Volume 28, Issue 7

Overlaps of Hartree-Fock-Bogoljubov states occurring in modified HFB theories (e. g. projected HFB) are calculated using group theoretical methods. For this purpose the Bogoliubov-Valatin transformation is generalized. The resulting nonunitary transformation leaves the Fermi commutation relations invariant, but the characteristic property of the creation and annihilation operators, namely that they are hermitean conjugate to each other, is lost. A suitable factorization of the new transformation is derived, which also applies to the unitary Bogoliubov-Valatin transformation but the structure of which is completely different from the well-known Bloch-Messiah decomposition. Furthermore, the relation between various representations of the HFB state vector is clarified.

A macroscopic theory of polaritons and long optical phonons in biaxial finite ionic crystals is presented. For the case of a crystal plate it is shown that the dispersion of surface and bulk polaritons is determined by a system of nonlinear equations. These equations may be combined to an explicit dispersion formula only for propagation directions parallel to the principal axes of the dielectric tensor of the crystal.

The quadrupole hyperfine structure of 39 K 127 I was measured on the rotational transition J = 1 → 2 at 7.2 GHz. Observations in various vibrational states resulted in the following quadrupole coupling constants: (eq 0 Q) 39 k= -4.12 (10) MHz, (eqνQ) 127 I = (- 85.32 - 2.93 (v + 1 / 2 ) ±0.12) MHz.

The quadrupole hyperfine structure of 27 A 1127 I was measured on the rotational transition J = 1 → 2 and 14 GHz. Observations in various vibrational states resulted in the following quadrupole coupling constants: eq 0 Q ( 27 Al) =-25.50(10) MHz, eq v Q{ 127 I) =-307.407-4.315 (ν+ 1 / 2 ) ±0.100 MHz. The magnetic spin-rotation-interaction of the iodine nucleous was included in the calculation. We obtained as coupling constant: c I ( 127 I) = + 13.3(10) kHz.

The quadrupole hyperfine structure of 27 Al 79 Br of the rotational transition J = 0 → 1 was measured. We obtained the following quadrupole coupling constants: eq 0 Q ( 27 Al) = -27.90 (50) MHz, eq 0 Q ( 79 Br) = +78.78 (20) MHz . The hyperfine structure of the rotational transition J = 1 → 2 of 27 Al 35 Cl, measured by Lide, was reassigned and the fit of the spectrum resulted in the molecule parameters: e q 0 Q( 27 Al) = -29.8 (50) MHz , e q 0 Q( 35 Cl) = - 8.6 (10) MHz .

A cw high-power ENDOR spectrometer is described. Freed's theory of coherence effects on ENDOR line shapes of free radicals in solution was tested with cw NMR fields up to 30 Gauss. The neutral radical Perinaphthenyl (PNT) with groups of three and six equivalent protons served as example. A satisfactory agreement with the theory was found, even in quantitative terms. Very reasonable values for relaxation times T 1e , T 2e and T 1n of the PNT could be determined by fitting Te -1 /W e , W n /W e and using measured values for B MW, B NMR and the EPR line width.

A general scheme is described for self correcting the various coherent phase errors that arise in multi-pulse sequences used for artificial narrowing of the absorption line in solids. The scheme is found to work well experimentally and greatly facilitates the phase alignment procedure by reducing the sensitivity of the multi-pulse response to phase control settings and drifts. First order dipolar terms reintroduced into the average Hainiltonian by the phase errors are also discussed.

The Weyl-Wigner transformation enables us to construct a representation of quantum motion equations using functions in phase space. The states of the system are determined by the quasiprobability distribution in phase space and the motion is described by an orthogonal integral operator. This formalism is employed in the study of the classical meaning of the discrete symmetry groups, in the problem of defining the current probability and in the proving of the expression of cross section from the S-matrix.

Limits of validity of the assumption of local thermodynamic equilibrium in short spaced cesium plasmas are deduced from necessary conditions for the existence of local translational, internal, and radiation equilibrium. Results are presented graphically by curves of total pressure or electron density as a function of electron temperature required to satisfy the given conditions.

The problem of turbulent diffusion is re-examined. Its close connection with Schwinger's formulation of quantum field theory is established. For the transition probabilities we find a Dyson equation by using Zwanzig formalism with renormalization. The first nontrivial approximation of the memory kernel yields Saffman's result.

The steady, supersonic, barotropic, and inviscid flow of a rarefied gas plasma through an axisymmetric crossed-field device (imposed axial electric field and radial magnetic induction) is being analyzed, for arbitrary values of the Hall parameter. A previously developed perturbation method is used to obtain closed form solutions for the electric current density, flow velocity, and mass density within the annular duct. Conditions for optimal values of the Hall parameter are given.

The simple primitive rhombohedron with r 1 as the shortest atomic distance of the close packing of spheres (structure I) and the square with the side r 1 ′<r 1 (structure II) are experimentally suggested to be the structural elements of metal melts. In the melts with metallic binding in the lattice the rhombohedron chain I shows up as a zigzag chain with the distances , r 1, r 1 √3, r 1 √7, r 1 √12, r 1 √19, and so on in the atomic distribution curve, in the melts with homeopolar binding, however, the rhombohedron chain II appears as a straight chain with the distances r ν = ν·r 1 . In both cases the square chains I and II of structure II yield straight chains with the distances r 1 ′ and 2 r 1 ′ as also rν′ = v·r 1 ′. A schematic representation gives a rapid survey of the structure of monoatomic metal melts.

A discussion of the atomic distribution curves obtained by Fourier-analysis of electron diffraction patterns shows that thin films of the alloy (Ag + 50 at.-% Cu) are liquid-like amorphous. The amorphous alloy (Ag + 50 at.% Cu) is composed of the 3 regions Cu, (Ag + 50 at.-% Cu) alloy and Ag. Further investigations yield two different degrees of order. At lesser order only the distances of the 3 zigzag chains of the amorphous regions show up in the atomic distribution curve, while at more extended order the three (r 1 ) Cu, alloy, -distances of the hexagonal close packing are also observed. Finally, in the case of lesser order it is shown that the atomic distribution curve calculated from the 3 zigzag chains of the amorphous alloy (Ag + 50 at.-% Cu) is in good agreement with the experimental one.

The luminescence behaviour of crystalline K 3 CrF 6 is measured in the temperature range from 100 °K to 4.2 °K. The complex shows a very strong, broad fluorescence emission at temperatures lower than 20 °K. additionally also the phosphorescence transition can be observed. At temperatures higher than 20 °K only fluorescence is measured. The 2 E→ 4 A 2 -transition does not split suggesting O h -site symmetry. Excitation- and luminescence spectra at 4.2 °K are the basis for a calculation of the energy eigenvalues. The crystal field parameters are fitted by the experimental data. The vibrational sidebands of the electronic transitions 2 E - 4 A 2 an 4 T 2 4 A 2 are compared with Raman- and IRresults. From the temperature dependence and measured vibrational frequencies the zero phonon transitions of fluorescence and phosphorescence can be found

The absolute fluorescence yields of triphenylcarbonium derivatives are correlated with the change of bond order between central-C-atom and phenyl group during the electronic transition. The fluo rescence yield is reduced by a rotation of the phenyl group only if the π-electron system of the phenyl group is sufficiently strong coupled to the other part of the molecule. The change of bond order can be assumed as a measure for the coupling.

The molecular structure of Trimethylphosphate O = P(OCH 3 ) 3 has been determined in the vapour phase by electron diffraction. The best fit of the experimental scattering intensity was obtained by assuming two rotational isomers with C 3 -symmetry occuring in a ratio of approximately 3:1. The geometric parameters and mean square amplitudes are given in the article.

LEED/Auger studies with Ir(110) revealed that the clean surface is reconstructed to a 1X2- structure, whereas the normal 1X1-structure can be stabilized by small amounts of carbon impurities. Carbon monoxide adsorbs with a mean heat of adsorption of 37 kcal/mole and forms a 2X1- structure without affecting the substrate "extra" diffraction spots. Adsorbed oxygen forms 2X2- and c2X2-structures, whereby the diffraction features of the 1X2-structure disappear indicating that oxygen atoms cause place exchange process of the Ir surface atoms which is not the case with adsorbed CO. Carbon monoxide tends to dissociate at elevated temperatures. The catalytic oxidation of CO proceeds in a manner similar to that found with Pd and Pt surfaces.

The conductometric behaviour, at 35 °C, of solutions of lithium chloride in sulfolane-methanol mixtures was investigated, the concentration of the salt ranging within 0.8 x 10 -3 and 8 x 10 -3 moles/l and the dielectric constant of the solvent within 42 and 30. Using the Fuoss, Onsager and Skinner treatment, the parameters ⋀ 0 , α L , A and α A were calculated. An increase of the Waiden products with the sulfolane content of the solution was observed as well as an non-coulomb behaviour of the association constant. Data are discussed and interpreted on the basis of ion transfer energies and the properties of the solute and the solvent mixtures.

An argon ion laser operating at 4765 Å and a helium-cadmium laser operating at 4416 Å have been used as radiation sources to study Brillouin scattering in seven organic liquids. The Brillouin spectra were investigated at 90° with a pressure scanned Fabry-Perot spectrometer. The measured frequency shifts between the Stokes and anti-Stokes lines were used to determine the hypersonic velocities of thermal waves at frequencies between 4.8 and 7.2 GHz. No dispersion of the hypersound could be detected.

The general valence force constants and vibrational amplitudes have been evaluated for the metal hexahalo species of groups IV -VI elements using recent infrared and Raman spectral data. The results are employed to study the trend of variation among different species as well as the influence of cations on the relative stiffness of the chemical bonds. It has been found that the chemical bonds in the environment of a cesium cation are stronger than those of a tetraethylammonium cation.

A detailed study of the Green's function analysis of the vibrations of substituted and perturbed molecules is made. The similarity in approach of this procedure with the parametric study of force constants is pointed out. The significance of the signs of the different parameters entering the '"mixing parameter matrix" is discussed for any nth order case, using the definition of potential energy distribution.

A molecular model with five degrees of freedom, three for the overall rotation, one for the internal rotation and one for another vibration, is discussed. The treatment is restricted to C 3 -symmetric internal rotors. Regarding this special symmetry the classical kinetic energy is formulated. Two possible sets of molecule orientated coordinate systems, one the instantaneous principal axis system, the other an axis system in which the vibrational angular momentum disappears, and the transformation between them are discussed. A general expansion for the potential energy is given. The Hamiltonian is derived for the special case of a molecule with a symmetry plane restricting the vibrational motion to an in-plane vibration. The numerical methods to evaluate the coefficients of the kinetic part of this Hamiltonian and the possibilities to solve the eigenvalue problem, including a remark to the Van-Vleck perturbation treatment, are discussed.

A commercial interferometer has been modified for high resolution gas phase work by addition of a variable temperature cell of 3 m path length. The data reduction method is described, and examples of the performance are given. Two rotation-vibration bands of diacetylene, ν 9 and ν 7 -ν 9 , have been analyzed to yield ν 9 =220.139(5), ν 7 =482.13(1), and B 0 = 0.14649(7) cm -1 .

The ligand field reflectance spectra of tetrahedrally coordinated Cu 2+ -ions in different oxidic host structures (several spinel compounds, Ca 2 ZnSi 2O7 , Zn 2 SiO 4 , several garnets, ZnO) and at different temperatures (300 °K - 4 °K) are analysed. For Cu 2+ -ions in compressed tetrahedra with D 2 d-symmetry the two expected bands: 2 B 2 ( 2 T 2 ) → 2 E ( 2 T 2 ) [t 1 ] and 2 A 1 ( 2 E) [t 3 ] respectively were found, while in cases of lower symmetry the transition 2 B 2 ( 2 T 2 ) → 2 B 1 ( 2 E) [t 2 ] is observed in addition. For the spinel mixed crystal series [Zn 1 - x Cu x ] (4) [Cr 2 ] (6) O 4 (0≦x ≦ 1,0) a first order transition from the cubic to a tetragonal (c/a < 1) structure occurs at :r = 0.47. The transitions t 1 and t 3 show a remarkable UV-shift for x>0,47, indicating an increasing Jahn-Teller distortion of the CuO 4 - tetrahedra with increasing x. The Jahn-Teller-splitting of the 2 T 2 -groundstate [t 1 ] was found to range between ≈ 3000 cm -1 and 8500 cm -1 for the different compounds. The bands could be fitted using "angular overlap" parameters e λ (λ = σ, π ⊥ , π || ). Finally the spectrum of Cu 2+ -doped ZnO could be analysed on the basis of trigonally compressed CuO 4 -tetrahedra with a 2 T 2 -groundstate splitting of ≈ 3000 cm -1 .

A renormalization procedure is described which gives the correction Δη to the crystal viscosity η when high intensity acoustic flux propagates in a piezoelectric semiconductor. Δη is attributed to the additional loss which a sound wave suffers from its production of forced higher harmonics via the electron gas. In the multimode case, the theory is based on the concept of "mode dressing". Numerical results are given for Δη/η for an Akhieser type of small signal lattice loss and for conditions found in acoustoelectric domains. It was found that Δη can exceed η appreciably when the frequency of the acoustic flux is one order of magnitude below the frequency of maximum linear electronic gain. The results are applied to the anomalous fast decay of low frequency phonons in high flux acoustoelectric domains.

Deviations from Friedel's law in the case of anomalous transmission of X-rays have been estimated in as-grown silicon crystals. The results of measurements on a double crystal spectrometer agree with the dynamical theory of elastically deformed crystals. Using this theory, we have obtained information about growth deformation in crystals containing a small number of dislocations or in dislocation-free ones. Radii of curvature of crystal lattice planes of the order of km, orientation differences of the order of 0.1" and relative changes of lattice constants of the order of 10 -3 % have been estimated. Dislocation loops were observed at the boundary between the dislocation-free and the distorted part of the crystal.

The anomal transmission of CuK radiation through "thick"' perfect crystal slices of Germanium is strongly temperature dependent. This temperature dependence was measured between 293 and 6 K in the (220) symmetric Laue case and used to evaluate the Debye temperature θ M . The wellknown uncorrected value θ′ M = 290K was obtained near room temperature. Taking into account TDS and Compton scattering in addition to the photoelectric absorption the corrected value θ M = 294 or 296 K was found, depending on the source of data. With decreasing temperature the corrected θ M increases slightly up to a maximum at very low temperatures, as predicted by Batterman and Chipman and by Salter.

The eigenvalue problem of the Ewald-v. Laue dynamical theory of X-ray diffraction by perfect absorbing crystals has been solved in the case of simultaneous diffraction of CuKα-radiation by the (lll) and (l̅ll) planes of Germanium. The calculated intensities of the three beams agree fairly well with those measured on platelets of different thickness.

Side light investigations of the flame in the laser cavity resulting from the oxidation of acetylene showed the presence of H 2 O in this system. Stimulated emission in the fundamental band of CO is partially absorbed by the water formed in the reaction. This explains the very low total output of the C 2 H 2 -O 2 chemical laser.

The spin-flip probability S(θ) in the inelastic scattering of unpolarized 15.0-MeV neutrons to the first 2 + state in 12 C has been determined at θ = 140° (lab.) by measuring the scattered neutrons in coincidence with the subsequent 4.44- MeV deexcitation γ-rays emitted normal to the scattering plane. Time-of-flight technique with carbon recoil detection in a plastic scintillator has been used. The neutron spin-flip probability is S = 0.21±0.06.

In a countercurrent ion migration process the ion of an element (e. g. a metal cation) can form various unstable complexes with the anion of the countercurrent electrolyte. The total concentration of such an element in its stationary and locally constant distribution in a countercurrent ion migration column is then determined by the average mobility of all equilibrated species containing this element. From stationary distributions in their dependence on concentration the mobilities of the various species can be determined if the constants of the different equilibrium stages are known and vice versa.

Sold-liquid equilibria were studied by a visual method in order to draw the polythermal projections of the (Li, Ag, Na) NO 3 and (Li, Ag. K) NO 3 ternary systems. The five pertinent binaries are also discussed and data concerning the characteristic points and crystallization regions are given.

The microwave spectrum of trimethylchlorosilane has been investigated between 8 and 20 GHz. The quadrupole splitting of the K = 0 lines of the transitions J = 2 → 3 and 3 → 4 have been determined. The quadrupole coupling constant of the Cl-35 atom is determined to -34.701 MHz, and the rotational constant is determined to B 0 = 2197.382 MHz.