A discussion of the relativistic equal-time equation

Ruan Tu-nan et al. [1] have proposed an equal-time equation for composite particles which is derived from Bethe-Salpeter (B-S) equation. Its advantage is that the kernel of this equation is a completely definite single rearrangement of the B-S irreducible kernel without any artificial assumptions. In this paper we shall give a further discussion of the properties of this equation. We discuss the behaviour of this equation as the mass of one of the two particles approaches the limitM ₂→∞ in the ladder approximation of single photon exchange. We show that up to orderO(α⁴) this equation is consistent with the Dirac equation. If the crossed two photon exchange diagrams are taken into account the difference between them is of orderO(α⁶).     

On the connection between the vacuum polarization potential in muonic atoms andg-2 of the muon

A simple connection, between the vacuum polarization potential used in muonic atoms and the muon anomaly arising from the second-order vertex graph with electron vacuum polarization insertions, is established. In particular, the leading log-term and the orderm _e/m _μ term are essentially the same in the two cases. We make use of this connection to determine the vacuum polarization potential in order α³(Zα).     

Mass corrections to the tau decay rate

In this note radiative corrections to the total hadronic decay rate of the τ-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate rationR _τ to the order0(α _s ² m²) and find that they contribute appreciably to the Cabbibo supressed decay modes of the τ-lepton. We also discuss corrections of mass dimensionD=4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.     

Recoil corrections to the hyperfine splitting of exotic atoms

All recoil corrections to the hyperfine structure to orderα ⁴ are given, for arbitrary nuclear spins.     

Electronic properties of metals at low temperatures

A many body theory of an electron gas is developed to find the internal and correlation energies at low but finite temperatures. The contribution from the first order exchange, second order (regular and anomalous) exchange, and ring diagrams are treated. The Fermi momentum and the correlation energy are determined as functions of the density by two different methods, one being based on iteration and the other a direct solution of the number density relation. It was found that the iterative solutions which are correct to ordere ² ore ⁴ become negative forr _s of order 5 while the direct solutions do not, indicating the invalidity of the former. Hence, the correlation energy evaluated to the same orders by iteration will not be satisfactory in the same range. The highest order iterative solution which includes terms of ordere ⁶ does not show such a breakdown. These terms which give the contribution of orderr _s to the correlation energy are therefore important and tend to reduce the magnitude of the correlation energy. The corresponding curve is indeed close to that determined by the direct method for smallr _s but a significant deviation takes place at largerr _s . The Coulomb interaction seems less effective at higher temperatures. The internal energy is also determined as a function of density and temperature.     

Investigation on crystalline structure and dielectric relaxation behaviors of hot pressed poly(vinylidene fluoride) film

The dielectric relaxation behaviors of hot pressed poly(vinylidene fluoride) (PVDF) film have been studied using dielectric spectroscopy in the frequency domain from 20 Hz to 5 MHz at temperatures between 20 °C and 200 °C. Crystalline/amorphous interphase is suggested with methods of FTIR, XRD, and DSC. Frequency and temperature dependence of dielectric spectroscopy reveals the relaxation behavior and structural dynamics of the samples, and three types of relaxation processes are suggested, α_Ac relaxation process contributed by the hopping transport process near the periphery of conduction band or valence zones at Fermi energy, α_c relaxation process related to the structure change of crystal lattice trapped dipoles in crystalline regions, and α_a relaxation process arising from segmental dipole rearrangement of interphases in amorphous regions. Cole-Cole and Havriliak-Negami experimental equations were utilized to analyze these relaxation processes, and differences of Arrhenius parameters for α_Ac and α_c relaxation processes obtained from Cole-Cole and Havriliak-Negami equations were discussed in detail. Activity energy of different relaxation processes obtained from Arrhenius equation and VFT equation indicates non-single thermal activation mechanism for hot pressed PVDF film.     

Z-dependent theory of many electron atoms. I. SimplestS-sums

Simplest possibleS-sums 〈p, α ¦q, Β〉 _kl occuring in the second orderZ-dependent theory of many-electron atoms, are defined by Eq. (7) of the text. 〈l, α ¦l, Β〉 _kl are written in closed form for positiveα, Β andl integer ≧0; 〈p, α ¦q, Β〉 _kl for integerp>l,q>l can be reached by means of recurrence relations. The new method is demonstrated and tested on examples previously calculated in the literature.     

The localization of local and gap modes by the sign count method

In the theory of local states it is usual to bring the linear problem ¦glI _N ?D¦=0 into a non-linear one ¦R(λ)¦=0, where the ordern of the condensed stiffness matrixR(λ) is much smaller than the orderN of the matrixD. Powerful methods exist for determining the number of the eigenvalues ofD in some interval without solving the equation ¦glI _N ?D¦=0 explicitly. It is shown, that analogous methods can be applied to the condensed matrix R(λ), when computing the eigen-valuesλ outside the frequency spectrum of the ideal lattice.     

Spin alignment of yrast levels populated by pre-equilibrium (α, xnγ) reactions

Angular momenta of yrast levels following pre-equilibrium (α, xnγ) reactions at E_α, = 110 MeV were found to be aligned as well as those following the equilibrium (compound) (α, xnγ) reactions at E_α = 20–50 MeV. They are uniform against the neutron multiplicity x. The degrees of the spin (angular momentum) alignment with rank 2 for the yrast levels with spins 8–12 average about α₂ ≈ 0.87 ± 0.05. The good spin alignment indicates that both the neutron emission and the γ-emission are stretched in angular momentum space. This supports the pre-equilibrium neutron emission process, where the momenta carried away by the neutrons are not in random directions but rather in the beam direction. The result is well reproduced by the pre-equilibrium neutron emission process followed by neutron evaporation and the K-band γ-deexcitation process.     

Quasi-confinement in theSU(3)-gluon plasma

We investigate a phenomenological equation of state for the gluon plasma, which differs from the ideal gluon gas equation of state in three aspects: (a) it is assumed that gluons withlow momentum are subject to confining interactions anddo not contribute to the energy spectrum of free gluons; (b)only gluons withhigh momentum are considered as an ideal gas with perturbative corrections of orderO(α_s); (c) a non-perturbative vacuum pressure is included. We show that feature (a) allows for a reasonable perturbative treatment of the interaction between gluons with high momentum. The equation of state reproduces lattice data for the thermodynamical functions of theSU(3) pure gauge theory above the deconfinement transition temperatureT _c. This result suggests that a possible way to describe the gluon plasma is in terms of perturbatively interacting gluons and non-perturbative “glueball” states.     

Giant resonance decays in 20Ne, 22Ne and interference effects with quasifree scattering processes

The charged particle (c) decay from excited states up to the giant quadrupole resonance (GQR) in ²⁰Ne has been studied in a kinematically complete ²⁰Ne(α, α′ c) coincident experiment at E_α = 155 MeV. Angular correlation functions and branching ratios are extracted for the α₀, α₁ and p₀ decay channels. The (α, α′ α₀) angular correlation functions are analysed in PWBA in terms of coherent interference with the quasifree scattering process leading to the same final states. Good fits to the data are achieved over a large range of excitation energies. Branching ratios have been extracted and compared to results of Hauser-Feshbach calculations. Above E_x = 12.5 MeV excitation energy a discrepancy was found between the experimentally observed α₀ branching ratios and the HF predictions. These results yield evidence for a direct α₀ decay mechanism of the split isoscalar giant quadrupole resonance in ²⁰Ne. Some results are presented also for a ²²Ne(α, α′ c) coincidence experiment. Qualitative comparison has been made between the general decay behaviour of the two Ne isotopes.     

On the order of the herringbone transition of N2 on graphite: a Monte Carlo study

Using the anisotropic planar-rotor model we investigate the herringbone phase transition of N₂ in the (√3 × √3)R30° commensurate phase on graphite by large scale Monte Carlo simulations. The effective correlation length ξ is measured near the transition temperature T₀. The data, extrapolated to T₀, yield a large but finite ξ at T₀ demonstrating that the herringb ordering is a weak first order transition.     

Unraveling the radical chain mechanism in the pyrolysis of β-O-4 linked lignin: The role of aliphatic substituents

Lignin pyrolysis involves complex radical reactions, whereas the radical chain process, especially the influence of aliphatic substituents, has been rarely studied. Herein, the typical β-O-4 lignin dimer, phenethyl phenyl ether (PPE), and three aliphatic substituted derivatives of PPE, namely α-OH substituted, β-CH₂OH substituted, and α,β-disubstituted PPE (αPPE, βPPE, and αβPPE) were employed as model compounds. DFT calculations, electronic analyses, and fast pyrolysis experiments were combined to investigate three core steps of the radical chain mechanism in lignin pyrolysis, i.e., homolysis, hydrogen abstraction, and radical decomposition. The pathway involving successive C_β-O homolysis → α-hydrogen abstraction → C_β-O breakage of α-dehydrogenated radical is dominated for the pyrolysis of aliphatic substituted β-O-4 linked lignin, with the formation of phenolics. The hydrogen abstraction reactions at the C_α site are obviously superior to those at other sites for PPE derivatives, due to the p-π conjugate stability. Notably, α-hydrogen abstraction can be significantly promoted by the π-electron-dispersing α-OH substitution. The decomposition step of dehydrogenated radicals can be facilitated by the electron-donating β-CH₂OH substitution, where the C_β-O breakage of the α-dehydrogenated radical is dominant. Totally, aliphatic substituents can improve the radical growth stage and change the competitiveness of the hydrogen abstraction and radical decomposition reactions. The fast pyrolysis experiments of PPE and αPPE gave direct proof that the generation of characteristic products from the radical chain process, i.e., benzaldehyde and phenylacetaldehyde, was enhanced by the α-OH substitution. The present work offers the potential to give a comprehensive image of the radical chain mechanism in lignin pyrolysis.     

Effect of palladium oxidation state on the kinetics and mechanism of the charge transfer reaction taking place at the Pd/YSZ interface

Electrode polarization and conductivity measurements were carried out at the Pd/YSZ interface and at conditions close to the Pd–PdO thermodynamic equilibrium. The steady-state current–overpotential characteristics were analyzed with a Butler–Volmer type of equation. Both, apparent exchange current density, I_o, and anodic/cathodic charge transfer coefficients (α_a/α_c), were calculated. Based on the experimental results, it was concluded that the charge transfer at the electrode is rate-determining in the case of PdO during anodic operation and Pd during cathodic operation, while in the other case mass transport of adsorbed oxygen species along the electrode/solid electrolyte interface is in competition with the charge transfer process.     

Development of a Lyman-α laser system for spectroscopy and laser cooling of antihydrogen

Hydrogen Lyman-α radiation (121.56 nm) is important because it allows for the excitation and detection of ground-state hydrogen atoms by a one-photon process. The trapping of antihydrogen, recently reported by the ALPHA collaboration at CERN, has revived interest in Lyman-α lasers. In order to perform high precision tests of matter-antimatter symmetry violations or gravity-antimatter interactions with antihydrogen, laser cooling using the 1s ? 2p single photon transition is essential. Recent theoretical simulations predict that even with a pulsed Lyman-α source, laser cooling of antihydrogen would be possible. Here we describe the implementation of a high power vacuum-ultraviolet (VUV) laser at the Lyman-α transition of hydrogen. The VUV light was generated using a two-photon-resonant four-wave mixing process in a phase-matched mixture of krypton and argon. Two wavelengths (ω _R → 202.31 and ω _T → 602.56 nm) were mixed in a sum-difference scheme (ω _VUV = 2ω _R ? ω _T ) with a two-photon resonance at (4s ²4p ⁵5p[1/2]₀ ← 4s ²4p ⁶(1S ₀)) transition in Kr. With an Ar/Kr mixture of 3.9:1 we obtained 10 ns pulses of 0.1 μJ of energy at a repetition rate of 10 Hz.     

On the corrections of the wave function in weakly bound quarkonium

A non-relativistic quark-antiquark system with perturbative gluonic interactions (quarkonium) is considered, which allows a systematic expansion in the strong coupling constant α_s. In a non-abelian gauge theory, non-trivial corrections of the wave function already occur to O(α_s). We emphasize the existence of a renormalization, which is “natural” for such a system leaving only little freedom in the choice of the renormalization point Λ. The general corrections to O(α_s) including coulombic binding are presented. An explicit application to the lowest-order gluonic corrections of the leptonic decay of quarkonium is made. In this process the new term is sometimes much larger than the gluonic correction at the photon vertex and it varies greatly between different coulombic (S-wave) bound states.     

Inner-shell ionization ofZ=25–32 elements by 5-48 MeV32S ions

TheK-shell ionization cross sections of Mn, Ni, Cu, Zn and Ge under³²S bombardment have been measured in the energy range from 5 to 48 MeV. The cross sections are compared with available theories based on a direct Coulomb ionization mechanism and with the predictions of theK-vacancy sharing process. This last process can reasonably account for the measured cross sections at high bombarding energies. The energy shifts of theK _α- andK _β-lines and theK _α/K _β-intensity ratios have also been measured. This information is used to deduce the defect configuration of the atoms. The mechanisms responsible for the multiple vacancy production are discussed.     

Quark deconfinement in a semiclassical string-bag model

We describe the effective static quark-(anti)quark colour potential inside hadronic bags in terms of linear strings and semiclassical corrections of order?/r. According to (chromo-) electrostatics we generalize this potential to colour non-neutral configurations making use of the mirror charge method. A thermodynamical study of quark-antiquark pairs and many-quark systems shows a virtually higher order phase transition from the hadronic phase to colour deconfinement. The free plasma stage, furthermore, is achieved only at temperatures much higher thanT _c≈200 MeV. Hadrons increase in size by a factor of 1.5 fromT=0 toT=T _c.     

Kinetic studies of the electrochemical nitrogen reduction and incorporation into yttria stabilized zirconia

The kinetics of the electrochemical reduction of molecular nitrogen at gold micro electrodes on yttria stabilized zirconia (YSZ) solid oxide electrolyte is studied by steady state polarization measurements. From the η / lg i plot for both cathodic and anodic polarization the apparent transfer coefficients α_a and α_c are evaluated. The sum of α_a + α_c exceeds unity and thus a multistep electron transfer process is suggested. The concept of the stoichiometric number is applied to the electrode reaction N₂ + 6e⁻ = 2N³⁻ supposing that the overall process involves at least two intermediate species. On the basis of the evaluation of the experimental results the reaction N₂⁻ + e⁻ ⇌ N₂²⁻ is suggested as the rate determining reaction step for the cathodic nitrogen reduction and nitride formation.     

Probing electric field distribution in organic double-layer diode by electric field induced optical second harmonic generation

Analyzing spectroscopic optical properties of an organic double-layer diode comprised of α-NPD and Alq₃ layers, we studied the selectively probing of electric field distribution in one of the two layers by using the microscopic electric field induced optical second harmonic generation (EFISHG) measurement. Spectroscopic SHGs from Indium–Zinc-Oxide/N,N-Di(naphthalene-1-yl)-N,N′-diphenyl-benzidine/tris(8-quinolinolato) aluminium/Al (IZO/α-NPD/Alq₃/Al) diodes were measured. Results showed that the SHG peaks were generated at 940 and 1050 nm from the α-NPD and Alq₃ layers, respectively, due to the EFISHG process, and the electric field in each layer can be selectively probed. The contribution of the accumulated charge at the double-layer α-NPD and Alq₃ interface was also identified by the d.c. voltage dependence on the EFISHG intensity.