Volume 25, Issue 7

A theory is given which permits a connection between an inner structure of an electron and the motion of its center of mass obeying Dirac's equation. In order to describe inner properties of the particle a classical nonlinear spinor equation is derived from a Lagrangian. There exist rotational symmetric solutions which are simultaneously finite, stationary, normalizable and strongly localisated, and which yield the mass at rest, the spin and the magnetic moment of the particle in a correct manner. Since these solutions are in contradiction to Heisenberg's uncertainty principle the calculated properties cannot be directly observed in the laboratory system. Therefore an eight-dimensional configuration space is introduced containing the laboratory system and the center-of-masssystem. In this space the wave equation is formulated as a nonlinear differential equation for a spin tensor of second order. If the interaction with an external electromagnetic field is very weak a separation of this tensor equation into the nonlinear spinor equation mentioned above and into Dirac's equation is possible. Observable quantities in the laboratory system can be obtained by integration over the inner coordinates

The instability of a diffusion-dominated positive column of a gas discharge in a longitudinal magnetic field is investigated both experimentally and theoretically. Dispersion relations are derived for the case of an m = l helical instability considering the finite length of the column. Regions of instability are calculated for various wavelengths of the instability. Experiments were carried out in a positive column of variable length, ranging from 8.5 to 40 cm. at varying pressures of about 0.1 Torr of Neon. There is a satisfactory agreement between theory and experiments. The main results are: a) in long tubes instability occurs at a distinct magnetic field, calculated first by Kadomtsev and Nedospasov. Stable intermediate regions are possible at higher fields depending on the relations between the plasma-parameters; b) in short tubes the column is stable again for higher magnetic fields; c) in very short tubes there is no instability of this kind. The observed frequency spectrum agrees with the theoretical values

In the case of stationary countercurrent electrolysis the one dimensional space dependence of the different concentrations is governed by a system of nonlinear first order differential equations. Here one takes into account the dependence of the electric field on the concentrations. One considers a mixture of completely dissociating salts with a common anion solved in an aqueous solution of the completely dissociating acid with the same anion. The equations are solved rigorously both in the homogeneous and the inhomogeneous case. One gets the concentrations and the space coordinate explicitly as a function of a parameter w, which is the electric potential divided by the diffusion coefficient. For infinitely long tubes the Kohlrausch-condition remains valid also in regions, where the profiles of the concentrations are influenced by diffusional transport. The results are applied to a process investigated by other authors

Composite states of quasiparticles are studied in the frame of Bopp's quantum theory of elementary particles in a lattice space. By solving the homogeneous Bethe-Salpeter equations in the combined chain and ladder approximation the theory is found to contain a massless pseudoscalar particle (the Goldstone boson), a scalar particle of mass 2 m and an axialvector particle of mass 2 m - d, d > 0, where m is the mass of the quasiparticles and d a small quantity depending on the number of lattice points (or equivalently the cutoff). The method of summation of chain and ladder diagrams by means of the Fierz formula is treated in some detail. Analogies with the model of Nambu and Jona-Lasinio are pointed out. Finally some remarks on the scattering problem are added

Raman spectra of NaCl crystals doped with Ag + ions up to 3.5 mol% have been measured in 4 scattering geometries. In the impurity induced part of the Eg- and F 2g -spectra the strongest peaks are located at 85 and 171 cm -1 . Their intensities increase proportional to the silver concentration. The second order Raman spectrum on the other hand appears to be independent of the Ag + content. The spectra are fully explained by theory and by the assumption of Ag + pairs

Observation of various rotational transitions of four Group Ilia monofluoride allowed the Dunham coefficients Y 01 , Y 11 , Y 21 and Y 12 to be determined. From the hyperfine structure of the AlF, GaF and InF spectra, the nuclear electric quadrupole coupling constants, e q v Q, and spin-rotation coupling constant, C I , were obtained for several vibrational states, v: e q v Q( 27 Al 19 F) = -37,75(8) + 0,44(8) (v + 1/2) MHz, e q v Q( 69 Ga 19 F) = -107,07(8) + 1,09(7) (v + 1/2) MHz, e q v Q( 71 Ga 19 F) = -67,46(8) + 0,68(7) (v + 1/2) MHz, e q v Q( 115 In 19 F) = -727,06(20) + 6,64(20) (v + 1/2) MHz. Stark effect measurements on GaF and InF in the ground vibrational state resulted in the following electric dipole moments: 69 Ga 19 F: |μ̄| = 2,45 (5) D, 115 In 19 F: |μ̄| = 3,40 (7) D

The Hamiltonian for a molecule with internal rotation, rotating in an external magnetic field is derived. Spin effects are neglected

The low energy gamma-ray spectrum of 171 Er has been studied with the use of both Ge (Li) gamma-ray and a high resolution iron free double focusing beta-ray spectrometer. The data provide K-conversion coefficients and multipolarities of eight gamma-rays. Spin and parity assignments 7/2+, 3/2+, 5/2+ and 5/2+ are given to the 636, 676, 738 and 913 keV levels respectively

The concept of non-local elastic response is explained. Neglecting retardation effects, the nonlocal elasticity theory of ionic crystals of type A + B - is derived from the atomic lattice theory by means of the Euler-Maclaurin continuization. The electric part of the theory is comprised in material tensor functions which can be calculated from the long range coupling functions (interatomic potentials). The coupling functions are obtained classically on the basis of Coulomb's law and given in ordinary and Fourier space representation. From these functions the optical and acoustical phonon dispersion curves are calculated. The theory developed here is intended to replace the atomic lattice theory in situations where the lattices sums of the atomic theory are unmanageable

Es wird die Theorie einer zylindrischen Photoionisationskammer bei großer Dichte und kleinem Ionisationsgrad entwickelt. Unter den zugrunde gelegten Voraussetzungen läßt sich das Problem auf die simultane Lösung der mit Produktionstermen behafteten Kontinuitätsgleichungen für Ionen und Elektronen und der Poisson-Gleichung reduzieren. Physikalisch ist der Bereich zwischen den Elektroden durch drei Zonen gekennzeichnet: die beiden Raumladungsgrenzschichten an den Elektroden und das quasineutrale Gebiet dazwischen. Mathematisch ergibt sich eine analoge Aufteilung durch eine asymptotische Entwicklung der dimensionslosen Grundgleichungen nach einem sehr großen Parameter a. Man erhält explizite Lösungen für die Stromspannungs-Charakteristik, die Sättigungsströme und die Teilchendichten. Die Kenntnis dieser Größen legt es nahe, die Photoionisationskammer für die Eichung von Langmuir-Sonden zu verwenden

Coincidence measurements between photoelectrons and photoions produced by 21.21 eV quanta from helium are described. The photoelectrons are energy analysed by a retarding field spectrometer, the photc'ons mass analysed by a magnetic mass spectrometer. The coincidence curves show the fragmentation of a molecular ion as a function of the internal energy of that ion. Molecules investigated are H 2 O, NH 3 , CH 4 , CD 4 , C 2 H 2 , C 2 H 4 , C 2 H 6 , HCOOH, and CH 3 OH. In some cases fragmentation does not seem to occur completely, though the internal energy of the ion is sufficient

Für eine Elektrolytmischung aus zwei Komponenten, deren Moleküle in einer Stufe dissoziieren und die ein gemeinsames Ion (Kation oder Anion) besitzen, werden die diemischen Potentiale der Komponenten und der in der Mischung vorhandenen Teilchenarten zueinander in Beziehung gesetzt. In Analogie zur „idealen assoziierten Mischung" oder „idealen vollständig dissoziierten Mischung" wird die „ideale unvollständig dissoziierte Mischung" definiert. Die Aktivitätskoeffizienten der Komponenten dieser idealen Mischung haben im gesamten Konzentrationsbereich den Wert 1. Die Betrachtung des Verdampfungsgleichgewichtes liefert Ausdrücke zur Berechnung der Aktivitätskoeffizienten aus Partialdampfdruckmessungen. Einige Spezialfälle werden erörtert

Neue Messungen am System Cellophan (600) + Wasser im Temperaturbereich zwischen 10 °C und 90 °C werden mitgeteilt und diskutiert. Es handelt sich um die Permeabilität, die Überführungswärme und die thermoosmotische Permeabilität, die für Permeation und Thermoosmose maßgebend sind, sowie um die Temperaturabhängigkeit des Wassergehaltes der Folie bei Quellungsgleichgewicht. Es wird untersucht, ob Cellophanfolien in flüssigem Wasser als Porenmembranen bzw. als Löslichkeitsmembranen anzusehen sind. Besondere Aufmerksamkeit wird der Richtungsumkehr der Thermoosmose bei einer mittleren Temperatur von etwa 56 °C gewidmet

An apparatus for measuring X-Ray small- and wide angle scattering of solid materials and especially of molten metals with temperatures up to 1100 °C is described. Alloys of the eutectic system Al -Sn with tin-contents up to 30 At.-% are investigated. The influence of surface oxide layers on the scattered intensity is discussed. Correlation functions as well as the Guinier approximation yielded inhomogeneities with mean diameters up to 10 Å in the investigated melts. Therefore the dimensions of these so-called short range segregation zones correspond to those of the first coordination sphere

A set of kinetic equations has been developed which allows to calculate the rate parameters of intramolecular excimer formation, dissociation and of radiative and non-radiative desactivation processes. Experimental data necessary for evaluating the equations are monomer lifetime and relative fluorescence intensities of monomer and excimer fluorescence in solution with and without added quenching substance. Spectroscopical data of biscarbazolyl propane, diphenyl propane and derivatives are used in order to calculate the rate constants. It is shown that the stronger excimer fluorescence of diphenyl propane, as compared with biscarbazolyl propane, is due to the high rate constant of excimer formation in the former substance

Variational principles are established in the frame of macroscopic fluid theory including anisotropic pressure to compare an incompressible regime with any compressible one. It is shown that quite a general static equilibrium is not less stable than the same basic state of compressible fluid

Raman spectra of an AsJ 3 -single crystal were recorded using a quasicontinuous ruby laser, a double monochromator and a special registration electronics. The polarization measurements allow the assignments of the internal, translational and rotational modes of AsJ 3 (factor group S 6 ). Since SbJ 3 and BiJ 3 have the same space group and the same number of molecules per unit cell, one can assign the wavenumbers of the crystal powder Raman spectra in analogy to AsJ 3 . The depolarization ratios of the Raman lines of AsJ 3 in solutions were also determined

In order to calculate the spectral density of current fluctuations in a high d. c. electrical field, a method using the one-electron density matrix is proposed. The nonperturbed problem is considered to be that of the electrons in an external field. The other interactions of electrons are expressed by means of a relaxation time matrix. To fit the expression of the current, given by the Boltzmannian formalism, a form of the diagonal terms of this matrix for electron-phonon interaction is suggested and closed formulae for the current fluctuations spectrum are obtained

The linear thermal expansivities of polycrystalline samples of mixtures of Li 2 SO 4 with K 2 SO 4 and with Na 2 SO 4 have been measured with a “Fused-Quarz Tube” apparatus 1 . Phase transitions are accompanied by changes in the expansion coefficient and also by volume changes. The observed expansion coefficient is constant over wide temperature intervals. Simple crystal structures show higher expansivities than more complex structures. The “pre-melting” phenomenon in Li 2 SO 4 does not measurably influence the thermal expansion. A method has been devised to correct the observations for the plastic flow of the crystals close to the melting points

A general transient theory of light amplification in absorbing media is developed for small amplification and for small signal. The amplification by stimulated thermal Rayleigh scattering has been studied in detail for various shapes of the laser pulse. A transient gain is predicted when the frequencies of the pump and signal pulse are the same. The dependence of the amplification from the scattering angle was investigated. For narrow angles (Θ < 2 x 10 -2 rad) scattering of higher order in angle was calculated. A method of measuring the Rayleigh linewidth with one laser pulse is proposed

Using well defined input pulses the amplification by stimulated thermal Rayleigh scattering was investigated experimentally as a function of time (within the pulse), of absorption coefficient, and of interaction length. The frequency difference between the two interacting light pulses was varied with an accuracy better than Δν/ν = 10 -8 . Amplification was measured in the backward direction and at several degrees from the forward direction. The various experimental observations are in good agreement with theory. The possibility of determining material parameters in this amplifier system is discussed

The dielectric relaxation time of rigid polar molecules in dilute solutions is shown to depend exponentially on an effective molecular radius which is independent of the solvent. This relation contains a temperature-dependent structure parameter, the coefficients of which are used to calculate the activation energy and -entropy of the rate process. The resulting entropies are now more satisfying due to a new formulation of the scattering factor. Similarly the viscosity of the solvent and its structure parameters are related by an exponential law. A characteristical length in this relation is a measure of the "hole distance" of the rate process. From both exponential laws follows that the dielectric relaxation time raised to the power of the ratio of effective molecular radius to hole distance is proportional to the viscosity of the solvent

The profile of the He II λ = 4686 Å line has been measured in a plasma with an electron density of 5.5-1017 cm -3 and a temperature of 6 - 10 4 °K. The measured halfwidth is consistent with that predicted by the Griem and Shen theory. On the far wings the intensity approaches the value expected when ions and electrons are treated by the static theory, although the electrons are far outside the static broadening regime

The nuclear quadrupole resonance (NQR) spectra of 14 N in ethylenimine have been detected at 77 °K. Comparing to the reported microwave experiment on the gaseous state, it is found that the solid state shift in the quadrupole coupling constant is much smaller than that of ammonia

The analysis of fallout from the Chinese nuclear test of September 29th, 1969, showed the typical features of a hydrogen bomb explosion. The fissionable material was probably 239 Pu combined with 238 U. However, the use of a combination of 235 U and 238 U employed in all earlier Chinese experiments cannot be excluded