Volume 27, Issue 8-9

Representation of Magnetic Fields by Generalized poloidal and Toroidal Scalars Every solenoidal vector field can be represented by unique poloidal and toroidal scalars. This description is especially appropriate to the geometry of a sphere. A generalization which can be applied to a more or less complicated geometry could be elaborated by means of transforming integrability conditions of space into integrability conditions of surfaces. This formalism enables us to give simple proofs of other important representations of vector fields by two scalars (magnetic coordinates, complex-lamellar fields).

An Trying to write the NΘ-eigenstates of the Lee-model in a more compact way, we define operators containing the NΘ-scattering-amplitudes. With these operators, the structure of the Hamiltonian can be strongly simplified. - It is now possible to solve the eigenvalue-problem in the NΘΘ-sector with few simple, pure algebraic, calculations.

For a system of independent electrons moving in a common one-body potential V (r) an integral representation of Dirac's density matrix is evaluated in the approximation that V(r) at the point r is replaced by a linear potential with a gradient equal to the gradient of V at r. The particle density ᵨ, ∇ᵨ and the kinetic-energy density ε k are derived from the density matrix. After eliminating the potential and its gradient a parametric representation for ε k in terms of ᵨ and y = |∇ᵨ | ½ ᵨ -⅔ is obtained. Explicit analytical expressions are given in the limits y → 0 and y → ∞ and compared with the inhomogeneity corrections of Kirzhnits and v. Weizsäcker.

From the general polariton dispersion theory it can be shown that in an uniaxial crystal the frequencies of optical phonons * which are identical to those of the short wavelength polaritons depend on the angle Θ between the optic axis and the phonon wave vector. For Θ=0 and Θ=Π/2 the phonons are exactly transversal or longitudinal so that they can be assigned to be of totally symmetric or twofold degenerate type. Careful measurements of the directional dispersion of all phonon modes of LiNbO 3 form a firm basis for a new complete assignment. 6 of the total number of 13 dispersion branches previously given in the literature had to be reassigned.

The infrared and Raman spectra of the complex salts K 5 [Mn(CN) 6 ], K 5 [Tc(CN) 6 ] and K 5 [Re(CN) s ] have been recorded in the range from 4000 to 40 cm -1 . All expected fundamental vibrations have been observed and could be assigned to the irreducible representations of the sym­metry point group Oh . The calculation of the force constants is based on the concept of the generalized valence force field. The low CN-valence force constants indicate the relatively strong Π-bonding character of the metal carbon bond, which is especially pronounced for K 5 [Tc(CN) 6 ).

Due to the exclusion principle the distribution of electronic charge in an ionic crystal differs from a superposition of free-ion charge densities even in the simple Heitler-London picture. This charge density deformation engenders three-body long-range forces the influence of which on lattice vibrations is not accounted for by the usual Kellermann matrix. To obtain a better separation of long-range from short-range forces in CaF 2 , SrF 2 , and BaF 2 , i. e. to avoid absorbing long-range interactions in an adjustable short-range force field, explicit formulae are derived for three-body contributions to the shell-model equations of motion. The additional dynamical matrices pertain to arbitrary wavelengths. In adding to the force field terms which are not purely volume dependent the present descirption of three-body forces is somewhat at variance with recent work on alkali halide dynamics. The deviation from pure volume dependence originates in overlap charges residing in internuclear regions.

The orbital valence force field has been employed to calculate the force constants for tetra-chlorides, tetrabromides, and tetraiodides of titanium, zirconium, and hafnium making use of recent vapor-phase Raman spectral data. The results are compared with the Urey-Bradley force constants, and it has been found that these are well comparable. The applicability of the Lennard-Jones potential has been examined to understand the nature of non-bonded interactions. The force constants have also been utilized to study the relative strength of the chemical bonds in tetrahalides and hexahalide anions

The orbital valence force field (OVFF), and the Urey-Bradley force field (UBFF) have been employed to calculate the force constants for six molecules and ions (AlCl 4 - , AlBr 4 - , AlI 4 - , Til 4 - , Os 16 O 4 , and Os 18 O 4 ). The results have been discussed in the light of the relative stability of the bonds. The applicability of the Lennard-Jones potential is also examined. The kinetic constants have been computed and the results have been correlated with the corresponding force constants.

In this paper a simple method for the determination of all antisymmetric terms allowed according to Pauli principle is presented. Using group theory it allows to evaluate the terms for all electronic configurations of the type l r with l≦ 3.

Beside the well-known ESR-spectrum of Fe 3+ -ions in α-Al 2 O 3 we observed two further lines of very low intensity which are to be characterized as forbidden transitions with selection rules Δm s =2 and 4. Computations for the transitions with Δm s = 4 are in good agreement with experiment. The transition with Δm s =2 shows small but unambiguous deviations for the position of the resonance field and large deviations for the relative intensity. This effect is not compatible with the concept of a crystal field of trigonal symmetry up to the fourth order.

R. K. R. curves have been constructed for the ground state of alkali halide diatomic molecules and compared with the well behaved empirical potential function. It is found that the modified form of Rittner's potential accurately reproduces the R. K. R. curves.

The half-lives of the 121.78 and 366.5 keV levels in 152 Sm were measured by delayed coincidence technique. The values (1.35 + 0.05) ns and (42 + 18) ps were found respectively. Transition probabilities and nuclear deformation parameters were deduced.

The internal friction which is a diffusion dependent physical property has been used as a means to determine the kinetics of short range order in (Cu-30% Zn) alloy. Curves of relative (Q~ l /Q0~ 1) against annealing time have been plotted for various annealing temperatures. An average activation energy of 1.7 eV was found for the ordering process, which is equal to the activation energy for zinc diffusion in coarse grained copper. When an alloy having short range order (SRO), is quenched from high temperatures, excess vacan-cies are liberated which will enhance diffusion, and hence the ordering rate during subsequent anneal-ing. Due to this enhanced ordering rate, the equi-librium degree of short range order canbe achieved in reasonable times even at rather low temperatures, provided that vacancies are mobile at these tempera-tures. For copper-zinc alloys in the alpha phase, the existence of SRO has been theoretically 1 establish-ed and experimentally demonstrated by many wor-kers (cf. CLAREBROUGH et al. 2). Evidence from diffuse X-ray and/or neutron scattering experiments is not available because of the small difference in scattering power of copper and zinc 3 atoms. Long range order in alpha brass above — 30 °C is im-probable 3 because of the rather low ordering en-ergy of the system.

The effect of static elastic stress on the NMR signal in LiCl 35 , Rb 85 Cl 35 , and Rb 87 Br is used to determine the gradient elastic constants relating the electric field gradient at the given nucleus to the elastic deformation. In contrast to previous experiments the quadrupole distortion produced by internal lattice distortion (point defects, dislocations etc.) is considered. Neglecting these distortions leads to an error in the determination of the gradient elastic constants by an order of magnitude.

Monte-Carlo-Calculation for the Backscattering of keV-ions at Poly cry stalline Solids Assuming a random distribution of the target atoms and taking account of electronic stopping too, the Monte-Carlo technique, based on a single collision model, was used to simulate the scat-tering of keV-ions at polycrystalline solids. The reflection coefficient, angular and energy distribu-tion and penetration depth of the reflected particles have been calculated for various ion-target combinations and energies. Furtheron, the angle of incidence of the primary beam was varied. Calculated values of the reflection coefficient and its dependence on angle of incidence are found in good agreement with experimental results. The percentage of particles scattered after a given number of collisions was also investigated. I. Einleitung Die Streuung von keV-Ionen an polykristallinen Festkörperoberflächen hat in den letzten Jahren gro-ßes Interesse gefunden, unter anderem auch als Me-thode zur Oberflächenanalyse 1 . Verschiedene Metho-den zur Berechnung der Streuung sehr leichter Ionen an Festkörperoberflächen wurden entwickelt 2-4 . Ausgehend von der LINDHARD-SCHARFF-SCHIÖTT-Theorie 5 über die Wechselwirkung von energetischen Ionen mit Festkörpern und den Berechnungen von WINTERBON et al. 6 haben BOTTIGER, DAVIES, SIG-MUND und WINTERBON 7 Streukoeffizienten für ver-schiedene Ion-Targetkombinationen aus Berechnun-gen über die Abbremsung von Ionen in einem un-endlich ausgedehnten, isotropen Medium erhalten.

The infra-red spectrum of red amorphous selenium has been studied in the region of 1 μm to 25 μm. The formation of Se 8 -ring molecules as well as polymeric chains Se n has been observed by investigating non-fundamental vibrations. Additional absorption bands at 7.85 μm (1274 cm -1 ), 8.95/9.35 μm (1117/1070 cm -1 ) and 12.35 μm (810 cm -1 ) are reported. They are assigned to multiphonon processes of the type E fundamental of Se n at 74.1 μm (135 cm -1 ).

The phase diagrams of the systems Li 2 SO 4 - Rb 2 SO 4 and Li 2 SO 4 - Cs 2 SO 4 have been determined by means of differential thermal analyses and electrical conductivity measurements. We have also modified our previously published phase diagram of the system Li 2 SO 4 - Na 2 SO 4 , especially in the region near the equimolar mixture.

The potassium-calcium age determination method was applied to two sylvite samples from the upper Zechstein salinar deposit of the Werra region, Germany. Age values were obtained of 133 million years for one sample and of 40.5 million years for the other one, a recrystallised sample.

The reactions producing vibrationally excited CO in the continuous wave CS 2 - O 2 chemical laser are considered. Fundamental and overtone transitions were observed in the systems CS 2 + O 2 , CS 2 + N 2 O, O 2 + CS and it is concluded that the two reactions O + CS → CO+S and O 2 + CS → CO + SO are the reactions in which vibrationally excited CO are produced. The second reaction appears to be responsible for overtone laser action at low buffer gas partial pressures and low discharge currents.

A coaxial gas laser was operated in the superradient mode with molecular nitrogen. Pulse-shape, peak power and integrated output of the UV superradiant pulses at 337 nm were studied as functions of various parameters of excitation and gas discharge (ignition voltage, discharge pressure, tube length, tube diameter) at a repetition frequency of 5 Hz. At the present time the equipment can deliver superradiant pulses with a peak power of 30 kW and a width (FWHM) of 3 ns. The results of these investigations are important for a successful operation of a coaxial superradiant light source with a pulse repetition frequency of some kHz by flowing gas technique.

Thermal resonator effects are studied in laser pumped organic dye lasers with the longitudinal pumping arrangement. If the distribution of the pump light is a Gaussion, a diverging lens is induced by the thermal gradient in the dye solution. This thermal lens was compensated by using a suitable resonator set-up with an adjustable telescope. Divergence and bandwidth of the tunable laser were reduced considerably by using the proper compensation. If the angular position of the pump beam is shifted, the axes of laser resonator and thermal lens are different, causing beam deflection and wavelength shifting of the output laser beam. Therefore, high stability and mode purity of the pump laser is important to get a well defined output laser beam.

The ions effusing ambipolar out of the positive column of a mercury-argon low pressure dis­charge are analyzed in a quadrupol mass spectrometer. Besides the Hg + -ion we find the Hg 2 + -ion molecule. The measured current ratio i(Hg 2 + )/i(Hg + ) in the mass spectrometer is proportional to the mercury vapour pressure pHg in the discharge. i(Hg 2 + )/i(Hg + ) lies between 10 -2 at pHg = 10 -3 Torr and 1 at pHg = 0.1 Torr. - At constant argon- and mercury pressures i(Hg 2 + )/i(Hg + ) is inversely proportional to the discharge current. - At constant discharge current and mercury vapour pressures the ratio i(Hg 2 + )/i(Hg + ) is nearly independent of the argon pressure. An analysis of our measurements with the help of balance equations for excited Hg-atoms in the resonance level ( 3 P 1 ) and in the metastable 3 P 0 and 3 P 2 levels is carried out. It turns out that the only relevant process leading to the Hg 2 + *ion molecule is the reaction Hg * + Hg*→ Hg 2 + +e of Hg-atoms in the levels 3 P 0 , 3 P 1 and 3 P 2 . It can be shown that the Hornbeck-Molnar-process Hg**+Hg → Hg 2 + +e and the reactions Hg + +2Hg→Hg 2 + + Hg, Hg + +Hg+Ar→Hg 2 + +Ar play an unimportant role in the Hg 2 + -ion formation.

CdS thin film solar cells with a p-Cu 2 S - n-CdS-heterojunction were made by vacuum evaporation of CdS films on Mo substrates and dipping of these films into Cu + -ion solution. The influence of various annealing times and repeated dipping into Cu + -ion solution were investigated and discussed. Etching the CdS films with various etchants gave different results. In this way the solar cells yielded efficiencies up to 5.2%. The influence of interfaces of Ag and Zn between the Mo-substrat and the CdS film was studied.

ab initio calculations using a minimal basis set of Gauss functions have been carried out on the molecules CH 4 , C 2 H 2 , C 2 H 4 , N 2 , HCN and CH 3 NH 2 in order to test the usefulness of the basis set in predicting properties such as charge distributions and dipole moments in large molecules.

The magnetic field dependence of CIDNP is presented for two reaction products of independently generated alkyl radicals. It is shown that nuclear spin relaxation of the products influences the intensity distributions within multiplets, and how this relaxation can be included in the calculation of CIDNP effects from the radical pair theory. Analysis of the experimental results supports the recent view that CIDNP is created in pairs of radicals which undergo many diffusive displacements before reencounter.

A theoretical and experimental study of the phenomenon of diffusion slip in a binary gas mixture is presented. To provide some physical insight, a very general variational expression given earlier by Loyalka is rederived via the use of a method developed recently. The case of Maxwellian diffuse specular reflection is considered in some detail and the inadequacies of previous theoretical results based on the early arguments of Maxwell, kinetic models and simple intermolecular force laws are discussed. Although in general, the variational results (or the equivalent results given here) together with the assumptions of Lennard Jones potential and diffusive reflection give a satisfactory agreement with the available experimental data, it is found that for isobaric (isotopic) mixtures, in the choice of the intermolecular and gas-surface interaction parameters special care should be taken in that the results are quite sensitive to small variations in the values of these parameters.

The variation-perturbation uncoupled Hartree-Fock scheme is applied to the calculation of the electric dipole polarizabilities of Mg and Ar-like atomic systems. The results are compared with more elaborate coupled Hartree-Fock calculations and with experimental data and indicate the validity of the method.

Alkyl iodides especially methyl iodide from the offgas of reactors and of reprocessing plants are difficult to remove. In earlier investigations it was shown that silver zeolites are qualified for a total fixation of methyl iodide, only when these sieves were exhaustively loaded with silver ions. In order to explain why only exhaustively loaded silver zeolites of type X are able to remove methyl iodide completely from the air, the reaction products from the chemisorption reaction were identified. The proportion of the silver ions that had reacted was calculated. Exhaustively loaded Ag-LMS-X pellets heat-treated at 400 °C (water content 0.94% by wt.) react with CH 3 I to form dimethylether. If the same pellets were gently dried with P 2 O 5 (water content 15% by wt.) dimethylether and methanol were the products. The identification was done by gas chromatography and infrared spectroscopy. The chemisorption reaction can be described in the following way: a) CH 3 I + HOH+Ag + →AgI + CH 3 OH + H + b) CH 3 I + CH 3 OH+Ag + → AgI + CH 3 OCH 3 + H + If only small concentrations of methyl-iodide and an excess of water vapour are present only methanol is expected. The experimental results are in good agreement with the assumptions.

The microwave spectrum of the (CH 3 ) 2 NNO and (CH 3 ) 2 15 N 15 NO species have been studied and the rotational constants evaluated. By comparison of the inertia defects of the two species it can be stated that the nuclear frame of the molecule is planar, which is in agreement with the reported electron diffraction results. The dipole moment of the (CH 3 ) 2 15 N 15 NO species has been determined. Further studies on the internal rotation of the two methyl tops are in progress together with the analysis of the spectra of other isotopically substitued species.

The molecular structure of Trimethylazidosilane, (CH 3 ) 3 SiN α N β N ω , was determined by electron diffraction of gases. In contrary to published results this molecule has neither C 3V - nor C s -symmetry but C 1 -symmetry. The following results for the geometrical parameters were obtained: r a (N ω -N β ) =1.150 ű0.011, r a (N β -N α ) =1.198ű0.008, r a (Si-N)=1.734ű0.007, r a (Si-C)=1.854ű0.003, r a (C-H)=1.082ű0.003, ∢Si-N α -N β =128°±l.6°, ∢ᵨ=36.2°±4.9° (ᵨ is the out-of C 1 SiNα-plane angel of the Azidodiaine about thel Si - N α -bond), ∢N α -Si-C 1 =107 o ±3.1 o , ∢N α -Si-C 2 =110.1°±3.2 ,∢N α -Si-C 3 = 105.2°±2.6°, ∢C 1 -Si-C 2 =110.4 o ±2.9°, ∢C 1 -Si-C 3 =108.8 o ±3.1°, ∢C 1 -Si-C 3 =115°±3.4°and ∢Si-C-H=114.2°±1.6°.

For sufficiently symmetric molecules without a permanent electric dipole moment, it is shown that refractive indices, Kerr constants and electrooptical absorption measurements in suitable non-polar solvents can be utilized to determine the components αcgx, αgy, αgz of the polarizability tensor of solute molecules in the electronic ground state. Since the required quantities are avail-able for anthracene, tetracene, perylene and bianthryl, an evaluation of the polarizability tensor components is made possible. In solutions where the solvent molecules possess a permanent electric dipole moment or a sufficiently large quadrupole moment, as for example benzene, the fluctuations of the reaction field cause a contribution to the Kerr constant which may be an essential reason for its solvent dependence.

The conductometric behaviour of lithium chloride in water-sulfolane mixtures, at 35 °C, was investigated within the salt concentration 2x10 -4 ÷1.5x10 -2 moles/1, and within the solvent media dielectric constant range 75 (pure water) ÷ 43 (pure sulfolane). A few solutions of RbCl and CsCl suitable for comparison, were also investigated. A 0 , A, a L , a A and A0 η values, drawn from the experimental data, are discussed and compared with previous results on sodium and potassium chlorides. The main conclusions which may be drawn from the conductometric behaviour of the alkali halides are: a noticeable association, unusually increasing in the sense CsCl ≦ RbCl <KCl < NaCl of lithium chloride, in pure sulfolane.

Solutions of the stationary dynamo equations are derived such that outside a torus the magnetic field is the axisymmetric vacuum field of a circular loop, while inside the torus in the limit of large aspect ratio both the velocity and the magnetic fields have helical symmetry.

Nuclear relaxation times T 1 , T 2 , T 1ϱ and T 2ϱ are calculated in the weak collision limit for the case of anisotropic spin-spin interaction which includes dipole-dipole coupling and electron-coupled interactions in their most general form.

In the lattice of subspaces of the Hilbert space elements can be defined which may be con-sidered as generalized implications. It is shown, that these elements satisfy the most important relations which are known to be valid for the classical implication. These results seem to justify the interpretation of this lattice as a propositional calculus sometime called quantum logic.

The dielectric constant ε' and dielectric loss ε" are measured for concentrated solutions of n-dodecanol and n-octanol with five non-polar solvents at five frequencies between 2 and 400 MHz at three temperatures between 20 and 60 °C. The effective dipole moments have been calculated and found to decrease with increasing dilution. The relaxation times of the concentrated solutions are lower than that of the pure alcohols, decrease with dilution and are dependent on the nature of the non-polar solvents.

In this work a method for a relative exact determination of the lifetime of nuclear levels which are populated and de-populated only by a γ-γ-cascade with unseparable energies is presented. The capacity of the method is shown on the ex-amples of the 184 keV level of 67 Zn and the 158.6 keV level of 117 Sn.

The influence of the excitation intensity on the laser spectra of solutions of 4-methylumbelliferone in HCl/C 2 H 5 OH has been investigated. There are three distinct laser emissions at 4100 Å, 4900 Å and 5300 Å, respectively, the third of which only occurs within a HCl-concentration range of 10 -2 m/l < c HCl < 2.5 m/l. This emission is quenched if the laser threshold for the emission of the neutral form of 4-methylumbelliferonc at 4100 Å is exceeded.

The spectral density of light scattering from weakly ionized plasmas embedded in a homogeneous magnetic field B is given by the work of WILLIAMS and CHAPPELL 1, 2 and KLINGENBERG 3 . The spectral density has been computed for electron plasmas and is analyzed for the case k ⊥ B ( is the difference between the wave vectors of the incident wave and the scattered wave) in the regimes k D ≫ 1 and k D ≪ 1 (D is the Debye length).

Exoelectronemission of Polymers Exoelectronemission is used for radiation dosimetry. Poly-mers do not show exoelectronemission.

The thermoelectric powers of the solid high-conductivity phases of the salts: Agi, KAg 4 I 5 , RbAg 4 I 5 , NH 4 Ag 4 I 5 , (CH 3 ) 4 NI·6.5 AgI, Ag 2 HgI 4 and Ag 3 SI have been measured by means of a silver-electrode thermocell. On the basis of the data the transport entropies of the silver ion have been calculated. Moreover the possibility to obtain heats of transport from thermoelectric measurements has been briefly discussed.

DICAVE und EMERY 1 haben aus Messungen mit einer Diaphragmazelle im Temperaturgradienten 20 bis 40% größere Diffusionskoeffizienten gefunden als in Versuchen unter isothermen Bedingungen. Dies von der Theorie her unverständliche Ergebnis legte weitere Messungen nahe.