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).     

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.     

The Spectra of Cosmic Pions and Nucleons at Low and High Geomagnetic Latitudes at the Top of the Atmosphere

The spectra of cosmic pions and nucleons at an atmospheric depth of 100 g cm^?2 have been derived from sea level muon spectra at low and high latitudes. The derived spectra of pions and nucleons at low and high latitudes follow the relations N(Eπ) dEπ = 0.23 E_π^?2.68dEπ and N(E_p) dE_p = 2.98 E dE_p per cm² sec str GeV in the energy range 15–1200 GeV. Below 15 GeV it is found that the exponent of the energy spectrum is very much dependent upon the incident energy and latitude of the location. The major difference between low and high latitude pion spectra can be explained in terms of geomagnetic effects.     

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.     

Electron Emission from Clean Solid Surfaces by Fast Ions

Total backward electron yields from 27 elemental, non-crystalline, clean solids were measured during bombardment by H⁺-, H-, H-, He⁺- and Ar⁺-ions in the energy range from 100 keV to 800 keV. The yields were found to exhibit an oscillatory dependence on the atomic number of the target material correlated with the periods of the periodic system. These Z₂-oscillations are relatively insensitive to the type of projectile and the impact energy at the high projectile energies of this experiment. Present theories of electron emission cannot explain the main experimental results. The reasons for this failure are discussed.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Diffusion Model of Saturation Current Collection by a Planar Langmuir Probe in a Strong Magnetic Field

Plasma presheath and saturation current collection by a planar Langmuir probe in a strong magnetic field perpendicular to the probe surface ares described with the diffusion model. The model takes into consideration the geometry of the probe, that is its size and shape, and dependence of the cross-field charged particles' transport into the effective collection region of the probe on the parallel-field transport to the probe. Experimental study of planar Langmiur probe I—V characteristics in D.C. discharge argon plasma in strong magnetic fields confirms the possibility of deriving the cross-field diffusion coefficient, D, from the measured electron satuation current. Additional dependence of the electron saturation current on the parallel-field diffusion coefficient, D, and the ion temperature, T_i, derived in the approximate Stangeby's study using the diffusion model of current collection by a planar surface (Stangeby, P. C., J. Phys. D: Appl. Phys. 15 (1982) 1007) can be eliminated with more rigorous calculation. Series of measurements on two neutral pressures and various magnetic fields gave reproducible values of D, approximately given by relation D ≈ (δn/〈n〉) k_BT_e/(eB).     

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”.     

NOETHER'S Theorem and Higher Conservation Laws in Ultrashort Pulse Propagation

LAMB has constructed a number of local conservation laws for the differential equation σ_τ = sin σ describing ultrashort pulse propagation in a resonant medium. On the other hand it is known that from any solution of this equation others may be found by BÄCKLUND transformation. In this paper we introduce extended BÄCKLUND transformations B_a and compose them to form infinitesimal invariance transformations B_a+ε B from which via NOETHER'S theorem a system of conservation laws follows. Some of them are recognized as LAMB'S conservation laws. Another conservation law results from a scale invariance called LIE'S transformation.     

Kinetic Study of the Emission of the First Negative System in an Argon-Nitrogen Plasma at Atmospheric Pressure

Quantitative optical spectroscopy measurements of the emission spectra of the N(B²∑_u,)ν′→X²∑_gν″ transition (first negative system) in an Ar-N₂ microwave discharge at atmospheric pressure have allowed determination of the rate coefficient of the production of N molecules in the B² ∑_u, state with vibrational level ν′ = 0. The N(B²∑_u, ν′) molecules are produced by the reaction in a surface-wave-induced microwave discharge (2450 MHz) sustained in an open-ended dielectric tube. The rate coefficient K (T) has been obtained for ν′ν″ = 0 for different gas temperatures by varying the incident microwave power. The K₀₀(T) values are between 7.10^?10 and 4.10^?10 cm³ s^?1 for the temperature range 2500 to 3450K.     

Einsteins Feldtheorie mit Fernparallelismus und Diracs Elektrodynamik (Unitäre Feldtheorie mit dem Vektorpotential als Bezugstetrade)

Einstein's Field Theory with Tele-Parallelism and Dirac's Classical Theory of Electrons (Unified Field Theory with the Vector-Potential as a Reference-Tetrad) The Einstein-Maxwell theory of gravitation and electro-magnetism with Dirac-gauge AⁱA_i = m²c⁴/e² of the vector-potential A_i can be written as a purely geometrical field theory. The geometry of this field theory is Einstein's “Riemannian geometry with teleparallelism” and the vectorpotential is given by the time-like component of the tetrads h which define this tele-parallelism; we have -Physically, this unified field theory implies a generalization of the Einstein-Maxwell equations by introduction of a “current without current” describing Faraday's “gravoelectrical induction” corresponding with Dirac's electronic current λA_i.