Volume 26, Issue 4

In the framework of Lorentz invariant theories of gravitation the fieldtheoretic approach of the generally covariant Jordan-Brans-Dicke-theory is investigated. It is shown that a slight restriction of the gauge group of Einstein's linear tensor theory leads to the linearized Jordan-Brans-Dicke-theory. The problem of the inconsistency of the field equations and the equations of motion is solved by introducing the Landau-Lifschitz energy momentum tensor of the gravitational field as an additional source term into the field equations. The second order of the theory together with the corresponding gauge group are calculated explicitly. By means of the structure of the gauge group of the tensor field it is possible to identify the successive orders of the scalar-tensor theory as an expansion of the Jordan-Brans-Dicke-theory in flat space-time. The question of the uniqueness of the procedure is answered by showing that the structure of the gauge group of the tensor field is predetermined by the linear equations of motion. The mathematical proof of this fact confirms formally the meaning of the equations of motion for the geometry of space.

Dynamics of quantum field theory can be formulated by functional equations. To develop a complete functional quantum theory one has to describe the physical information by functional operations only. Such operations have been defined in preceding papers. To apply these operations to physical problems, the corresponding functionals have to be known. Therefore in this paper calculational procedures for functionals are discussed. As high energy phenomena are of interest, the calculational procedures are given for spinor field functionals. Especially a method for the calculation of stationary and Fermion-Fermion scattering functionals is proposed.

A representation of symmetry transformations motivated by the functional formulation of quantum field theory is rigorously discussed in a functional Hilbert space. The set of generating functionals is equipped with an inner product by means of the Friedrichs-Shapiro-integral and completed to an Hilbert space. Unitarity, continuity, and reducibility are investigated for the symmetry operations in this space. Also non-unitary transformations are considered.

The potential energy surface has been calculated by two methods which are compared with re­spect to spontaneous fission. In the first one essentially the sum of the single particle energies is computed as was done in a previous paper 3 while in the second one the Strutinsky technique of renormalizing to a liquid drop model has been applied. Also the half-lives for electron capture are investigated together with the predictions of the half-lives for spontaneous fission and α-decay. The results support the existence of superheavy nuclei in the regions around Z = 114 and Z = 164.

The properties of polaritons in uniaxial crystals with an arbitrary number of atoms in the unit cell are discussed in the harmonic approximation. For LiNbO 3 , which seems to become a very important substance for applications in tunable Raman lasers, the complete set of eigenfrequencies and eigenvectors (normal coordinates, electric field, electric polarisation) is calculated numerically. In the limiting case k→∞ (long optical phonons), which is treated in detail in this first paper, an example for each possible type of extraordinary phonon branches is discussed, namely a (T→L) -a (L→T)-, a (T→T)-and a (L→L) -branch of each type. The results are comparable with ex­perimental data only for the frequencies of the 45°-phonons, measured by Barker and Loudon. The agreement is very satisfactory.

It is shown that the resolvent in the Vθ-sector of the Lee model may be expressed by simple algebraic operations in terms of known matrix elements between states of the V-sector.

Level crossing technique, applying parallel electric and magnetic fields, has been used to determine the signs of the hyperfine structure constants A and B as well as the magnitude of the Stark-constant β . From the Stark-shift of the signal at 45 Oe in the wing of the Hanle-effect and of the level-crossing near 140 Oe to higher magnetic field strengths the ratios A/β > 0 and B/ß > 0 could be determined. An estimation of β by calculating the electric dipole matrix elements with Coulomb approximation yields a positive sign. Both signals and their shift with electric field then can be explained with the following results: A = + 14.0 (5) Mc/sec; 5=+327.6 (1.6) Mc/sec and β= +5.7(3) (kc/sec) (kV/cm) -2 .

Different cut-off criteria of partition functions have been utilized in order to evaluate the con­tribution of electronic excitation to thermodynamic properties of high temperature gases (5000 °K to 35 000 °K, 10 -2 -10 atm). It is shown that properties of single species are strongly affected by the cut-off criterion adopted, i. e. the contribution of electronic excitation to these properties is important. It is also shown that the reported absence of this contribution to total enthalpies and specific heats of plasmas is the result of an almost complete compensation between "reactional" and "frozen" terms which are all dependent on electronic excitation.

The γ decay of 143 Ce has been investigated using both a Ge(Li) γ ray and a high resolution iron free double focusing β-ray spectrometer. In addition to γ rays previously reported, more γ rays could be observed. Internal conversion coefficients and multipolarities of γ transitions were determined. Ten excited nuclear energy states have been established in 143 Pr at 57, 341, 491, 722, 939, 1045, 1061, 1161, 1382 and 1452 keV. Possible spin values have been assigned to all these states on the basis of conversion coefficients of γ rays. The level structure of 143 Pr is discussed in terms of existing nuclear models.

The velocity dependence of the total collision cross section has been measured for the system LiCs in the energy range from 15-1000 eV. Using the observed glory undulation together with spectroscopic data a potential for the singlet ground state of LiCs is proposed.

A wall-stabilized electric arc in an uniform bent tube is investigated. By the asymmetry of Ohmic heating and heat conductivity through the wall a displacement of the maximum of temperature is caused into the direction of the center of curvature, contrary to cylindrically symmetric geometries. By this an asymmetry of the thermal, electric and magnetic quantities is generated and produces a mass flux through the cross-section of the tube. A double whirl is formed by the self-magnetic Lorentz-forces. This convectiv heat flow displaces the maximum of temperature bade into the direction of the outer wall. Both influences are investigated and the final position of the maximum of temperature is discussed in dependence on the arc parameters. For numerical calculations the equations of continuity, motion, energy and the Maxwell's equa­tions of electromagnetic field are solved simultaneously. Results for a nitrogen plasma at nearly atmospheric pressure are presented.

In this paper optical space and time resolved measurements on the later development of Kanal (streamer) and Townsend discharges in nitrogen are treated. In both discharges fast luminous fronts (the so called ionizing waves) arise: in the streamer discharge between the primary streamer stage and the spark stage, and in the Townsend discharge during the transition to the glow. For the streamer discharge new experimental results are given, especially at high overvoltages. In the case of the Townsend discharge the development of an idealized, nearly one dimensional dis­charge is treated. The experimental results are in good agreement with theoretical considerations. In contrast to this idealized discharge often strong constrictions are found during the development to the glow, so that the discharge becomes nearly filamentary. The reasons for this behaviour are discussed and the way to avoid it.

By a special method the disjoining pressure of water caused by a molecular long range orienta­tion between fully hydroxylated and highly polished fused silica surfaces at different temperatures (0-74 °C) and plate distances ≦ 1000 Å was determined. Four marked maxima were found at about 15°, 32°, 45°, and 61 °C for not too small plate distances. At these temperatures many authors have detected anomalies in the temperature dependence of some physical properties of water. This evidence is discussed in regard to our results which particularly imply thermodynamic quantities derived from the aqueous surface zone.

Former measurements showed that benzene exhibits a disjoining pressure in extremely thin layers between fused silica plates in a temperature range just above the melting point. An extended theory for evaluating the disjoining pressure and various thermodynamic quantities of the liquid surface zone which displays a molecular long range orientation leads to results which indicate a small structural transition range at about 12 - 13 °C in bulk benzene. The splitting effect is more pronounced in layers adjacent to fully hydroxylated surfaces since in this case the benzene mole­cules in the first adsorbed layer are more tightly bound than in the case of surfaces entirely free from hydroxyl groups.

For the purpose of carrying out a thermodynamic analysis of the binary systems of germanium with copper, silver and gold, the enthalpies of mixing of liquid Cu-Ge and Au-Ge alloys were determined at 1150 °C. Further the enthalpies of mixing of Ag-Ge solid solutions and the enthalpies of formation of the ζ and ε 1 phases of the Cu-Ge system were obtained from the enthalpies of solution in liquid tin. It was possible to determine the enthalpy of transformation of germanium from its stable modification into a hypothetical, face-centered cubic structure (ΔH T(Ge) = 13.0 kcal /g-atom) which has a decisive influence on the stability of the solid phases in the systems under consideration. Liquid Cu-Ge alloys show energetic pecularities similar to those existing in the solid state and leading to the formation of electron compounds. A distinct influence of the valency difference of the components can also be demonstrated. In the gold-germanium system, however, the influence of the electronegativity difference of the components is dominant.

The electrical and thermal resistivities of noble metals copper, silver and gold have been de­termined at different temperatures in the free electron approximation using Sharma and Joshi's model for the phonon dispersion relations. A modified Houston's method is used to evaluate the formidable integral over the scattering vector. The normal and Umklapp contributions to the resistivity are considered separately from the conservation laws of wave vector. The theoretical and experimental resistivity curves are found to be of similar nature, but the agreement is not detailed. The Lorentz numbers of noble metals deduced from theoretical and experimental resistivity data show considerable deviation from Wiedemann-Franz law.

Low temperature heat capacities from 1.5 to 15 K have been measured for a number of transition metal borides with the compositions Me 2 B, MeB and MeB 2 , and their solid solutions. The measurements show that the borides are characterized by a narrow d-band with a relatively large density of electron states. The variation of γ with position of the transition metal in the Periodic Table for the borides is considerably different from that of the transition metals and solid solutions. This result suggests considerable differences in the shapes of the respective band struc­tures. There is evidence for an electron transfer from the boron atoms to the d-bands of the transition metal.

The lattice vibration spectra and the associated constant volume specific heats of the transition metals niobium, tantalum, chromium, and palladium have been determined by using Sharma and Joshi's three-force constant model which includes the effect of electrons on lattice vibrations in metals. The calculated values of the specific heats and the equivalent Debye temperatures are com­pared with available calorimetric data. The frequency versus wave vector dispersion relations along the three major symmetry directions of chromium and palladium are determined and compared with curves deduced from recent neutron scattering experiments. Reasonably satisfactory agreement between theory and experiment is obtained.

Interdiffusion of anions in fused alkali nitrates has been studied with a plane source diffusion technique; the concentration gradients in the diffusion cell being measured with a wave-front-shearing interferometer. By choosing the same cations in the experiments the diffusional mixing of different anions at low concentrations into three alkali nitrates has been studied. The diffusion coefficients of F - and Br - in LiNO 3 ; F - , Br - , I - , CO 3 2- , and SO 4 2- in NaNO 3 ; and I - and CO 3 2- in RbNO 3 were obtained over a temperature range of some 100 °C above the melting point of the different solvents.

The electrochemical behaviour of sodium chloride in water-sulfolane mixtures, at 25 °C and 35 °C, was investigated, the concentration of the salt ranging within (1÷7)·10 -3 moles/liter and the dielectric constant (D) of the solvent mixtures within 78 and 44. Analyzing the data by the Fuoss, Onsager and Skinner treatment, Λ 0 , a L , A , a A and Λ 0 η values were obtained. At both temperatures, Λ 0 is a smooth function of the solvent compositions; a re­markable association seems evident at D < 60 ; log A vs. 1/D plots are linear; the contact distances of the ions are lower than in other isodielectric media. Except for a limited region close to pure water, the Walden product Λ 0 η is constant (1.20 at 25 °C and 1.19 at 35 °C) in the whole solvent composition range.

The infrared absorption spectra of fifteen La 3+ , Pr 3+ , Nd 3+ , and Sm 3+ β-diketonates have been studied in the spectral region 750-250 cm -1 . The existence of three metal-oxygen vibration modes suggests D 3 symmetry for the chelates under study. The stretching force constants, f MO , of the MO bonds have been computed from the observed infrared M-O vibrations using the method of Müller. The value of f MO is nearly constant (~ 2.7x10 5 dynes/cm) in all the chelates suggesting similar bond strengths.

The triplet state of acridine orange dissolved in methanol/water matrix was investigated by ESR. In absence of oxygen a strong temperature dependence of the spectra was observed. At low temper­ature (100 °K) the zero-field splitting parameters calculated from the triplet spectrum are: X/hc = 0.0050 cm -1 , Y/hc= 0.0342 cm -1 , Z/hc=0.0387 cm -1 , at higher temperature (140 °K) : X*(hc=0.0056 cm -1 , Y*/hc=0.0206 cm -1 , Z*/hc = 0.0262 cm -1 . It was assumed that the low temperature spectrum is caused by isolated molecules in the triplet state while the high temperature spectrum must be attributed to the triplet exciton state of the acridine orange dimer. From the theory of the ESR triplet exciton spectra it can be shown that in the dimer state of acridine orange the molecular planes form an angle of 50° or 130°. However, it cannot be excluded that the dimer configuration differs in the ground or excited singlet state from the triplet state.

Die aus den Raman-Spektren erhaltenen Grundschwingungen von HSiJ 3 , HSiClJ 2 (I), HSiCl 2 J (II), HSiBrJ 2 (III) und HSiBr 2 J (IV) sowie von SiBr 2 J 2 und SiBrJ 3 werden mitgeteilt. Die Zuordnung erfolgt nach spektralen Übergängen und wird durch Kraftfelder gesichert. Die bisher unbekannten Mischhalogenide I - IV entstehen durch Äquilibrierung von HSiJ 3 und HSiCl 3 bzw. HSiJ 3 und SiBr 4 ; sie werden auch über ihre 1 H-NMR-Parameter τ (SiH) und J ( 29 SiH) charakterisiert.

H errn P rof. Dr. N ikolau s R ieh l zum 70. G ebu rtstag gew idm et In einer großen Zahl von Arbeiten 1 wurde die von 0 . Hahn eingeführte sogen. Emaniermethode benutzt, um Aussagen über Transportmechanismen und Fehlord­ nungen in festen Stoffen zu gewinnen. Nach der Theo­ rie dieser Methode2 setzt sich das Emaniervermögen, d. h. die Austrittswahrscheinlichkeit der Edelgasatome (e), zusammen aus einem Rückstoßanteil und einem Diffusionsanteil: £ = £ r + £ d . Der hier interessierende Rückstoßanteil ergibt sich nach 2, z. B. für ein kugel­ förmiges Korn, aus

Eine elektrische Bogenentladung bewegt sich in einem transversalen magnetischen Feld senkrecht zu diesem Feld und zur Stromrichtung. Im allgemeinen erfolgt diese Bewegung im Sinne der Ampereschen Re­ gel, bei niedrigem Druck jedoch kann sich der Bogen in entgegengesetzter, "retrograder" Richtung bewegen. Zur Deutung dieser retrograden Bewegung eines freibrennenden Lichtbogens wurde eine Reihe von Hy-* Sonderdruckanforderungen an Seminar für Didaktik der Physik, Pädagogische Hochschule Ruhr, Abteilung Essen, D -4300 Essen, Henri-Dunant-Straße 65. 1 Eine Übersicht findet man in A. E i d i n g e r u . W. R i e d e r , Arch. Elektrotechnik 43, 94 [1957].

For six vinylidene halides the generalised mean square amplitudes of displacements parallel and perpendicular to the bond for both bonded and non-bonded atom distances are cal­culated from spectroscopic data using the method of Morino and Hirato. The results are discussed and the mean amplitu­des of these molecules (H 2 C=CX 2 ) are compared with those from electron diffraction data for the similar molecules of the type C 2 X 4 .

Durch "Chemical Vapour Deposition" auf porös auf­gerauhtem Träger aus stabilisiertem ZrO 2 abgeschiedene SnO 2 -Schichten mit mehr als 8 At.-Proz. Sb können als Ka­thoden in Hochtemperatur-Brennstoffzellen bei 1000 °C ver­wendet werden; die Materialkombination übersteht Tempera­turzyklen zwischen Betriebs-und Zimmertemperatur ohne Be­einträchtigung der Haftfestigkeit oder der elektrischen Funk­tion.

Wir betrachten eine flüssige Mischung, die aus zwei Elektrolyten mit je zwei Ionenarten besteht. Dabei soll eine Ionenart den beiden Elektrolyten gemeinsam sein. Reispiele stellen die Salzschmelzen N aN 03-f AgNOs und PbCl2 + PbBr2 dar. An Hand dieses relativ ein­ fachen Typs von binären Elektrolytschmelzen, der schon vor kurzem1 hinsichtlich der Transporteigenschaften untersucht worden ist, sollen einige thermodynamische Gesetzmäßigkeiten abgeleitet und diskutiert werden. Diese betreffen die Abhängigkeit der Aktivitätskoeffi­ zienten von der Zusammensetzung sowie die Beziehun­ gen zwisdien den Aktivitätskoeffizienten der einzelnen Teilchenarten und denen der Komponenten. Obwohl man heute, auch bei der Thermodynamik der Elektro­ lytschmelzen, in zunehmendem Maße zur Beschreibung durch "Zusatzfunktionen" übergeht2, ist das hier zu besprechende Problem in Zusammenhang mit einer all­ gemeinen Formulierung der Grenzgesetze für unend­ liche Verdünnung wichtig. Molekularstatistisch sind ja die primären Einheiten nicht die Komponenten oder ionischen Bestandteile, sondern die wirklich vorhande­ nen Teilchenarten. Die beiden Elektrolyte der binären Schmelze werden als Komponente 1 und Komponente 2 bezeichnet. Die­ jenige Ionenart, die nur in der Komponente 1 bzw. 2 vorkommt, wird Teilchenart a bzw. b genannt. Die den beiden Komponenten gemeinsame Ionensorte heißt Teil­ chenart c. Die Zahl der Ionen der Sorte a bzw. b, die aus einem Molekül der Komponente 1 bzw. 2 bei der Dissoziation hervorgehen, wird mit r a bzw. vb bezeich­ net, während das Symbol vc bzw. vc' die Zahl der Ionen der Sorte c bedeutet, die aus einem Molekül der Kom­ ponente 1 bzw. 2 stammen. So gilt etwa für die Salz­ schmelze N aC l(l) +M gC l2(2) : n = ^Na+ = 1,

Wie wir bereits kürzlich am Beispiel des kristallinen K 2 PtCl 4 zeigen konnten 1 , tritt bei quadratisch koordi­nierten Platinkomplexen eine Anisotropie der chemi­schen Verschiebung des 195 Pt-KMR-Signals in der Grö­ßenordnung von 1% auf. Um den Einfluß von im Sinne der "spektroskopischen Reihe" verschieden starken Li­ganden auf die magnetische Anisotropie zu überprüfen, haben wir nun zusätzlich Kristalle der Verbindungen (2) - (4) der Tab. 1 untersucht.