic defect structure of Fe _x O are discussed.     

Helicity amplitudes and electromagnetic decays of hyperon resonances

We present results for the helicity amplitudes of the lowest-lying hyperon resonances Y^*, computed within the framework of the Bonn Constituent-Quark model, which is based on the Bethe-Salpeter approach. The seven parameters entering the model were fitted to the best-known baryon masses. Accordingly, the results for the helicity amplitudes are genuine predictions. Some hyperon resonances are seen to couple more strongly to a virtual photon with finite Q² than to a real photon. Other Y^*'s, such as the S₀₁(1670) Λ-resonance or the S₁₁(1620) Σ-resonance, couple very strongly to real photons. We present a qualitative argument for predicting the behaviour of the helicity asymmetries of baryon resonances at high Q².-1     

Pseudoscalar meson masses in unitarized chiral perturbation theory

This contribution summarizes the work explained in arXiv:hep-ph/0608290 where we perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. The pseudoscalar self-energies are calculated by the evaluation of the scalar self-energy loops with full S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT). These amplitudes, among other features, contain the lightest nonet of scalar resonances σ, f ₀(980), a ₀(980) and κ. The self-energy loops are regularized by a proper subtraction of the infinities within a dispersion relation formulation of the amplitudes. Values for the bare masses of pions and kaons and the η ₈ mass are obtained. We then match to the self-energies from standard Chiral Perturbation Theory (CHPT) to O(p ⁴) and resum higher orders from our calculated scalar self-energies. The dependence of the self-energies on the quark masses allows a determination of the ratio of the strange-quark mass over the mean of the lightest-quark masses, m _s/ , in terms of the O(p ⁴) CHPT low-energy constant combinations 2L ^r ₈ - L ^r ₅ and 2L ^r ₆ - L ^r ₄. In this way, we give a range for the values of these low-energy counterterms and for 3L ₇ + L ^r ₈, once the η-meson mass is invoked. The low-energy constants are further constraint by performing a fit to the recent MILC lattice data on the pseudoscalar masses, and m _s/ = 25.6±2.5 results. This value is consistent with 24.4±1.5 from CHPT and phenomenology and more marginally with the value 27.4±0.5 obtained from pure perturbative chiral extrapolations of the MILC lattice data to physical values of the lightest-quark masses.     

LaAg x In1−x

The structures of LaAg _x In_1–x alloys withx=0.75, 0.89 are determined by neutron diffraction on powder samples. The space group isI4/mmm (D _4h ^/17 ). The lattice constants splitting, the order parameter and the mean square vibrational amplitudes of the atoms are given in the temperature range from 20 KT300 K.     

A method of reduction of Einstein's equations of evolution and a natural symplectic structure on the space of gravitational degrees of freedom

A program is outlined which addresses the problem of thereduction of Einstein's equations, namely, that of writing Einstein's vacuum equations in (3+1)-dimensions as anunconstrained dynamical system where the variables are thetrue degrees of freedom of the gravitational field. Our analysis is applicable for globally hyperbolic Ricci-flat spacetimes that admit constant mean curvature compact orientable spacelike Cauchy hypersurfaces M with degM=0 andM not diffeomorphic toF ₆, the underlying manifold of a certain compact orientable flat affine 3-manifold. We find that for these spacetimes, modulo the extended Poincaré conjecture and the use of local cross-sections rather than a global cross-section, (3+1)-reduction can be completed much as in the (2+1)-dimensional case. In both cases, one gets as the reduced phase space the cotangent bundleT ^* T _M of theTeichmüller space T _M of conformal structures onM, whereM is a given initial constant mean curvature compact orientable spacelike Cauchy hypersurface in a spacetime (V, g _V ), and one gets reduction of the full classical non-reduced Hamiltonian system with constraints to a reduced Hamiltonian system without constraints onT ^* T _M . For these reduced systems, the time parameter is the parameter of a family of monotonically increasing constant mean curvature compact orientable spacelike Cauchy hypersurfaces in a neighborhood of a given initial one. In the (2+1)-dimensional case, the Hamiltonian is the area functional of these hypersurfaces, and in the (3+1)-dimensional case, the Hamiltonian is the volume functional of these hypersurfaces.     

Amplitude analysis of hypercharge exchange reactions

We present a smooth parametrization of the amplitudes for meson-baryon hypercharge exchange reactions which describes well all the data available at present for laboratory momenta above 3 GeV/c. The K_V¹ (K_T¹) amplitudes we find are very similar to the ?(ω) amplitudes, respectively, obtained already by other authors. The SU(3) assumption seems to be well supported by the experimental data.     

非线性柱形涂层复合介质有效的直流-交流电响应

利用摄动展开方法, 研究了由圆柱形带涂层杂质随机嵌入基质所形成的非线性复合介质在外加 的带有不同频率和振幅的混合电场E₀ + E₁ sinωt+E₃ sin3ωt作用下有效的直流-交流电响应, 分别推导了复合介质在杂质核、涂层及基质区域的电势分布, 并在低杂质浓度下给出了复合介质有效的非线性响应及它们之间的关系. 关键词： 非线性柱形涂层复合介质 有效的非线性响应 外加交直流电场