Band 19, Heft 13

Es wird versucht, die Heisenbergsche Skalentransformation mit Hilfe der Darstellungstheorie der konformen Gruppe zu erhalten.

An elementary theory for beam waveguides based upon geometrical optics as well as upon the HUYGENS undulatory theory is developed. A homogeneous FREDHOLM integral equation of the first kind is derived. It connects the field distribution as observed on a mathematical surface behind the n-th lens with the given initial distribution. If the spacing between the lenses is chosen such that the beam waveguide operates in a stable condition, then the eigendistributions are periodically reproduced along the beam waveguide. For these eigenmodes a homogeneous FREDHOLM integral equation of the second kind is formulated; the diffraction losses associated with the pq-th eigenmode are determined by the corresponding eigenvalue. As pointed out by HEFFNER, the laser beam may be considered a special superposition of eigenmodes uniformly displaced in the direction of propagation. This superposition yields mode patterns which are periodically reproduced from lens to lens. It is suggested that the laser resonator be matched with its optically analogous beam waveguide for an optimum transmission. The general theory is applied to a beam waveguide whose lenses are a distance of d = 3 f apart. It is demonstrated that the theory presented is completely consistent with the classical laws in the zero-wavelength limit.

We consider a plasma consisting of particle components with different temperatures. The components are uniformly distributed in the configuration space and MAXWELLIAN in the velocity space. Pair correlations are assumed to be small and higher order correlations negligible. It is shown from the BBGKY-hierarchy that the influence of the electrons on the ion kinetics can be taken into account by treating the ions as dressed particles. The hierarchy for these dressed particles provides the ion-ion correlation function. The electron-ion pair correlation is calculated from the POISSON equation using the ion-ion correlation and relating the electron-ion pair distribution to the average potential. By the same procedure we derive the electron-electron correlation making use of the electron-ion correlation. The results are compared with those of other authors.

For nonthermal plasmas, the population densities of the ground level and the lower lying excited states can deviate considerably from a SAHA- and BOLTZMANN population density which are only valid for plasmas in (local) thermal equilibrium. To obtain the actual population densities of the lower lying- states of the He I-Atom in a nonthermal, optically thin as well as in a partially optically thick plasma the corresponding rate equations have been solved. Due to the metastable state 2 3 S we have distinguished between the singulet and the triplet system. The coupling between the two systems has been accomplished by appropriate collisional processes. Numerical values are given for the population densities in terms of „SAHA“-population densities for both the lower singlet- and triplet levels in the case of an optically thin plasma. The relaxation times necessary for establishing a steadystate have been calculated. The influence of the triplet-system on the particle densities of the singletsystem is shown. For low electron densities the ratio n i (triplet) /n i (singlet) becomes larger than 3. By solving the complete system of rate equations and comparing the solutions with measured densities one can derive unknown total cross sections for reactions between excited states.

Im Anschluß an BÖTTICHER und DAMMANN 1 wird der zeitliche Verlauf von Temperatur und Elektronendichte hinter der Front einer konvergenten Zylinderstoßwelle für verschiedene Radien berechnet und mit quantitativen spektroskopischen Messungen verglichen. Die Temperaturen werden aus der Absolutintensität optisch dicker Heliumlinien, die Elektronendichten aus der Kontinuumsintensität bestimmt. Zur Messung dient ein schnelles photoelektrisches Achtkanalspektrometer mit einer Genauigkeit von 10%. Die gemessenen Werte stimmen mit den an Hand des Modells berechneten überein.

Der bei Magnetsondenmessungen im Plasma auftretende Randfehler wird an einem Modell untersucht. In Graphitstäbe verschiedener Durchmesser und bestimmter Leitfähigkeit sind Störungen in Form von Bohrlöchern unterschiedlicher Dimension eingebracht. Das im Bohrloch mit einer Magnetsonde gemessene magnetische Feld bei einer Kondensatorentladung wird mit dem berechneten ungestörten Feldverlauf verglichen. Das Ergebnis zeigt eine starke Abhängigkeit des Randfehlers vom ungestörten radialen Stromprofil sowie von der durch den Skin-Effekt bedingten zeitlichen Stromänderung. Die Annäherung des Randfehlers an den Volumfehler und damit die Möglichkeit zur Fehlerabschätzung durch den Volumfehler ist nur für große Störverhältnisse (Stördurchmesser/Leiterdurchmesser → 1) gegeben. Bei den in der Praxis benutzten Störverhältnissen ≪ 1 ist der Randfehler auf jeden Fall größer als der nach dem Störvolumen abgeschätzte.

With a beam of neutral particles (inert gas atoms and molecules of H 2 and N 2 ), produced by charge-exchange, the ionization efficiency up to energies of 300 eV and the threshold in collisions with particles of the same kind were investigated. The threshold, determined by extrapolating the experimental curves, is (in good agreement with the impact conservation laws) twice the ionization energy. The rise of ionization with energy (up to 100 eV) can be expressed by a power-function with a mass dependent exponent between two and three. There was no hint for the ionization to go through a maximum in the lower energy range.

Second virial coefficients, viscosity, thermal conductivity and diffusion coefficients of binary gas mixtures have been computed for the MORSE potential in conjunction with a set of combination rules for the unlike interactions. These calculated values are compared with the experimenta l values with a view to derive inferences regarding the adequacy of the recently proposed MORSE potential. On the basis of this detailed comparison of theory and experiment some specific and useful conclusions have been drawn which enable one to understand the relative footing of this potential in reference to the other two realistic potentials, viz. L-J (12-6) and exp-six.

Der Diffusionskoeffizient des Schwefels im flüssigen Kupfer wurde im Temperaturintervall 1130 bis 1400 °C und bei Konzentrationen von 0 — 0,65 Gew.-Proz. Schwefel mit der Kapillare-Reservoir-Methode bestimmt. Im genannten Temperaturbereich wird die Abhängigkeit des Diffusionskoeffizienten von der Temperatur durch die Gleichung D= (3,44 ± 0,21) -10 -3 · exp { — (6890 ± 400)/RT} beschrieben.

Growth and shaping of KCl whiskers from the vaporous phase are discussed and demonstrated with micrographs. The particular conditions for the generation of these whiskers are linked to a simple mechanism related to the ideas proposed by AMELINCKX 1 involving the interaction of spiral growth about a dislocation and impurities. The generation of short pyramids and long whiskers, of dendritic branches and kinks as well as whisker-tips and surface phenomena are described.

In the present paper the epitaxial growth of silver on rocksalt crystals cleaved in vacuum has been investigated. If one presumes, that the orientation of the metal foils is strongly influenced by gas layers growing on the crystal surface after cleavage, it is possible to predict the dependence of the crystal-orientation on the deposition conditions. Systematical investigations of silverfoils demonstrated the validity of this presumption. Beyond this it was possible to observe the gradual deposition of gas layers by varying the time between cleavage of the substrate and the beginning of silver-deposition.

Relations between different cubic ligand field parameters Δ are derived in the framework of LCAO theory on the basis of group theory. From the symmetry of the ligand system and the transformation properties of the d-orbitals, the values of the Δ parameters are related to the octahedral parameter. These ratios Δ/Δ Oh , partially including π- and δ-antibonding effects, are — ⁴⁄₉ for the tetrahedron, — ⁸⁄₉ for the cube, — ½ for the tetradecahedron, + ⁸⁄₉ for the tetrakishexahedron and triakisoctahedron when equal central atom ligand distances are considered. The proposed procedure, including also lower symmetries, is compared with the Ξ-method of JØRGENSEN, PAPPALARDO and SCHMIDTKE 1 , giving it a more developed physical significance.

Intensities at 1849 Å of various types of low pressure mercury lamps were measured. The values ranged from 10 16 to 2·10 17 quanta/sec, depending on the type of lamp. The LOSSING type lamp yielded an output of 8·10 16 quanta/sec in a 2 cc reaction volume, the largest output per unit volume tested. The intensity of the line at 1849 Å relative to that at 2537 A was measured with a Seya-Namioka grating monochromator. The line at 1849 A was 10 to 15% of that at 2537 A in an electric discharge lamp. In a microwave-operated lamp, the intensity of the former line was 5% of the latter. Ethylene was used as an actinometer to measure the quantum yield at 1849 A. The quantum yields of hydrogen and acetylene from ethylene were 0.8 ± 0.1 and 1.0 ± 0.1, respectively.

In solvents containing hydroperoxides, tetraarylhydrazines decompose in the presence of light to yield the corresponding diarylnitric-oxides. High-resolution ESR-spectra of five p-substituted members were recorded, and all coupling constants as well as the g-values measured. These differ considerably from those of the corresponding diarylamino-radicals.

In the molecular compounds: SnCl 4 · 2 X [Χ = POCl 3 , (C 2 H 5 ) 2 O]; 2 SbCl 3 · X (X = Benzene, Naphthalene, Biphenyl, p-Xylene); HgCl 2 · Dioxane; POCl 3 · AsCl 3 the NQR-frequencies of Cl 35 , Sb 121 and Sb 123 have been investigated at liquid nitrogene temperature. The shifts of the NQR-frequencies in these compounds, compared with the pure components, are discussed qualitatively.

Measurements of long transversal nuclear magnetic relaxation times T 2 exceeding 0.05 — 0.5 sec in low viscosity liquids are performed in most cases with the CARR—PURCELL-method 3 , as improved by GILL and MEIBOOM 2 . The latter furnishes a compensating effect against maladjustments of the pulse lengths t i in the CARR-PURCELL sequence, brought about by a π/2 phase shift of the radio frequency during the first pulse. This effect is investigated theoretically and experimentally for the second echo of a pulse sequence, where the compensation first occurs. For this purpose the influence of pulse lengths t i , of the relaxation times T 1 and T 2 and of deviations from resonance Δω is calculated explicitly. The results show that the π/2 phase shift necessary for the GILL-MEIBOOM method can be replaced by a small resonance shift. The effect of radiation damping is demonstrated experimentally.

Die Theorie der Transporterscheinungen wird allgemein für isotrope Zweibandleiter mit beliebigem ε (k)-Verlauf der Bänder dargestellt. Spezielle Transportintegrale für parabolische Bänder und für das nichtparabolische InSb-Leitungsband (KANESche Form) werden in der Näherung schwacher (uB ⟪ 1) und starker (μΒ ⟫ 1) Magnetfelder bei Streuung an akustischen und optischen Phononen sowie an Ionen numerisch berechnet und tabellarisch zusammengestellt.

Die galvano- und thermomagnetischen Effekte von 4 InSb-Proben verschiedener Störstellenkonzentration wurden im Temperaturintervall von 20—450°C zwischen 0 und 7 kG untersucht. Es wurden gemessen: spezifisch elektrische Leitfähigkeit, absolute differentielle Thermospannung, Wärmeleitfähigkeit, HALL-Koeffizient, ETTINGSHAUSEN-NERNST-Koeffizient, RIGHI-LEDuc-Koeffizient, Änderung der spezifisch elektrischen Leitfähigkeit, der differentiellen Thermospannung und der Wärmeleitfähigkeit im Magnetfeld. Die experimentellen Ergebnisse des eigenleitenden InSb lassen sich von der dem nichtparabolischen Leitungsband des InSb angepaßten Transporttheorie für isotrope Zweibandleiter am besten wiedergeben, wenn Streuung der Elektronen an optischen Phononen angenommen wird.

The DEBYE characteristic temperatures for some of the cubic semiconductors have been calculated using the VRHG approximation and the series expansion method as developed by BETTS, BHΑΤΙΑ and WYMAN. It has been found that the VRHG approximation is simpler than the series expansion method. The values obtained using this approximation are also, in general, in good agreement with the experimental values and the values obtained by some other workers.

This paper is concerned with an ideal spin-l/2-HEisENBERG-model for thin ferromagnetic films. A general method is given for the calculation of the one-spinwave eigenstates and their spectrum in dependence on the lattice type and the orientation of the surfaces of the film. The function that characterises the shape of the spinwave perpendicular to the film must fulfil a linear eigenvalue-difference-equation as well as a set of boundary conditions. For next-neighbour interactions this system may be evaluated for an especially simple case. For it spinwavestates of the form of cos-sin-functions as well as surface states are found. Their momenta are given by some transcendental equations, which are discussed. For all other cases the given difference-equation cannot be solved in a closed form, but at any rate it is a starting point for numerical calculations. In a subsequent paper it will be shown that the special case mentioned above covers some important surface orientations of the cubic lattice types. For films of these orientations the dependence of the magnetization on temperature and thickness of the film will be derived from the spinwave spectra.

In a preceding paper (I) the spectra of the one-spinwave-eigenstates of an ideal HEISENBERG-model for thin ferromagnetic films were derived for a special type of surface-orientations. Now these results are applied to the cubic lattice types. First a theory is given for the calculation of certain coefficients by which the general equations of (I) are related to the special lattice types and surface orientations. It is shown that some of the most important orientations of the cubic lattice types belong to the case treated in (I). For these orientations the dependence of the spontaneous magnetization on temperature and thickness of the film is calculated from the spinwave spectra. The formula obtained for this function was evaluated on a digital computer. The results, some of which are plotted, are discussed and compared with experimental dates. In all cases the deviations from the magnetization of the compact material are found to be small, down to very thin films.

Due to the interaction of an electron with both optical and acoustical modes in piezoelectric polar crystals, modified expressions for the self-energy and effective mass of the polaron are to be expected. The lattice vibrations are considered in the limit of large wave-length and an electrostatic approach to the interaction of charges in the lattice has been used. The HAMILTONIAN for a piezoelectric crystal of arbitrary lattice structure is given. With special reference to crystals of zincblende-type, approximate solutions for the self-energy and effective mass are found by thermodynamical pertubation theory. A numerical estimate for ZnS as a particularly favourable example, shows a negligible modification of the ground-state energy, but concerning the effective mass a contribution due to acoustical phonons of more than 50% of the optical-mode term.

In anisotropic (homogeneous) crystals the thermoelectric field produced by a temperature field is in general not irrotational; charge carriers moving on closed curves in the crystal gain energy in this field. Therefore stationary closed electric currents must be flowing in these crystals. The current distributions and electrical potentials in some „two-dimensional“ temperature fields are calculated. These closed electric currents producing JOULE-, THOMSON-, and BRIDGMAN heat influence the temperature distribution in the crystal, and contribute to the heat current by convective heat transport. The total heat flow is increased by a factor which depends on the geometry of the crystal and on the temperature distribution, but which not exceeds [1 + (ε ∥ — ε ⟂ ) 2 /4 L], where (ε ∥ — ε ⟂ ) is the anisotropy of the thermoelectric power and L is the LORENZ number.

Es wird untersucht, welche der bisher entwickelten Verfahren der Elektronentheorie der Metalle geeignet sind, um die Information über die Elektronenstruktur zu liefern, die zur Berechnung des elektrischen Widerstandes bei nichtfreien Leitungselektronen benötigt wird. Die auf GOMBÁS zurückgehende Pseudopotentialmethode scheint hierfür am ehesten brauchbar zu sein, weil mit ihr ohne allzu großen Zeitaufwand die Wellenfunktionen ψt und die Elektronenenergien E 8 für beliebige Werte von t ermittelt werden können. Zur Vorbereitung auf eine folgende Berechnung des elektrischen Widerstandes von Lithium wird dieses Verfahren dazu benützt, um für dieses Metall die Zustandsdichte N (E), die FERMI-Energie ζ und die E t -Abhängigkeit in der Umgebung der FERMI-Ober-fläche zu ermitteln. Außerdem wird für hochsymmetrische Richtungen im f-Raum die EfAbhängigkeit bestimmt und diese mit den Ergebnissen anderer Autoren verglichen.