Volume 30, Issue 8

The method of correlated basis functions is studied and applied to the Fermi systems: liquid 3 He, nuclear matter and neutron matter. The reduced cluster integrals xijkl... and so the sub-normalization integrals Iijkl... are generalized to coinciding quantum numbers out of the set {i, j, k, I,...}. This generalization has an important consequence for the radial distribution function g (r) (and then for the liquid structure function) ; g(r) has no contributions of the order O (A -1 ). For 3 He the state-independent two-body correlation function g(r) is calculated from the Euler-Lagrange equation (in the limit of r → 0) for the unrenormalized two-body energy functional. For nuclear matter and neutron matter we adopt the three-parameter correlation function of Bäckman et al. Then the energy expectation values are calculated by including up to the three-body terms in the unrenormalized and renormalized version of the correlated basis functions method. The experimental ground-state energy and density of liquid s He can be well reproduced by the present method with the Lennard-Jones-(6 -12) potential. The same method is applied to the nuclear matter and neutron matter calculations with the OMY-potential. The results of the energy expectation values indicate a practical superiority of the unrenormalized cluster expansion method over the renormalized one.

A procedure is developed which renders the simultaneous description of angular and energy relaxation of wall electrons in a plasma possible. The plasma is assumed to be field free, allowance is made for elastic and inelastic collisions with neutrals, as well as for electron-electron encounters. The procedure is based on an expansion in terms of the eigenfunctions of a suitable part of the kinetic equation. In the zeroth order, the problem is reduced to a boundary value problem of the Sturm type, and subsequent solution of a singular integral equation by standard technique. To account for the rest of the kinetic equation, we construct a Green′s function which forms the basis for an iteration process. The application of the procedure is illustrated with an example.

The paper deals with the microwave free-space diagnostics of high collision arc discharge plasmas. It is found that information about the electron density N and the collision frequency ν in such a plasma can be obtained from the energy transmitted through the plasma by an electromagnetic wave. The phase of the electromagnetic wave cannot be used since it is almost the same as that of a wave passing through vacuum. These basic concepts are verified experimentally at a frequency of 37.5 GHz. It is shown how the time dependence of the electron density in a plasma with constant and with time variable collision frequency may be evaluated.

Direct Determination of the Rate Constants for the Sr-and Ba-exchange Between the Small and Large Channels in LMS 13X The rate constants for the intracristalline Sr-and Ba-exchange between the small and large diameter channels of LMS 13X were measured. For this matter the method of interrupting the ion exchange was modified. It is assumed, that a first order reaction takes place. Using the rate constants and the diffusion coefficients, which were measured by Hoinkis and Levi, the total exchange of Sr 2+ and Ba 2+ could be calculated.

The ratios of the Larmor frequencies of 10 B and 2 H and of 11 B and 10 B have been measured with the NMR method and a magnetic moment has been calculated for 10 B in the B (OH) 4 - -ion. For this, an investigation of the dependence of the NMR signals of 10 B and 2 H on the concentration of some boron salts in solutions of H 2 O and D 2 O was necessary. Using hyperfine interaction constants from literature, the hyperfine structure anomaly 10 ∆ 11 of boron in the 2 P 1/2 atomic ground state has been calculated. A difference in the magnetic shielding between the isotopes 10 B and 11 B in different compounds could not be detected.

To measure the Kr-85 content in the atmosphere we developed a simple method. Within a time internal of five to ten days (depending on the moisture of the air) five to ten m 3 of air (NTP) are pumped through activated carbon (pressure 300 torr, temperature 77 °K). When sampling time is over, the carbon is heated to 470 °K. This gives a gas sample of 4 1 with more than 90% of the atmospherical krypton in 3 hours. With a further step of enrichment, the volume of the sample is reduced to 100 ml. The final separation of krypton from O 2 , N 2 , CO, CO 2 and Xe is made by gaschromatography at room temperature with methane as eluent gas (duration 25 min). The Kr-fraction is transported to a proportional counter (200 ml). The overall yield is 90%. The overall error of the Kr-85 content is near 1%. Data are given for the time of 15. 6. 1973 to 29. 12. 1974.

A method is described to determine for the first time the 85 Kr concentration in seawater. Samples of 220 l of seawater are degassed aboard a research vessel. The krypton contained in the gas sample is isolated in the laboratory and its 8s Kr activity is measured in a gas counter. The background of the lowel-level counting-array is 0.026 cpm; surface water samples yield a netto count-rate of 0.13 cpm. The reproducibility of the method was checked by gas standards (krypton-air mixtures) and moreover by three surface water samples; both sets agree within ± 1 σ, or ± 5%. The mean value of three samples of great depths (1600, 2000, 2000 m) is 5% of the surface water concentration. This figure represents the possible contamination of the samples by atmospheric 85 Kr during the various preparation stages (blank value). Two profiles have been measured from the North Atlantic (about 40°N, 18°W, November 1972). A strong decrease of the 85 Kr concentration is found in the upper 1000 m. In a simple one-dimensional vertical diffusion-advection model the profiles can be simulated with a coefficient of apparent vertical eddy diffusion of 5 cm 2 / sec in the depth range of 300 to 1000 m (main thermocline). A possible application of oceanic 85 Kr data is the combination of depth profiles with those of other tracers, in particular 3 H. Another application of the 85 Kr method is the dating of groundwaters younger than 20 years.

Results are reported of a mass spectrometric investigation of the content and isotopic com-position of potassium from the mesosiderite Emery (silicate phase) and the chondrite Elenovka (bulk). Normalized to the Nier value of 39 K/ 41 K=13.47 the 40 K in Emery (K-content 220 + 25 ppm) was found to be enriched by (4.03 ± .30)%, the potassium from Elenovka (760 ± 50 ppm) to be indistinguishable from terrestrial potassium. - Evidence is presented that the excess 40 K in the silicates from Emery (Ca-content 6.06 weight %) has been produced essentially by secondary cosmic ray neutrons via the 40 Ca (n,p) -reaction. The total excess of (2.57 ± .39) x 10 14 40 K-atoms/g Ca together with the excitation function of the 40 Ca (n,p) -reaction and the neutron flux spectrum of Arnold, Honda and Lal yields a dose of fast neutrons (2 MeV ≦ En ≦ 100 MeV) Φ · T = (7.2 ± 1.1) x 10 16 neutrons /cm 2 and an average flux during the cosmic ray exposure age T = (134 ± 12) Myrs of Φ = (17.4 ± 3.1) neutrons /cm 2 sec. - A comparison of the neutron induced production rate of 40 K from Ca with that of 21 Ne from Mg and 38 Ar from Ca indicates the Arnold, Honda, Lal flux spectrum to be adequate for E n ≲ 20 MeV but that it underestimates the number of neutrons with higher energies.

Estimates suggest that the nonlinear transverse radiation pressure produced within a plasma by a convergent annular high power laser beam may lead to the focusing of an intense relativistic electron down to a radius of ~10 -4 cm. The transverse radiation pressure results from the dielectric property of a plasma in conjunction with the phenomena of the self-focusing of intense laser light. The tightly focused electron beams would make possible the release of thermonuclear energy by micro-explosions.

The backward emission of secondary electrons from thick targets of graphite, aluminum, copper, molybdenum and tantalum under the impact of protons, deuterons, 3 He-ions and a-particles has been measured for incident energies in the MeV-range. The data are discussed within the scope of theoretical considerations based on low-energy studies taking into account the contribution due to ;< 5-rays.

The microwave spectrum of IBr was measured in the low rotational transition J = 3 ← 2 in order to resolve the hyperfine structure as completely as possible. Rotational constants and quadrupole coupling constants were derived for both nuclei. The observation of the rotational spectrum in different vibrational states yields the vibrational dependence of the rotational constants as well as of the hyperfine parameters. The Dunham potential coefficients a 0 , a 1 , a 2 , a 3 are given.

Between the first and second maxima of the atomic distribution curves of molten Au, Ag, and solid liquid-like amorphous Ga a small, but sharp maximum at [r1′] Au, Ag · √2 3.84 Å and [r1] Ga · √3 4.83 Å occurs. Hence [ri′] Au,Ag = 2.72 Å and [ri]Ga = 2.79 Å follows as the shortest atomic distances of structure II and of the spherical close packing (structure I), respectively. According to the structural model of Richter and Breitling in molten Au and Ag the shortest oblique distance of the square chain I of structure II shows up by the [ri′] Au,Ag· √2-distance. On the other side in solid amorphous Ga the shortest oblique distance of the rhombohedron chain II of structure I appears at the [ri]Ga· √3-distance. In both cases the respective maximum must be very small because of the large variations in distance of the shortest oblique distances.

The paper introduces shear stress quantities, which are the difference of two stress tensors, the actual one and one produced by rotating the axes. This quantities have physical significance. In the vectorial representation in the principal stress space and the principal shear stress space the paper give some interesting relations. The authors observe that Hill′s anisotropic yield criterion can be derived from their shear stress quantities by introducing a measure tensor and gave a physical explanation to Hill′s condition.

The pure rotational spectrum of trans-acrolein in the ground vibrational state has been assigned in the frequency region from 8 GHz to 180 GHz. The measured absorption lines encompass a-type transitions from the q R K , q Q 1, q Q 2 branches and 6-type transitions from the r P 0 , r P 1 , r P 2 , r R 0 brandies for values of J up to 23. The rotational constants have been refined and all quartic and sextic centrifugal distortion constants have been determined using Watson's reduced Hamiltonian. This information has been used to predict line positions of astrophysical interest to warrant the interstellar line search for trans-acrolein.

All the harmonic, the diagonal cubic and quartic stretching and the semidiagonal cubic force constants of HCP have been calculated from Hartree-Fock wavefunctions by the force method of Pulay. The force constants are in good agreement with the experimental ones, except for F RR , F aa , F Rr , F Raa , and F raa the latter two being rather uncertain from experiment. From the harmonic force constants, harmonic frequencies have been calculated by the method of Wilson and Eliashevich. The equilibrium geometry of HCP has been calculated by the force relaxation method of Pulay.

We support the proposed ground state rotational bands in 12 C, 16 O, 28 Si and 40 Ca by calculating the form factors for the electro-excitation within a simple model. The model introduces two parameters for the size and the surface thickness of these nuclei and allows for the prediction of the transition probabilities and form factors within the rotator model. The model unambiguously predicts the sequence of rotational levels 0 + , 3 + , 4 + ... for 16 O and 40 Ca, and 0 + , 2 + , 4 + ... for 12 C and 28 Si in agreement with the experiment. The comparison of the calculated form factors with the experimental data shows excellent agreement in the cases 28 Si and 40 Ca and is less satisfactory in the cases 12 C and 16 O.

The UV absorption spectra of some 1, alkyl, cyclopropyl, methyl ketones are recorded in different solvents. For the 1, methyl, cyclopropyl, methyl ketone (3) a Δ - π* band is observed in organic solvents. The spectra are discussed in terms of a second order perturbation of both Walsh and MO′s of cyclopropane and the carbonyl group. It is found that the hypsodiromic shift of the n-π* band in the cyclopropyl ketones is due to a destabilization of the π* MO. The appearance of a Δ - π* in (3) is due to a rotation of the carbonyl group from the bisected conformation and a stabilization of the π* MO.

The powder pattern of crystalline cubic deuterated acetylene recorded by thermal neutron diffraction technique and the Pa3 crystal structure assigned to the high phase of C 2 H 2 are com-pared. The observations are not in disagreement with the theoretical pattern. Values for the lattice parameters in a narrow temperature range are given.

Acetylene-d 2 , C 2 D 2 , is known to exist in two crystal structures. The neutron powder diffraction data of the orthorhombic phase for temperatures between 4.2 K and 148.7 K have been analyzed and the refined lattice parameters and the calculated unit cell volume tabulated. By expressing the observations as functions of the vibrational energy, values for the Debye characteristic temperature and the static lattice and zero-point quantities are calculated with the method of least squares. Theoretical values for the coefficient of thermal expansion, quantities proportional to the isothermal compressibility, and the calculated density of solid C 2 D 2 are given. The average frequencies associated with the characteristic temperatures for the lattice vibrations along the a-and b-axes are calculated. Finally, an estimate for the latent heat of the cubic-orthorhombic transition is obtained from the Clausius-Clapeyron equation.

The rotational structure of the bending fundamental v 5 of monofluoroacetylene around 366 cm -1 was investigated. The measurements were performed using a Michelson type Fourier spectrometer with a resolution of about 0.05 cm -1 . The values B 0 =0.32373 cm -1 , a 5 - = - 6.00 x 10 -4 cm -1 , q 5 = 6.3 x 10 -4 cm -1 and D = 11.2 x 10 -8 cm -1 were obtained from the analyses of the P-, Q-, and R-branches. In addition, some hot bands accompanying the fundamental were studied.

An analysis of the electron spin resonance spectra of gamma-irradiated crystals of magnesium-hypophosphite, Mg (H 2 PO 2 ) 2 · 6 H 2 O, has shown that the main long-lived paramagnetic species produced by gamma-irradiation are HPO 2 - and PO 3 - ionic radicals. The hyperfine interaction tensor of the phosphorous nucleus has the principal values T || = 1674, T⊥ = 1221 Mc/s in HPO 2 - and T || = 2490, T⊥ = 1847 Mc/s in PO 3 - . In HPO 2 - , interaction of the unpaired electron with the proton gives rise to an almost isotropic hyperfine coupling of 233 Mc/s. These results indicate that the orbitals occupied by the unpaired electron in both HPO 2 - and PO 3 = are sp 3 -hybrid σ-orbitals centered on the phosphorous nuclei.

The photophysical and kinetic constants are completely determined by photostationary and time-dependent fluorescence measurements. Deviations from the usual reaction scheme at higher concen-trations are caused by a quenching process of the excimer by the unexcited monomer. This diabatic process which is not observed with pyrene and naphthalene takes place in spite of the short excimer lifetime. A possible correlation between internal conversion and diabatic reactivity is discussed.

Thermal emf measurements have been carried out on AgI using reversible silver electrodes be-tween 75° and 300 °C. A sharp change in the magnitude of the thermoelectric power (Θ) has been observed at 146 °C corresponding to the β to a phase transition. The results may be represented by the equations β-AgI: θ =- [(0.351 ±0.032) (10 3 /T)+0.203 ± 0.083]mV/K, 70-146 °C, a-AgI: θ =- [(0.052 ± 0.011) (10 3 /T)+0.531 ± 0.031]mV/K, 146-300 °C. From these the heats of transport of the Ag + interstitials and ions respectively in the two phases have been calculated to be (0.351-h/2), h being the heat of formation of a Frenkel defect pair in β-AgI, and 0.052 eV, whereas the activation energies for conduction are 0.38 and 0.051 eV respectively. These results are compared with those of previous authors.

A theory of the optical band shape for A 1g - T 1u transitions is developed based on the method of the characteristic function. It covers the region of weak coupling between the electrons and the phonon modes of a 1g , e g and t 2g symmetries, and takes account of the phonon dispersion. It is bound that the cumulant function of the characteristic function can be described by a two-time phonon correlation function which includes the multi-phonon correlation due to the Jahn-Teller effect. A Dyson equation of the phonon correlation function is solved under specific conditions where the contribution from the e g modes is neglected and the phonons have a Lorentzian dispersion. Analytical expressions are given for intensity, peak shift and broadening of a few lower phonon side bands, and it is found that the one phonon side band of the t 2g mode shifts to higher frequencies than that of the a 1g mode.

Electronic transport properties of undoped, Te- and Sn-doped Bi-Sb-alloys of approximate composition Bi 94 Sb 6 were measured within the temperature range 10-300 K. Besides the electrical conductivity and thermoelectric power the magnetoresistance, the Hall effect and the thermoelectric power in a magnetic field were investigated. Measurements in low magnetic fields yield the mobility tensor for Te-doped samples and in connection with the Shubnikov-de Haas oscillations in higher magnetic fields the effective mass tensor of the electrons. Corresponding investigations on Sn-doped p-conducting samples in this paper give the mobility tensors of light and heavy holes and approximately the effective mass tensor. Here quantum oscillations of the thermoelectric power in a magnetic field were analysed.

Results of measurements of the diffusion coefficient D for the ideal liquid system chlorobenzene+bromobenzene are presented. They cover the whole composition range at 295 K (≈ 22 °C). Within experimental accuracy, D is a linear function of the mole fractions. The product D η (η: viscosity) is a more complicated function of composition.

The energy of the conduction state in liquid argon, krypton, and xenon was measured by means of the photo-effect. The data are used to calculate the scattering lengths. The relation between scattering length and electron mobility is discussed.

The dissociation energy, D 0 0 , of EuO has been redetermined and found to be 4.80 + 0.11 eV. This value is substantially lower than previous data indicated. The results of recent atmospheric release of europium metal are discussed in light of this finding.

Second hyperpolarizability values of benzene are cal-culated using the “finite perturbation theory” and the CNDO/2, MINDO/1 and MINDO/2 methods.

It was found that when exciting the photoluminescence of water solutions of rhodamin B in the anti-Stokes region the concentrational changes of quantum yield decrease with the decreasing frequency of the exciting light.

LaNiO 3 loses oxygen in well-defined equilibrium stages. Electron diffraction studies show the presence of super-structure due to vacancy ordering in an anion-deficient sample.

The temperature variation of the specific volume of two nematic liquid crystals (HBT and OBT) has been observed in both the nematic and isotropic regions. A sudden jump is observed in the vicinity of the nematic-isotropic transition indicating a first order phase transition. Pretransitional effects are found to occur only on the nematic side of the transition. This accords with the Maier-Saupe theory. Some parameters such as S K , A, the adiabatic compressibility, the Rao number, and the van der Waals constant are also determined.

E-type delayed fluorescence of 1,1′-dicoronyl (III) has been established by measurement of luminescence lifetimes and activation energy.