Volume 21, Issue 11

The use of an EUCLIDean space in astronomy corresponds in the framework of general relativity to the introduction of an EUCLIDean “space of comparison”. We generalize this method till now used only in special cases and analyse the motion of test particles in the EUCLIDean space of comparison. The inertial mass of test particles is a tensor in the space of comparison. Independent of any CORIOLIS force the mass tensor is able to cause anisotropy effects that can be observed on principle.

The LIE algebra U of the invariance group of any field theory with a homogeneous quadratic Lagrangian shows a remarkable structure: If D 1 , D 2 , D 3 are any three elements of U then the expression ½ (D 1 D 2 D 3 +D 3 D 2 D 1 ) also belongs to U. This general property allows, starting with known invariance transformations or conservation laws, to derive an infinite number of conservation laws.

In sections 1, 2, 3, 4 the many-time and one-time functional calculus is developed for the anharmonic oscilator in analogy to the requirements of nonlinear spinor theory. In section 5 the N.T.D.-method is discussed for the eigenvalue functional equation. It is shown that the N.T.D.-method admits different representations, namely a symmetric one and an unsymmetric one. The proof of convergence is given for the symmetric one in section 6. In section 7 the connection between the unsymmetric and the symmetric representation is discussed and in section 8 follow numerical values in comparison with SCHRÖDINGER theory.

The method of correlation function is extended to the case of paramagnetic impurities. The BOLTZMANN equation is obtained and subsequently applied to a derivation of the concentration dependence of the transition temperature, of the linearized GINZBURG—LANDAU equation, and of the diffusion approximation.

The frequency- and temperature-dependences of the nuclear relaxation times have been studied in several solutions of free radicals. Whilst the major contribution to the relaxation is in most systems from dipolar nuclear-electron coupling modulated by translational diffusion, rotational tumbling of solvent-radical complexes is more effective in solutions of water. The work confirms former conclusions from dynamic nuclear polarization studies. Moreover the validity of the STOKES-EINSTEIN formula is tested which is an excellent tool for the calculation of correlation times.

Electrical resistivity, thermal conductivity, and magnetic susceptibility have been measured, using the same sample of samarium, from 4 to 300 °K, from 5 to 200 °K, and from 4 to 300 °K, respectively. Two anomalies, one at 12 ± 1 °K and another at 106 ± 1 °K, are observed, resulting from an order-order magnetic transformation and an antiferromagnetic-paramagnetic transition, respectively. The Lorenz function is found to be larger at any temperature than that expected for pure electronic thermal conductivity. This implies that there is some phonon and possibly also some magnon thermal conductivity in samarium at low temperatures. The magnetic moment disorder electrical resistivity of samarium is determined to be 39.0 ± 0.5 μΩ cm, in fair agreement with the value to be expected from theoretical considerations.

A simple rotational viscometer has been constructed for measurements at elevated temperatures in the region 10 9 - 2 × 10 12 poise, and has been used to study the deformation of pure fcc lithium sulfate (temperature range 740-860°C) and mixtures of this salt with potassium sulfate. These substances resemble highly-viscous non-NEWTONian liquids, and for a given torque the apparent viscosity can be represented by the conventional relation η=η 0 exp (Q/R T). For pure lithium sulfate, measurements with a torque of 19 × 10 7 dyne-cm gave the values η 0 = 4.24 × 10 -4 poise and Q = 7.4 × 10 4 cal/mole for the two constants. Two mixtures containing 1.0 and 2.2 mole-% K 2 SO 4 , respectively, were studied. In the homogeneous solid solution phase the viscosity showed a dependence on the thermal prehistory of the salt during the first few days at a given temperature. This effect was not detected for the pure lithium sulfate or for the two-phase region of the mixtures. The temperature dependence of the viscosity was less pronounced for the homogeneous phase than it was for the pure salt, while it was very great in the two-phase region. It is suggested that viscosity (or electrical conductivity) measurements should be a possible method to determine the position of the solidus curve for mixtures of this type.

The mathematical formulation necessary for the evaluation of two-center integrals for SLATER-type orbitals has been presented. The formulation takes into consideration the arbitrary orientation of the two centers and presents a general expression involving the three quantum numbers, the effective charge of each of the two orbitals, the internuclear distance, and the usual A and B integrals. A flow chart for digital computer programming is also presented.

Die Grundzustände der Hydride NH und OH werden mit verschieden ausführlichen Sätzen von Versuchsfunktionen berechnet. Der Abfallparameter der 1s-Funktion vom Wasserstoffatom wird variiert. Ionenstrukturen N - H + und O - H + werden berücksichtigt und dabei für N - und O - auch Konfigurationen p 3 p′ bzw. p 4 p′ mit einem „weiter außen“ eingebauten p′-Elektron verwendet. Für die Grundzustände werden Dipolmomente berechnet. Angeregte Terme werden mit einem kleinen Satz von Funktionen behandelt. Zu den Grundzuständen und den angeregten Zuständen werden Potentialkurven gezeichnet und daraus mit Hilfe eines Polynoms vierten Grades spektroskopische Daten gewonnen.

For 2 ∑- 2 Π a transitions (e. g. PO β-system), a method is described for calculation of rotational constants B (ν) from the doublet splitting of the bandheads. In that way the classification of both the violet and the red shaded PO β-bands (some 30 bands are new analysed) into one system can be shown, which seemed to be doubtful recently. From the discrepancies between the observed and the calculated additional heads in some subbands the rotational constant D has been evaluated, which plays an important part particularly for higher values of J as correction term in our calculation. Small systematic deviations in the graph of the rotational constant B (ν) for some sequences Δν=ν′-ν″ are interpreted as an indication for the interaction between electronic and nuclear motion; the effect corresponds to a deformation in the flanks of the potential curve in the order of 0.001 Å for higher vibrational quantum numbers (ν>5). The potential curves for the PO β- and γ-system have been computed, and from their relative position the observed perturbation of the level ν′=10 (β-system) and the range of perturbation starting at ν′=0 (γ-system) is explained. By calculation of the band origins a cubic equation for the vibrational levels of the B 2 ∑-state is deduced. The extrapolation of the differences between two successive vibrational levels yields a new value of dissociation energy D 0 0 (PO) =5.15 eV.

Im Frequenzbereich 12—30 GHz wurden bei Temperaturen zwischen 700 und 750°C Rotationsübergänge von 15 Isotopenkombinationen des PbSe gemessen. Es werden Rotationskonstanten, Potentialkoeffizienten, Kernabstände und Massenverhältnisse von Blei- und Selenisotopen mitgeteilt. Als Mittelwert über alle isotopen Molekeln ergibt sich ein Kernabstand r e = (2,402223 ± 0,000032) Å. Unter Annahme eines MoRSE-Potentials folgt für die Dissoziationsenergie D =(4,17 ± 0,05) eV.

Infrared absorption spectra (4000—400 cm -1 ) and RAMAN spectra of the pentaerythritol halides have been examined. By comparison with spectra of similar compounds and by a normal coordinate analysis with the aid of the GF-Matrix-Method of WILSON and on the basis of a modified valence force field it was possible to assign a great deal of the normal vibrations. The influence of the halogen atoms on the frequency of characteristic vibrations has been discussed.

Die IR-Spektren von Triphenylen im Bereich von 200—3200 cm -1 in verschiedenen Aggregatzuständen werden verglichen mit der Polarisation der Banden in orientierten kristallinen Schichten. Die Zuordnung der IR-aktiven E′- und A 2 "-Banden kann fast vollständig gegeben werden. Pulveraufnahmen an einem RAMAN-Spektrometer mit Anregung durch die He-Linie 5876,6 A ergaben den größten Teil der totalsymmetrischen A 1 ′-Banden. Weniger vollständig gelang das Auffinden der IR-verbotenen Banden der Rassen A 2 ', A 1 '' und E″, bei denen Unklarheiten vor allem bei tiefen Frequenzen blieben. Aus Gas- und Lösungsspektrum ergibt sich bereits eine merkliche Abweichung von der D 3h -Symmetrie (am Beispiel der 620 cm -1 -E′-Bande). Beim Übergang zum kristallinen Zustand treten neue Banden auf, die für eine Verstärkung der Deformation in diesem Aggregatzustand sprechen.

Der Einfluß des Hetero-N-Atoms auf die Elektronendichteverteilung in Pyridin wurde bei einer Reihe von monosubstituierten Pyridin- und Benzolderivaten mit Hilfe vergleichender Messungen von Gruppenintensitäten I Gr der im Substituenten lokalisierten Valenzschwingungen untersucht (Gr = CH 3 , CH 2 , CN und NH 2 ). Neben einem Reichweiteeffekt ist ein stark alternierender Effekt auf I Gr zu beobachten. Durch Einbau einer CH 2 -Gruppe zwischen Ring und funktioneller Gruppe (Φ —CH 2 —Gr) wird die Wirkung beider Effekte abgeschwächt. Verglichen mit der entsprechenden Benzolverbindung nimmt I Gr monosubstituierter Pyridinderivate bei den Gruppen — CH 3 , — CH 2 und — CN ab, bei — NH 2 hingegen zu. Dieser Sachverhalt läßt sich u. E. folgendermaßen interpretieren: Das Hetero-N-Atom induziert auf Grund seiner Elektronenakzeptorwirkung in den Bindungsorbitalen Momente der Richtung A - —B + (A sei das ringnahe Atom). Bei Gruppen der Polarität A - —B + führt dies zu einer Erhöhung, bei Gruppen der Polarität A + —B - zu einer Verkleinerung des resultierenden Bindungsdipolmoments. Obwohl im allgemeinen kein einfacher Zusammenhang zwischen I Gr und den Ableitungen der Bindungsdipolmomente (მμ/მR)j, Gr und den Bindungsdipolmomenten μ j , Gr selbst besteht, gilt möglicherweise allgemein: Die Gruppenintensität nimmt als Folge der Akzeptorwirkung eines Heteroatoms ab, wenn die Polarität der in der Gruppe enthaltenen Bindungen A + —B - ist. Bei umgekehrter Polarität nimmt andererseits I Gr zu. Die Größe der Änderungen hängt von der Art der Gruppe ab. Mit Hilfe der erhaltenen Gruppenintensitäten war es ferner möglich, dem Hetero-N-Atom des Pyridins folgende Substituentenparameter (ΗΑΜΜΕΤT-Konstanten) zuzuordnen: σ N, ortho = 0,68 ± 0,10; σ N, meta = 0,33 ± 0,10; σ N, para = 0,66 ± 0,10 .

The kinetics of unimolecular decomposition of organic ions in the presence of electric fields up to 10 8 V/cm is discussed. The results are deduced from the mass spectra obtained by field ionization of organic molecules. The time interval between formation and decomposition of the ions can be derived from the shape of the mass lines. It is shown that field induced decomposition can occur at a minimum time of about 3 · 10 –14 sec after field ionization. The optimum time resolution with these experiments, 10 –12 sec, is given by the resolving power of the mass spectrometer. The results can be interpreted in terms of five different mechanisms : 1. Field induced dissociation. Excitation of the molecular ion to a state above the dissociation limit is possible at high enough fields. Spontaneous dissociation within one vibrational period will then be possible because the excitation energy is contained in the reaction coordinate. 2. Field induced dissociation by tunneling of radicals through the potential barrier. This may occur after excitation of the molecular ion to a state lying in an interval between the dissociation limit and about half a vibrational energy quantum below this, provided the field strength is high enough. The maximum observable life time of ions resulting from this process is about 6·10 –12 sec. 3. Field induced dissociation, delayed by re-orientation of the molecular ion. Certain orientations of the molecular ion are favoured with respect to field dissociation. The maximum re-orientation time for a favourable position is of the order 3·10 –12 sec. 4. Field induced statistical dissociation. This is due to fluctuation of energy within the ion, as in the case of common reaction kinetics, but with lowering of the dissociation limit by the field. The time intervall for these processes lies between about 10 –13 and 10 –11 sec. 5. Statistical decomposition in the space of low or zero field strength. This process is due to energy fluctuation within the molecular ion excited to a state above the dissociation limit, lowered only by a minute amount by the weak field. The range of life times is about 10 –11 to 10 –8 sec. Processes of the same type, occurring at zero field strength within about 10 –8 and 10 –6 sec, are called — as usually — “metastable” processes. The processes described here are derived mainly from the FI mass spectra of paraffins, alcohols, ethers and ketones. Dissociation is hindered, in some cases, by high electric fields.

The temperature dependence of field dissociation of organic molecular ions as described in this paper can be interpreted qualitatively by means of simple models. Very fast decomposition processes, occurring about 10 -12 sec after field ionization, are not only due to the lowering of the dissociation energy by the field, but also due to fluctuation of vibrational energy, especially at higher temperatures. The fragment ion insensities are increased by formation of adsorbed layers on the tip anode at low temperatures, especially with substances having high dipole moments. In the case of molecules containing a polar group and an alkyl chain, only the former is ordered preferrentially, with the dipole moment parallel to the field lines, whereas the latter is relatively mobile in the electric field. The relative fragment ion intensities depend on the orientation of the alkyl chain relatively to the polar group, however, this effect does not depend appreciably on temperature because of the mobility of the alkyl chain. The only exception from this rule was observed with pentanol. The pentanol molecules are adsorbed at the tip anode with the alkyl chains preferrentially parallel to each other. This leads to a preferred formation of C 2 H 5 + fragment ions. With increasing temperature, the adsorbed layer is removed and a statistical orientation of the alkyl chain becomes more important, thus reducing the relative C 2 H 5 + abundance.

Es wurden eine erweiterte Intensitätsfunktion und eine erweiterte Radialverteilungsfunktion für Elektronenbeugung an Gasen berechnet. Die Bestimmung der Atombewegung in einem Molekül mit Hilfe der Elektronenbeugung wird in diesem Zusammenhang von neuen Gesichtspunkten aus diskutiert. Eine aus den Erweiterungen resultierende Korrektur für die gemessenen Atomabstände wird angegeben.

A check is made of a stabilization theorem of ROSENBLUTH and KRALL (Phys. Fluids 8, 1004 [1965]) according to which an inhomogeneous plasma in a minimum-B field (β ≪ 1) should be stable with respect to electrostatic drift instabilities when the particle distribution functions satisfy a condition given by TAYLOR, i. e. when f 0 = f(W, μ) and ∂f/∂W < 0 Although the dispersion relation of ROSENBLUTH and KRALL is confirmed to first order in the gyroradii and in ε ≡ d ln B/dx z the stabilization theorem is refuted, as also is the validity of the stability criterion used by ROSEN-BLUTH and KRALL, ⟨j·E⟩ ≧ 0 for all real ω. In the case ω pi ≫ | Ω i | equilibria are given which satisfy the condition of TAYLOR and are nevertheless unstable. For instability it is necessary to have a non-monotonic ν ⊥ distribution; the instabilities involved are thus loss-cone unstable drift waves. In the spatially homogeneous limiting case the instability persists as a pure loss cone instability with Re[ω] =0. A necessary and sufficient condition for stability is D (ω =∞, k,…) ≦ k 2 for all k, the dispersion relation being written in the form D (ω, k, K,...) = k 2 +K 2 . In the case ω pi ≪ | Ω i | adherence to the condition given by TAYLOR guarantees stability.

In optically thin plasmas produced by strong shock waves the SAHA equation is no longer valid to describe the conditions directly behind the shock wave. Photoionisation may be neglected in the balance of production and recombination of charged particles. For the case of nonequilibrium a calculation assuming various ratios of electron to ion temperature (ϑ= T e T) shows that the shock wave parameters are described sufficiently well by the Korona-equation. Temperature, density ratio and electron density are increased with increasing ϑ whereas the pressure ratio is independent of the kind of equilibrium and ϑ.

Based on the VLASOV equation a method is derived to deliver velocity distributions in the case of a one-component plasma which produces a force-free or in part force-free magnetic field. This formalism is applied to simple fields of the type H=(H x (z), H γ (z), 0) .

Das Emissionsspektrum eines mit Wasserstoff-cluster-Strahlen erzeugten Plasmas wird längs der Strahlrichtung untersucht. Bei einem Elektrodenabstand von 26 cm wird in einem Bereich von 14 cm nur die Emission des Wasserstoffs beobachtet, in Elektrodennähe treten auch Linien des Elektrodenmaterials auf.

By X-rays, ultraviolet, and γ-radiation or by heating to more than 1850 °C in powdered or sintered boronnitride centres are produced, which give an EPR-spectrum with 10 lines a=7.8 ± 0.1 Gauss apart with g=2.0027 ± 0.0003 for BN of natural isotopic composition (81.17% 11 B; 18.83% 10 B), and a single line for 10 BN enriched to 91% 10 B. The spectra are analysed as built up from 4 systems of spectra, caused by surroundings of 3 boron atoms, 3, 2, 1, or 0 of which are 11 B, each occuring with the proper probability. The intensity of the different systems was calculated by assuming GAussian line shape and equal | ψ (0) | 2 and line width for 11 B and 10 B. It is possible, that the EPR is caused by impurity atoms on the places of N or in the centre of B 3 N 3 -rings. Other spectra caused in BN by X-rays or by neutrons in a pile are discussed elsewhere 3, 8 .

The paper supplies numerical information on coherent effects of bremsstrahlung and electron pair production in diamond crystals in the energy range from 1 to 40 GeV. The information is collected in a number of graphs and tables showing the intensity and polarization of bremsstrahlung and the cross section and asymmetry ratio for pair production as a function of crystal orientation. The basic formulas for the interpretation of the diagrams are given. The experimental problem of a precise orientation of the crystal, which is closely connected with the production of coherent radiation, is discussed on the basis of these formulas.

Aus zehn aktivierungsanalytischen Bestimmungen des Argon-Gehaltes an einem Probenmaterial einheitlicher Zusammensetzung (Sylvinit) ergibt sich der mittlere statistische Fehler einer Einzelbestimmung zu ± 4,4%. Die Entgasung der Minerale erfolgte durch vollständige Sublimation der Proben. Die Überführung des erhaltenen Edelgases in das Gaszählrohr gelingt mit Hilfe von Trägerargon mit einer Ausbeute von 99,99%. Die erreichte Analysengenauigkeit entspricht derjenigen, die für massenspektrometrische Bestimmung angegeben wird. Die einfache und schnelle Durchführbarkeit der aktivierungsanalytischen Methode lassen sie insbesondere für eine routinemäßige Anwendung vorteilhaft erscheinen.

Zur Massen-Geschwindigkeitsseparation von geladenem, künstlich beschleunigtem Staub wurde ein elektrostatisches Filtersystem entwickelt und erprobt. Der logische Teil dieses Filters kann auch zur Messung der Ladung und Geschwindigkeit von kosmischem Staub dienen.

Es wird eine Beziehung für die gestreute Intensität bei Röntgen-Kleinwinkelaufnahmen an Systemen polydisperser Partikel angegeben. Daraus ergeben sich 2 Werte für die optimale Präparatdicke, von denen der eine maximale Streuintensität liefert, während der andere optimale Monochromasie der gestreuten Strahlung ermöglicht.

Die atomaren Bildungsenthalpien gasförmiger Verbindungen, ΔH* 298 , zeigen innerhalb einer Gruppe des Periodischen Systems eine lineare Abhängigkeit von der Ordnungszahl des elektronegativeren Bindungspartners. Eine ähnliche Gesetzmäßigkeit beobachtet man bei den entsprechenden Standardentropien, S 298 0 , wenn man sie im doppeltlogarithmischen Koordinatensystem gegen die Molekulargewichte aufträgt. Die Genauigkeit interpolatorisch ermittelter Daten wird hier durch Vergleich mit einer zweiten Methode erhöht, die sich auf die Beziehung zwischen S (MX n 1 ) und S (MX n 2 ) stützt. Abschließend wird eine Zusammenstellung von Entropie- und Enthalpiewerten der wichtigsten gasförmigen Verbindungen gegeben. Die Tabellen, ergänzt durch Inter- bzw. Extrapolation mit Hilfe der angegebenen Schätzmethoden, entsprechen dem Stand von 1965.