Experimentelle Untersuchungen zur Ionisierung und Umladung von Alkanolen durch 6-25 keV Wasserstoffionen

Experimental Investigations of Ionisation and Charge-transfer of Alcohols by 6-25 keV Hydrogen Ions Ionisation and charge-transfer cross sections were measured for the interaction of H⁺, H and H ions (in the energy range 6-25 keV) with alcohols (methanol-octanol). The cross sections depend significantly on the target molecular structure like molecular length, ionisation potential, polarizability and atomic bonds in the target molecule.     

Anwendung der GRYZINSKY-Theorie zur Berechnung der Ionisierungs- und Umladungwirkungsquerschnitte für die Wechselwirkung von Wasserstoffionen und Alkanolmolekülen

An Application of GRYZINSKY -theory to Calculations of Ionisation and Charge-transfer Cross Sections for the Interaction of Hydrogen Ions with Alcohol Molecules Ionisation and charge-transfer cross sections were calculated for the interaction of H⁺, H and H ions (energy range 5-25 keV) with alcohols (methanol-butanol). A modified GRYZINSKY approximation is used for the calculation of the cross sections. The calculated values have been compared with experimental determined cross sections. The agreement between experimental results and theoretical results is satisfactory.     

Desorptions- und Reaktionskinetik der Erdalkalien Calcium und Strontium mit Chlor an Wolfram. Part II: Kinetics of the Elementary Steps of the Surface Reaction M + Cl ⇌ MCl (M = Ca,Sr)

Desorption- and Reactionkinetics of the Alkaline Earth Elements Calcium and Strontium with Chlorine on a Tungsten Surface — Part II: Kinetics of the Elementary Steps of the Surface Reaction M + Cl ? MCl (M = Ca, Sr) Utilizing pulsed molecular-beam-technique the kinetics of desorption of Strontium, Calcium, and Chlorine as well as that of the molecules SrCl and CaCl, which are formed at the hot tungsten surface, was investigated. Thereby, the following values were obtained for the activation energies of desorption: ? = (3.76 ± 0.05) eV, ? = (3.32 ± 0.07) eV, ? = (4.16 ± 0.05) eV, ? = (4.2 ± 0.3) eV and ? = (3.9 ± 0.3) eV. Combining these results with the steady-state-results from part I [1] the temperature dependency of the rate constants of dissociation and recombination of MCl-molecules at the tungsten surface could be determined. The values obtained for the dissociation energies D of SrCl and CaCl on tungsten are (0.5 ± 0.5) eV and (0.3 ± 0.5) eV, respectively. The molecules are stabilized on the surface by the activation barrier for dissociation D? only, which was found to be (2.8 ± 0.5) eV for SrCl and (2.3 ± 0.5) eV for CaCl.     

Hyperfine Structure of the Configuration lll

The matrix elements for the hyperfine structure of the configuration lll in SL-Kopplung are expressed as linear combinations of the electron coupling constants α_li(10), α_li(01), α_li(12).     

Desorptions- und Reaktionskinetik der Erdalkalien Calcium und Strontium mit Chlor an Wolfram. Teil I: Chemisches Gleichgewicht der Oberflächenreaktion M + Cl = MCl im stationären Zustand (M = Ca,Sr)

Desorption- and Reactionkinetics of the Alkaline Earth Elements Calcium and Strontium with Chlorine on a Tungsten Surface — Part I: Chemical Equilibrium of the Surface Reaction M + Cl ? MCl in the Steady State (M = Ca, Br) Utilizing positive and negative surface ionization the reaction M + Cl = MCl (M = Ca, Sr) was studied at a hot tungsten surface under steady state conditions. Comparing the results obtained either by simultaneous M- and Cl₂ -exposures or by MCl₂ -exposure the existence of chemical equilibrium could be confirmed for the reaction in the temperature interval 1600 K.2000 K; at higher temperatures this equilibrium can be disturbed considerably by the desorption of the reacting components. From the experimental results we obtained under conditions of chemical equilibrium the energy of dissociation of MCl-molecules in the gasphase (D = (3.9 ± 0.15) eV, D = (4.2 ± 0.15)eV) and in the case of a strong disturbance of the equilibrium the difference between the activation energies of desorption and of dissociation of MCl-molecules on the surface (? - D? = (1.6 ± 0.2) eV, ? - D? = (1.4 ± 0.2) eV).     

DC Conductivity and Peierls instability in the quasi-one-dimensional organic charge density wave conductor (fluoranthene)2X

Due to the high anisotropy of the dc conductivity (σ_|/σ_⊥ ≈ 10⁴) the organic conductor (fluoranthene)₂X can be regarded as a model system for studying the Peierls instability in quasi-one-dimensional systems. The temperature dependence of the dc conductivity σ_| (T) along the highly conducting crystal axis exhibits the typical behaviour of a quasi-one-dimensional metal with a Peierls transition at about 180 K to a charge density wave (CDW) ground state. As expected for a highly one-dimensional conductor the exact transition temperature depends on three-dimensional coupling effects and therefore on the size of the counterion X^? = PF, AsF, SbF. Above the Peierls transition σ_| (T) can be described quantitatively within a model of CDW fluctuations leading to a pseudo gap in the electronic density of states. Below, the existence of a real energy gap at the Fermi level with a BCS-like temperature dependence determines the charge transport over more than eight orders of magnitude in the electrical resistance. For the intrinsic energy gaps 2 Δ (0), which characterize the ground state of the Peierls semiconductor, values of 120-180 meV have been found for different crystals.     

Response of finite many-electron systems beyond the time-dependent local density approximation: Application to small metal clusters

A linear response formalism is developed which is based on density functional theory within the local density approximation, but which is now corrected for its spurious self-interaction errors, in the way originally proposed by Perdew and Zunger for ground state calculations. The original formulation is extended to incorporate self-interaction corrections in the scrrening terms. The general formalism is then applied to the calculation of the static and dynamic response of the metal clusters {Na₈, Na₉⁺}, {Na₂₀, Na} and {Na₄₀ Na} within the jellium model. Comparison with experimental data and with other theoretical calculations indicates that the present formalism accounts for the overall (and most of the fine) features of the photoabsorption spectrum of these systems, providing a systematic improvement with respect to previous approaches. The remaining discrepancies are rationalized in terms of the effects to be expected by correctly accounting for the discrete structure of the ionic cores.     

On a Mechanical Model of the Bopp-Podolsky Potential

For an arbitrary given distribution of dislocations and disclinations the general state of stress of a mechanical continuum is investigated. The medium is reacting with stresses and momentum stresses (Cosserat continuum). By means of differential geometry it is shown that the deformations _ik and ?_ik of two arbitrary materials with identical distributions of defects differ merely by a displacement field u_i(x^r, t). If _ik are the eigendeformations of an isotropic medium, then in the linear theory the field u_i of a Cosserat continuum can be separated from _ik. If the problem is static the u_i obey the potential equation of Bopp-Podolsky electrodynamics. As source only torsion (dislocations and torsion of disclinations) is acting. To give an example the field u_i for straight dislocations and disclinations is calculated. Especially the problem of singularities is discussed.     

On a simple formula for the energy of the lowest octupole state

A recently introduced way of parameterizing the energies of 3 states in many even-even nuclei, based on the microscopic structure of the low-energy octupole mode, is slightly modified so it now includes all (non-doubly magic) nuclei with A ? 30.     

Anregungswahrscheinlichkeiten Probleme der Makrokausalität und Teilchendichte in der relativistischen Wellenmechanik. III

We discuss in relativistic quantum mechanics the excitation of atoms by photons, assuming an electromagnetic interaction of the form A. It turns out, that when localized in a region V at a certain time x⁰ a photon would excite atoms also outside the light-cone of V. We arrive thus at a contradiction between quantum mechanics and special relativity.     

Sea Level Muon Spectrum Derived from Bugaev Model

The pion and kaon spectra in the atmosphere are derived from primary nucleon spectrum determined by GRIGOROV et al.; they satisfy the relations N(E_π) dE_π = 0.187 EdE_π and N(E_k) dE_k = 0.017 E dE_k, respectively. By using the pion-kaon atmospheric diffusion equation the sea level muon spectrum is calculated and the result compared with the magnetic spectrograph data of ALLKOFER et al. and AYRE et al.     

Magnetic field dependencies of the critical current and of the resonant modes of dc SQUIDs fabricated from superconductors with s + id order-parameter symmetries

The magnetic field dependencies of the critical current and of the self-induced resonant modes of dc SQUIDs fabricated from superconductors with s + id order parameter symmetries are calculated. Combining the complementary results of the two dependencies, an unambiguous determination of the ratio of the s and d wave components is possible. Two cases of SQUID configurations are analyzed for which the flux coupled to the two Josephson junctions of the dc SQUID is either negligible or significant.     

Die Super-Eich-Symmetrie in der Allgemeinen Relativitätstheorie (Einsteins A-Gruppe)

On Super-gauge-symmetry in General Relativity (Einstein's A Transformations) The super-gauge-invariance of general-relativistic field theories is given by Einstein's A-group of the transformations of the affine connections Γ which preserve the absolute parallelism. This invariance principle means that all informations about world geometry come from astronomical observations. However, the postulate of the invariance under these A-transformations implies strong conditions for microscopical structure of matter which may be interpreted as “super-gravity”.     

Proper quantization rule as a good candidate to semiclassical quantization rules

In this article, we present proper quantization rule, ∫k(x) dx ‐ ∫k₀(x) dx = nπ, where and study solvable potentials. We find that the energy spectra of solvable systems can be calculated only from its ground state obtained by the Sturm‐Liouville theorem. The previous complicated and tedious integral calculations involved in exact quantization rule are greatly simplified. The beauty and simplicity of proper quantization rule come from its meaning – whenever the number of the nodes of the logarithmic derivative ?(x) = ψ(x)^‐1dψ(x) /dx or the number of the nodes of the wave function ψ(x) increases by one, the momentum integral will increase by π. We apply two different quantization rules to carry out a few typically solvable quantum systems such as the one‐dimensional harmonic oscillator, the Morse potential and its generalization as well as the asymmetrical trigonometric Scarf potential and show a great advantage of the proper quantization rule over the original exact quantization rule.     

Transition from SU(2)L × SU(2)R × U(1)B-L representation to SU(2)L × U(1)Y by q-deformation and the corresponding classical breaking term of chiral U(2)

The minimal Standard Model exhibits a nontrivial chiral U(2) symmetry if the VEV and the hypercharge splitting Δ = (y-y)/2 of right-handed leptons (quarks) in a family vanish and Q = T₀ + Y independently in each helicity sector. As a generalization, we start with SU(2)_L × SU(2)_R × U(1)_(B-L) and introduce Δ as a continuous parameter which is a measure of explicit symmetry breakdown. Values 0 ? Δ ? 1/2 take the neutral generator of the isospin ½ representation to the singlet representation, i.e. ‘deformes’ the LR representation into the minimal Standard one. The corresponding classical O(3)-breaking term is a magnetic field perpendicular to the x₃-axis. A simple mapping on the fundamental Drinfeld-Jimbo q-deformed SU(2) representation is given.     

On the Theory of Gravitational Field in Finsler Spaces

Some structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as g_λχ(x, y) = γ_λχ(x) + h_λχ(x, y) is proposed, where γ_λχ denotes the Riemann metric of Einstein's gravitational field, while hλχ the Finsler metric induced by the Riemann metric h_ij(y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as ?ⁱ = K(x, y) y^j in the internal field, is grasped by the Finslerian parallelism δyⁱ (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δy^χ = e(x) δyⁱ. The whole metrical Finsler connection D for g_λχ(i.e., Dg_λχ = 0) is determined by taking account of the intrinsic behaviour δy^χ.     

Gas‐phase basicities of acetophenones toward lanthanum cation [La(OMe)]

The relative free energy changes (lanthanum cation basicity, LaCB[L₂]) for the reaction [La(OMe)₂]L ? La(OMe) + 2L were determined in the gas phase for m‐ and p‐substituted acetophenones based on the measurement of ligand exchange equilibria using an FT‐ICR mass spectrometer. The substituent effect on ΔLaCB[L₂] of acetophenone is described in terms of the Yukawa–Tsuno equation, ΔG = ρ(σ° + r⁺ Δ σ ), with a ρ value of ?11.2 and an r⁺ value of 0.49. From this result, a ρ value of ?7.0 and an r⁺ value of 0.49 were estimated for the monomeric complex [LLa(OMe)] with the aid of theoretical calculations. This ρ value was found to be significantly smaller than that for protonation, and even smaller than Li⁺ basicity. Such a small ρ value has been attributed to the largely ionic (ion–dipole interaction) nature of the bonding interaction between La(OMe) and the carbonyl oxygen atom and, in part, to the long distance between La(OMe) and the substituent. Contrary to the ρ value, the r⁺ value is identical in both La(OMe) and Li⁺ basicities, suggesting that the r⁺ value of 0.49 can be regarded as a limiting one in a series of Lewis cation basicities of the acetophenone system, H⁺ (0.86) > Me₃Si⁺ (0.75) > Me₃Ge⁺ (0.71) > Cu⁺ (0.60) > Li⁺ = La(OMe) (0.49). Since the binding interaction between La(OMe) or Li⁺ and a neutral ligand is mostly electrostatic, the moderate r⁺ was interpreted to result from the redistribution of the induced positive charge within the acetophenone moiety upon binding with a metal ion rather than transfer of positive charge from a metal ion to the aromatic moiety. Copyright © 2010 John Wiley & Sons, Ltd.     

Positivity of the φ Hamiltonian

The renormalized φ Hamiltonian is bounded from below by a constant proportional to the volume.     

A novel probe for determination of electrical surface potential of surfactant micelles: N,N'‐di‐n‐octadecylrhodamine

The peculiarities of the structure of the fluorescent dye N,N'‐di‐n‐octadecylrhodamine advantage its using as an interfacial acid–base probe in aqueous micellar solution of colloidal surfactants. Two long hydrocarbon tails of the dye provide similar orientation of both cation and zwitterion on the micelle/water interface, with the ionizing group COOH exposed to the Stern region in all the systems studied. Further, the charge type of the acid–base couple, A⁺B^±, ensures similar values of the ‘intrinsic’ contribution, pK, to the ‘apparent’ pK value in micelles of different surfactants. This makes the indicator suitable for determination of electrical surface potentials, Ψ. The pKs have been obtained in cationic, anionic, zwitterionic, and nonionic surfactant systems, at various salt background. In total 17 systems were studied. At bulk counterion concentration of ca. 0.05 M, the pK values vary from 2.14 ± 0.07 in n–C₁₈H₃₇N(CH₃)Cl^– micelles to 5.48 ± 0.06 in n–C₁₆H₃₃OSONa⁺ micelles. The Ψ values, corresponding to the Stern region of micelles, have been evaluated as Ψ = 59.16 pK–pK for T = 298.15 K. The pK parameter was equated to the average value of 4.23 in nonionic surfactants (4.12–4.32, depending on the surfactant type). For cetyltrimethylammonium bromide and sodium n‐dodecylsulfate micelles, the Ψ values (±(7–11) mV) appeared to be +118 mV and at bulk Br^? concentration 0.019 M and ?76 mV at bulk Na⁺ concentration 0.020 M, respectively. This satisfactorily agrees with the theoretical values +111 and ?84 mV, estimated using the Oshima, Healy, and White equation for these well‐defined colloidal systems. Finally, not only absorption, but also fluorescence spectra display the same response to changes in bulk pH. Copyright © 2007 John Wiley & Sons, Ltd.     

On the Generalized πN Potential A New Representation from Fixed-t Dispersion Relations

Starting from a recent paper [13] we derive a new representation of the left-hand cut contribution for the πN system. This representation makes it possible to calculate the generalized πN potential accurately from phase shifts and high energy models, because it contains only the imaginary parts of the partial wave amplitudes in the physical region. The analytic properties, the region of convergence and the physical content of this representation is discussed. We propose to use this left-hand cut contribution in bootstrap calculations, because it is more reliable than the approximate expressions which have been used in previous papers. – The left-hand cut contributions are calculated and compared with the nucleon and Δ (1236) approximation for the ƒ, ƒ, ƒ and ƒ partial wave amplitudes.