Volume 26, Issue 2

A Fokker-Planck equation for the non-resonant scattering of particles by general weakly turbulent electromagnetic fields is derived using a simple quantum-mechanical method. The equation is compared with the corresponding weak turbulence equation as given e. g. in Kadomtsev's book and two applications are discussed.

Spectral line intensities emitted by a quiescent PIG-discharge have been measured and the population densities up to a principal quantum number n = 24 have been derived from them. The experimentally determined population densities have been compared with theoretical ones calculated on the basis of a collisional-radiative model in which one accounts for electron and atom collisions. I t is shown that even in the case of different electron and atom temperatures, T e and T a , an evaluation of the Boltzmann plot at medium and moderately high quantum numbers always leads to the electron temperature, whereas the Saha-Eggert equation for the same states may yield incorrect electron densities. The theoretical calculations predict an inflection of the slope of the Boltzmann plot from T e to T a for very highly excited states. For the plasma para­ meters under which the PIG-discharge was operated (n e ≅ 2.5 × 10 12 cm -3 , T e ≅ 1200°K, n 0 ≅ 1.5 × 10 15 cm -3 , 300°K) the change of the slope should become visible for states having principal quantum numbers n > 18. Due to the large experimental error bars it was not possible to check this behaviour.

Determination The energy spectrum of a narrow electron beam (primary energy 25 keV, energetic width 0,08 eV) has been measured after having passed a low voltage helium discharge constricted by a metal capillary. Besides the resonance series, which is characteristic for the helium atoms in the ground state, electron energy losses are found due to transitions from excited states. In addition superelastic collisions occur which are caused by de-excitation processes. Population densities of the atoms in excited states are derived from the intensities in the electron energy spectrum using the wellknown transition probabilities. The result is compared with population densities obtained by means of Saha's equation as well as with those in both cases.

In part I of this paper we constructed a model representing quantum states by ensembles of dispersionsfree states. In part II we study further properties of this model and analyse their logical relations. It is also shown that the main results do not depend on the assumption that each self-adjoint operator corresponds to an observable.

In einachsigen Kristallen sind die Frequenzen der sog. außerordentlichen optischen Gitterschwingungen richtungsabhängig (Richtungsdispersion). Diese Richtungsabhängigkeit wurde in der Literatur bisher fast ausnahmslos durch die Poulet-Loudon-Näherung beschrieben. Im folgenden werden zwei erweiterte Näherungslösungen angegeben. Da inzwischen auch die exakten Lösungen (im Rahmen der harmonischen Näherung) bekannt sind, läßt sich die Genauigkeit dieser beiden Näherungen wie auch der Poulet-Loudon-Näherung jetzt gut beurteilen. Als Beispiele werden je zwei Schwingungszweige starker Richtungsdispersion von a-Quarz und dem tetragonalem BaTiO 3 im einzelnen diskutiert.

We treat the one-dimensional harmonic oscillator completely in the field theoretic calculus of many time generating functionals. Without the results of common quantum mechanics we compute eigen values and functionals of the energy preparing all information of the harmonic oscillator. As an example of functional integration and for applications in scattering theory we prove orthonormality relations of these functionals.

The nuclear charge form factgr from the high-energy elastic electron scattering on 6 Li has been calculated from the modified independent-particle shell model (IPSM) wave function. The usual harmonic oscillator type IPSM wave function has been modified by the inclusion of a nucleon-nucleon correlation function which involves extra-core nucleons only. The technique is extremely simple and provides an excellent agreement with the experimental data.

The periodic structure of the mixed state leads to some band splitting in rough analogy to the electrons in a metal. The density of states for tunneling perpendicular to the flux lines shows an appreciable depression at energies ħω ≈ (ħ2/2m) k F |l|, l being a reciprocal lattice vector of the flux lattice normal to the tunneling surface.

Es wird ein Mikrowellen-Mikrowellen-Doppelresonanz-Spektrograph mit gekreuzten Feldern beschrieben. Dieser Spektrograph hat den Vorteil, daß vom experimentellen Aufbau her die Pump-und Signalfrequenz unabhängig voneinander sind. Die theoretische Linienform für gekreuzte Felder wird abgeleitet und den entsprechenden Messungen gegenübergestellt.

The observation of the low lying rotational transitions J = 0 →1 of AgCl and J = 2→3 of AgBr resulted in improved quadrupole coupling constants: 107, 109 Ag 35 Cl: e q ν Q ( 35 Cl) = -36,50 (10) MHz (ν=0,1); 107.109 Ag 79 Br ; e q 0 Q( 79 Br) =297,10(15) MHz, e q 1 Q ( 79 Br) =297,65 (15) MHz. In con­trast to former measurements of KRISHER and NORRIS we obtained the following constants of 107 Ag 79 Br: Y 01 = 1943,6420 (50) MHz, Y 11 = -7,0745(70) MHz, r e = 2,393100(29) Å. The unknown rotational spectrum of AgJ was found. Measurements of the transition J = 3 →4 in four vibrational states resulted in the determination of the following molecular constants: Y 01 = 1345,1105(25) MHz, Y 11 = -4,2389(30) MHz, Y 21 = 1,70(80) kHz, Y 0 ,=-0,2540(2) kHz; r e = 2,544611 (31) Å; e q 0 Q( 127 J) =-1062,17(40) MHz, e q 1 Q( 127 J) = -1064,81 (40) MHz.

On the base of Schuster-Kubelka-Munk's theory, quantitative relations between the bulk absorp­ tion and diffuse reflectance spectra of undiluted and diluted semiconductor powder samples are established in the region of the long-wave tail of the absorption edge. Investigations in the long­ wave region of the diffuse reflectance spectra of V 2 O 5 , based on these relations, led to the result that in contradiction with earlier observations on single crystals 7, 22, 27 , allowed direct optical transitions between valence band and conduction band do not seem to be excluded. Quantitative optical activation energies are obtained from diffuse reflectance spectra.

Antimony monobromide was excited with the help of a microwave oscillator of 2450 mega cycles. Three new band systems in emission have been observed in the regions 2950 -3020 Å, 3050 - 3340 Å and 4905 -5340 Å; of which the first two have been discussed in this paper. All bands are degraded towards the red; they have been classified and attributed to the new molecule SbBr. Isotopic effects due to Br 79 and Br 81 have been observed in one of the systems.

Die Absorptionsspektren und Quantenausbeuten der Fluoreszenz von Rhodamin 6 G werden in zwei verschiedenen Wasser-Glycerinmischungen in Abhängigkeit von der Rhodaminkonzentration untersucht. Die beobachtete Konzentrationslöschung wird auf die Bildung von Rhodamindimeren zurückgeführt und die Abnahme der Quantenausbeute mit theoretischen Vorstellungen über die Kon­zentrationslöschung durch Energieübertragung zu den Dimeren verglichen.

In this paper measurements about the steady state of both Zeeman and dipolar energies of a spin system submitted to r. f. irradiation are presented. These experiments were performed in order to provide a quantitative check of the existing theories. Two samples are investigated, polycrystalline benzene in which relaxation is caused by molecular motions and a monocrystal of CaF 2 + 0.01% Ce +++ impurities. For both samples the regions of extreme narrowing and of large T 1Z /T 1D ratio are investigated. The results are discussed in terms of Provotorov's and Redfield's theories. While in the extreme narrowing region fairly good agreement is obtained some restriction to the Provotorov theory is observed in the region of long correlation times.

Es wurden Bedingungen ermittelt, bei denen eine Selbststabilisierung der Salzverteilung bei Verwendung starker Säuren als Gegenstromelektrolyten möglich ist. Die Grenzen, innerhalb derer sich die Selbststabilisierung vollzieht, wurden diskutiert.

Diffusion processes were investigated by means of quantitative electron-probe microanalysis in the system Pd-Ta. The annealing temperature amounted from 700 °C up to 1030 °C. In the diffusion zone the phases Pd 2 Ta, Pd 3 Ta, Pd 15 Ta 4 , Pd 5 Ta, Pd 6 Ta and Pd 17 Ta 2 were observed. The phase diagram only shows the phases PdTa, P d2 Ta, and Pd 3 Ta. From the law d = k√t it can be concluded for the growing process of the total diffusion zone, that volume diffusion predominates within this system. The values of log k 2 as well as the values of log D versus 1/T yield an Arrhenius plot. The corresponding values are given in tables for the total diffusion zone as well as for the single phases. The discussion of a scanning-picture shows greater diffusion velocity for the Palladium atoms than for the Tantalum atoms.

Die Molekülstruktur des Chlor-Isocyanats in der Gasphase wurde mit Hilfe der Elektronen­-beugung bestimmt. Dabei ergeben sich zwei mögliche Strukturmodelle, zwischen denen auf Grund der Elektronenbeugung alleine nicht unterschieden werden kann. Im Modell 1 ist die NCO-Gruppe linear, die N-C-und C-O-Bindungslängen weichen stark von den für ähnliche Moleküle bestimmten "Werten ab. Im Modell 2 ist die NCO-Gruppe um einen Winkel von ca. 10° geknickt, die N-C-und C-O-Bindungslängen stimmen gut mit den für ähnliche Moleküle bestimmten Werten überein. Außerdem ergibt sich für das Strukturmodell 2 ein um ca. 5° kleinerer ClNC-Winkel als für Modell 1. Unter Hinzunahme der aus mikrowellenspektroskopischen Messungen bekannten Rota­tionskonstanten kann eine Entscheidung zwischen den beiden Modellen zugunsten von Modell 2 getroffen werden. Audi semiempirische MO-Rechnungen sprechen für eine geknickte NCO-Gruppe in diesem Molekül.

Radial fluctuation functions which convey information about liquid microstructure are defined, determined from computer generated configurations, and discussed.

The determination of the activation volume of diffusion is one of the best methods for the in­vestigation of the relaxation of atoms or ions around defects. This paper discusses two experimental techniques for the determination of the activation volume for diffusion, by studying the effect of hydrostatic pressure on tracer diffusion and on ionic conductivity. Such experiments require a very clean hydrostatic pressure environment, accurate temperature control and measurement, and well defined specimen geometry. The difficulties encountered during such experiments are discussed. Results are given for the activation volumes of diffusion in beryllium and in sodium chloride.

The isotope effect of electromigration in some solid alkali halides was determined in their intrinsic ionic conductivity region. The external cationic mass effect (i. e., relative difference in cationic mobility/relative difference in mass) of lithium fluoride, chloride, bromide and iodide and potassium chloride was -0.243, -0.207, -0.195, -0.190 and -0.254, respectively, at 750, 540, 470, 370 and 600 °C, respectively. No difference of the mass effect was found between polycrystalline and single crystal potassium chloride. When the available data for the mass effect of the solid salts are plotted against the activation energy for electric conductance, there is a tendency for the mass effect to increase as the activation energy increases.

The correlation factor for impurity diffusion by a vacancy-mechanism is a function of the vacancy-jump frequencies in the surroundings of the diffusing atom. Since in Si and Ge the vacancy can act as an acceptor, a long-range Coulomb interaction between donor atoms and vacancies exists. The usual assumption, that only a few vacancy-jump frequencies in the immediate surroundings of the vacancy are different from the jump frequency in the pure matrix, is not justified in this case. A very general expression for the correlation factor of impurity-diffusion in the diamond structure is deduced. Vacancy-jump frequencies for jumps which originate from first-, second-, and third-nearest neighbours are treated explicitely. For more remote jumps the Coulomb force is taken into account as a drift force operating on the migrating vacancy. After specializing the general expression it is compared with the well-known ,,four-frequency-model" of Manning.

The pulse height spectrum of all heavy charged particles induced by 14.0 MeV neutrons in a 1" × 1" stilbene scintilla­ tor was measured using a pulse shape discriminator and the associated particle technique. The proton pulse spectrum was subtracted and the remaining alpha-pulse distribution is shown in a diagram. The sum of the cross sections for the reactions 12 C (n, n') 3 α and 12 C (n, α) 9 Be was determined to be σ c= (260 ±20) mb.

Relative intensities of P (J'+ 1) and R (J '-1) lines have been measured in the (ν′ = 3, ν") progressions of the Lyman bands of HD and H 2 . The intensity ratios are in good agreement with previous experimental data and with the results of theoretical calculations which account for the centrifugal dis­tortion.

In a microwave double-resonance experiment involving three rotational levels of propylene oxide perpendicular polarization of the pump and signal radiation was employed to prevent the higher-frequency pump radiation (24 GHz) from reaching the signal detector (11 GHz). For this purpose the independent cut-off characteristics of the TE 10 and TE 01 waveguide mode were exploited which depend only on the broad or small-face waveguide dimension, respectively.

The dissociation energy of the molecule PdGe w as determined by the mass spectrometric Knudsen cell method: D 0 0 (PdGe) =256.6± 12 kJ mol -1 (61.4 ± 3 kcal mol -1 ) .

The self-diffusion coefficients of the cation (D + ) and of the anion (D - ) have been measured in molten silver iodide be­ tween 580 °C and 620 °C with the porous-frit technique. At 610 °C it is found that D + = D - =5A × 10 -5 cm 2 s -1 . At the melting point (556 °C) D + melt (4.4 × 10 -5 cm 2 s -1 ) is very close to D + solid (4.3 × 10 -5 cm 2 s -1 ) . The Klemm friction coefficients do not indicate the existence of complex entities. D + and D - calculated according to the Nernst-Einstein equation agree with observed data within 20%.