Volume 26, Issue 6

The complexity of theoretical work in physics applications often forces severe neglections and crude approximations. Insufficient experimental knowledge of important parameters increases the uncertainty. In this situation the E-diagram method still allows to arrive at useful results through controlled choice of the approximations and sensible limitation of the aims. Choosing “unidirected” deviations only, existence limits can be calculated which restrict the existence of the system to a narrow region - the existence area - of the coordinate plane of variables under consideration. The example of the vacuum arc cathode demonstrates the procedure and its suitablility.

Twocentre harmonic oscillator overlap integrals, arbitrary transition integrals and collision energy etchange integrals for equal and different frequencies of the oscillators are contained in a generalized Franck-Condon-integral which is solved by operator methods in the second quantization representation.

Twocentre harmonic oscillator overlap integrals (Franck-Condon-integrals) are calculated in a simple way for twodimensional oscillators of different frequencies. Second quantization and operator technique are applied. It is further shown that transition and kinetic energy integrals can be derived in the same representation.

Using the acetylene, ethylene and ethane series, the applicability of the Modified Extended Hiickel Method in the determination of the atomization energies as well as stable configurations of molecules has been demonstrated. It is believed, moreover, that within the procedual framework of our proposed technique the proportionality constants Fσ (HH) =2.00, Fσ (CH) =1.75, Fσ (CC) = 2.10 and Fπ (CC)=1.45 should prove adequate in the semi-empirical study of the atomization energies, stable configurations (and potential barriers) of all the hydrocarbons, be they aliphatic or aromatic.

The viscosity of gaseous ammonia in the presence of a static homogeneous electric field is calculated using the Waldmann-Snider equation. Special attention is paid to the field dependence of the effect which is strongly influenced by molecular inversion. The latter causes a coupling of tensors of different rank in J in the expansion of the distribution matrix, thereby leading to an infinite set of equations which is solved numerically by a limiting procedure. The effect has a complicated dependence on pressure p and field E but to a good approximation turns out to depend on E/p a t pressures high with respect to an inversion pressure (about 5 atm for NH 3 , 300 torr for ND 3 ) and, in agreement with the experiments, on E 2 /p at low pressures.

Simple and accurate expressions for the velocity slip coefficient, the slip in the thermal creep, and the temperature jump coefficient are obtained by applying a variational technique to the linearized Boltzmann equation for a simple gas. Completely general forms of the boundary conditions are used, and the final results are presented in a form such that the results for any particular intermolecular force law or the gas-surface interaction law can easily be calculated. Further, it is shown that, with little extra effort, the present results can be easily extended to include the case of a polyatomic gas. It is felt that the present work, together with a recent paper in which the author has considered the solutions of the linearized Boltzmann equation for a monatomic multicomponent gas mixture, provide the desired basis for the consideration of the various slip problems associated with the polyatomic gas mixtures.

The 60 MHz PMR spectra of 2 -(4-iodophenyl) oxetane, 2-(4-bromophenyl) oxetane, 2-(4-fluoro-phenyl) oxetane, and 2-(4-chlorophenyl) oxetane have been analysed for the oxetane ring protons and the phenyl protons. In the three first mentioned compounds the spectra show a coupling of 0.46 - 0.63 Hz between the benzyl proton and the phenyl protons in ortho position relative to the oxetane ring, the other proton-proton couplings between the oxetane and phenyl parts being zero in the error limits. In the oxetane part, the halogen substituent in the para position of the phenyl ring mainly affects the chemical shifts of the protons with a slight effect on the proton-proton couplings. The ortho and meta couplings of the phenyl protons increase and the para coupling decreases with growing electronegativity of the substituent, in the order iodine, bromine, fluorine. The phenyl protons in 2-(4-chlorophenyl) oxetane produce a sharp singlet, which shows that they are chemically equivalent. This proves that chlorine and the oxetane group affect the shieldings of the phenyl protons similarly, which is supported by comparing the chemical shift differences in 2-(4-halophenyl) oxetanes to the ones in para-dihalo-substituted benzenes.

The stiffness of the polymer chains provokes a part of the acoustical low frequency phonons in polymer crystals to behave like free particles charged with mass, as far as their energy-momentum-relation is concerned. The influence of this "mass" on the 3-phonon-processes and on the phonon-electron-interaction in the isolated linear chain, in a Bravais lattice built up of linear chains, and in the isolated planar zig-zag-chain is investigated. It is shown that the "inert" phonons are especially exposed in the case of phonon-phonon-and phonon-electron-interaction.

Samples of fused SiO 2 and of a soda-lime glass were exposed to He, Ne, and Ar at temperatures between 523 and 763 °K, cooled to room temperature, transferred to a desorption cell, and then heated slowly and uniformly. The cell was connected to a mass spectrometer and the desorption rates were measured as a function of time. From the data, the parameters E and Do of the Arrhenius equation for the diffusion coefficient [D = D 0 exp(-E/RT)] were calculated. The results were found to agree rather well with literature data obtained on similar glasses using isothermal methods. Since the nonisothermal technique may be very useful for the study of granular materials and powders, the problems related to the presence of a grain size distribution and to the irregularities of grain shapes are treated in this study in some detail.

A Bommel-Dransfeld technique is used to analyse the frequency spectrum in GaAs acousto­ electric domains up to 8 GHz. Parametric frequency conversion is found to be only dominant at the very onset of domain formation. In the strongly nonlinear regime, the amplified noise is mainly concentrated around the shifting frequency of maximum nonlinear gain. The shift of the maximum gain frequency is generally discussed by a theory of nonlinear ultrasound amplification. An evaluation of the measured frequency shifts by this theory leads to the simple relation |x| ≈ 2 y between the domain electric field and the bunching rate.

The sandwich grid diode is a new means of producing extremly high elektrical fields at a solid surface. The ability to ionize gases and to produce field electrons with such a thin film system permits an estimate of the maximal field strength. It is interesting to note, that with this diode one can produce fields higher than 5-107 V/cm in gases up to atmospheric pressure without the risk of a discharge. This fact may become of some importance for the study of field induced desorption and catalysis.

Using separated isotopes the hyperfine structure of the 5p 2 P 3/2 -state in Ag I-spectrum was investigated by scattering the resonance line on an atomic beam in parallel magnetic and electric fields. With the theoretical positive sign of the Stark-constant β, the shift of the Heydenburg- and level-crossing-signals with electric fields can be explained by the following parameters: Ag (107) : A = - (32,4 ± 0.5) Mc/sec , Ag (109): A - - (37,3 ± 0.8) Mc/sec , β ( 2 P 3/2 ) = (5.15 ± 0.15) (kc/sec) (kV/cm) -2 , τ ( 2 p 3/2 ) = (6.3 ± 0.6 ) · 10 -9 sec.

Nach einer kurzen Einführung wird das SCF-MO-P(LCGO)-Verfahren auf die Verbindungen Methan, Äthan, Propan, Isobutan, Tetramethylmethan und Methyl-Cyclohexan angewendet und gezeigt, daß auf diese Weise qualitative Aussagen über die Elektronenverteilungen erhalten werden können, die sogar zu einer guten Proportionalität bezüglich der exakten Werte führen. Andererseits erlaubt die Analyse der Elektronenverteilungen, „effektive Atomladungszahlen“ einzuführen, deren Verlauf innerhalb eines Moleküls Anhaltspunkte für die Ladungsverteilung liefert.

Die Emissionsanisotropie der Photolumineszenz von Rhodamin 6 G in Wasser-Glycerin wurde im Konzentrationsbereich 5 · 10 -6 bis 8 · 10 -2 M/1 gemessen. Bei Konzentrationen c > 10 -2 M/l wurde ein Repolarisationseffekt festgestellt. Die Meßergebnisse wurden mit der Theorie der Konzen­ trationsdepolarisation, die die Löschung der Fluoreszenz durch nicht lumineszierende Dimere berücksichtigt, verglichen.

The activity coefficients of molten salts with three components will be defined, and the logarithms of these activity coefficients will be represented as power series in the mole fractions of the two other components with integral exponents. Power series with three empirical parameters have proved useful as first approach for low molecular nonelectrolyte solutions, and they also describe the activity coefficients of a ternary melt adequately. In the appendix a general formula will be given for the activity coefficients of a melt composed arbitrarily containing water as an additional com­ponent.

Im System Nb -Al-Si mit mehr als 60 At.-Proz. Niob wurde der isotherme Schnitt bei 1840 °C untersucht. Im Bereich von 75 bis 80 At.-Proz. Niob und 0 bis 7 At.-Proz. Silicium existiert A 15-Phase. Phasenfeld und Gitterkonstanten sowie kritische Stromdichten und kritische Temperaturen der supraleitenden A 15-Phase werden mitgeteilt. Bei einphasigen Proben Nb 75,3 Al 21.5 Si 3.2 wird im ternären System die höchste Sprungtemperatur von 19,2 K beobachtet.

The enthalpies of mixing at 25° of diethyl ether, di-n-propyl ether, di-n-butyl ether, di-isopropyl ether, propylene oxide, tetrahydrofuran, and tetrahydropyran with chloroform are determined by an isothermal titration method. As a result, the functions H M -f(N CHCl 3 ) are obtained with a step width of 0.025 of the mole fraction and a relative accuracy of 1 per cent or better. Evaluation of the heat of mixing data by means of equilibrium models ("ideal associated mixture") shows that the systems of aliphatic ethers with chloroform behave rather precisely as one-step equilibria of the type A + B = AB (A = ether; B = chloroform). In the systems of cyclic ethers with chloroform, a se­cond equilibrium step, AB + B = AB 2 , must be considered, the importance of which decreases with increasing ring size of the ether. The equilibrium data calculated for the seven ether-diloroform systems are discussed.

Zur thermodynamischen Berechnung der chemischen Transportreaktionen in den W olfram-Halo­gen - Sauerstoff-Systemen werden auf Grund empirischer Betrachtungen der Bindungsverhältnisse in den Molekülen die freien Bildungsenthalpien ⊿G B 0 der Verbindungen WO 2 Br 2 , WOBr 4 , WO 2 J 2 und der noch hypothetischen Verbindungen WO 2 F 2 und WOJ 4 für Temperaturen zwischen 500 und 3600 K ermittelt. Ferner werden die Gleichgewichtskonstanten K p für die Bildung der entsprechen­ den Verbindungen aus den Elementen im Normalzustand berechnet. Die Daten zeigen eine sehr hohe Stabilität der Wolframoxihalogenverbindungen und deuten auf eine wesentliche Beteiligung der Wolframoxihalogenide am Reaktionsgeschehen in den Systemen Wolfram - Halogen - Sauerstoff.

A detailed study has been made of the elastic scattering of lew-energy electrons in Thomas-Fermi Theory. The analytical expressions which have been obtained for the scattering length a and the total cross section o are illustrated numerically.

The Senftleben-Beenakker effect of the viscosity of dilute polyatomic gases is investigated theoretically for the case where an alternating magnetic field parallel to the usual static field is present. The starting point is a set of transport-relaxation equations obtained from the kinetic equation for the one-particle distribution by application of the moment method. The transport-relaxation equations are solved for the viscosity problem and the relevant viscosity coefficients averaged over many periods of the oscillating field are calculated as functions of the frequency of the alternating field and of the magnitudes of both magnetic fields. The importance of the obtained results for the dynamic behaviour of the thermomagnetic gas torque (Scott effect) is discussed.

A study of how strong electron collisions will influence the profile of the line core is made with­ in the framework of the impact theory. To this end the time-dependent Schrödinger-equation describing the change of state of the atom during the passage of one perturbing electron is solved numerically down to impact parameters equal to the de Broglie-wavelength 2 . In this range the classical description of the perturbing electrons is assumed to be still valid. In the dipole-only case the solution can be expressed exactly by elementary functions. The line profile clearly shows how important it is to consider the strong collisions. All the different ways of doing this lead to nearly the same results.

The Mössbauer effect of the 2 + (104 keV)0+ transition in 180 W has been observed. The source was 180 Ta which was produced by irradiation of a foil of natural tantalum by fast neutrons: 181 Ta(n, 2n) 180 Ta. The width of the resonance absorption line was (3 .1 ± 0.8) mm/sec which corresponds to the linewidth derived from lifetime measurements.

Die Beobachtung von Zweiquanten-Absorptionsprozessen im optischen Bereich ist durch den Einsatz lichtstarker Laser ermöglicht worden. Erst diese hohen Bestrahlungsstärken erlauben die Untersuchung nichtlinearer Absorptionsvorgänge 1 . Mehrquantenübergänge zwischen Zeeman-Niveaus dagegen treten in günstigen Fällen bereits bei verhältnismäßig niedrigen Energiedichten auf 2, 3 . Eine quantitative Analyse der Einbis Vierquantenübergänge in atomarem Sauerstoff ist in einer vorangegangenen Mitteilung beschrieben worden 4 . Dieser Beitrag behandelt Zweiquantenübergänge zwischen Zeeman- Niveaus in Halogenatomen.

Gamma ray energies in 233 U following the decay of 233 Pa were measured with the Risö bent crystal spectrometer. These gamma lines were detected during the study of the 232 Th(n,y) 233 Th reaction. Experimental details will be given elsewhere 1 . The energies were calibrated with the X-ray lines 2 and the annihilation line 3 . The energies of seven transitions between 270 and 420 keV were determined with an accuracy which is up to a factor of 10 better than previous measurements by Albridge, Hollander, Gallagher, and Hamilton 4 . The transition energies are shown in the level scheme 4, 5 (Fig. 1 ) . A least squares program was used to fit the level energies to the seven transition energies obtained in this experiment and to four transition energies (below 103 keV) measured precisely by Albridge et al. 4 . Level energies could be calculated with an accuracy of about 20 eV (Fig. 1).

An empirical relation has been found between the ionic radii of the crystal-lattices and the ultraviolet absorption wavelengths of the V K -centers. The relation is valid for V K - centers formed in alkali halide crystals with NaCl structure as well as for ammonium halide crystals with CsCl structure.

The temperature dependence of the Soret effect is measured by an optical method. A special slit cell is used with the slit plane parallel to the direction of the temperature gradient.

The current interpretation of heat is completely different from the earlier concept which was quite successful at the beginning. Then, it was thought that heat was a quantity which could be neither created nor destroyed and that it was present in every material body. A body should become hotter by absorption of heat and expand, melt, vaporize or decompose, if the temperature necessary for these processes is reached 1-5 . On this basis, Black explained the existence of latent heats 3 , Carnot calculated the effective work of ideal heat engines 4 , Clapeyron found the connection between vapor pressure and heat of vaporization 6 and Thomsen developed the first material-independent definition of temperature 7 . In spite of their success, these interpretations were in opposition to several experimental results showing that heat was obviously produced by consumption of work. These facts indicated a relationship between the two quantities.

The component η 3 of the viscosity of ammonia increases in an electric field. The effect depends on E 2 / p and tends to a saturation value close to that found from measurements in a magnetic field. In ammonia-helium mixtures the saturation value of the effect decreases and becomes negative at an ammonia concentration of about 40%.

Mit einer bei früheren Messungen 1 erprobten Apparatur wurden die Untersuchungen über die Photoablösung von Elektronen bei stabilen negativen Ionen fortgesetzt. Für Photonenenergien zwischen 0,5 eV und 3,5 eV wurden Größe und Energieabhängigkeit des Wirkungsquerschnittes bei Si - und NH 2 - bestimmt. Si - -Ionen wurden aus SiCl 4 mit einer Stromstärke von 10 -9 A erzeugt. Bei Si - hat der gemessene Wirkungsquerschnitt (Abb. 1) eine niederenergetische Schwelle bei einer korrigierten Photonenenergie von (0,56 ± 0,04) eV und einen zweiten Anstieg bei etwa 1,3 eV.

Gitterdefekte erhöhen den Energieinhalt eines Festkörpers. Dies zeigt sich bei chemischen Umsetzungen in einem zusätzlichen Beitrag zur Reaktionsenthalpie. Im folgenden wird über die Veränderung der Lösungswärme von Aluminiumpulver durch eine Sdiwingmahlbehandlung mit steigender Mahldauer berichtet. Die Zunahme der Lösungswärme entspricht den bei einer Wärmebehandlung ermittelten Werten der Speicherenergie 1 .