Volume 35, Issue 9

The BCS-formula for the energy gap ΔE is extended to include the magnetic exchange interaction of electrons with holes. With the improved expression for ΔE the transition temperatures of A15-structures are computed and found to be in a satisfactory agreement with the experimental values.

We present a refined calculation method for the phonon part (Franck-Condon Overlaps) of the transition probabilities of electron-phonon radiative and non-radiative transitions in crystals. The evaluation of the thermal averaged Franck-Condon integrals is a purely algebraic method and the transition probabilities we use are derived from first principles and completely atomistic. For the electronic transitions we take into account the frequency shift of the lattice and the change of the phonon normal coordinates. Explicit formulae of the phonon parts are derived and it is shown that the common transition probabilities used in literature are special cases of our functional calculation technique.

Viscoelasticity as it becomes apparent through the oscillatory motion in flow relaxation experiments is studied theoretically for liquids and liquid solutions containing nonspherieal particles. The coupling between the viscous flow and the molecular alignment which underlies the flow birefringence gives rise to a viscoelastic behavior. The relevant time scale is determined by the orientational relaxation time rather than the (often much shorter) Maxwell relaxation time. The possible relevance of the present theory for the viscoelastic behavior of some dilute aqueous detergent solutions is discussed.

Three improved versions of the Fielek Model are developed and discussed. The first model uses a modified Bhatia scheme for the volume interaction in place of the Krebs scheme. The second and third model assumes the core-core couplings to be central pairwise effective upto first neighbours only. The second model describes the d-shell-d-shell interaction on the same lines as those adopted for core-core interactions, while the third model assumes these interactions to be of the many body type. Suitable equilibrium conditions for the second and the third model are developed. These improved versions are employed to derive dispersion relations in tantalum. Comparison of these relations with-each other and also with the experimental findings leads to some important conclusions regarding the nature and range of the interactions coupling the various constituents of a bcc transition metal like tantalum.

The proton spin T 1 relaxation dispersion in the smectic A and C phase of TBBA, and for comparison also in the nematic phase, have been studied using time dependent fast field-cycling techniques in the Larmor frequency range from ν p = 100 Hz to 44 MHz. Our measurements considerably extend recent ones by Blinc et al., performed with other NMR methods for frequencies ≧ 140 kHz. The new experimental data are consistent with the reported ones for Sm C but not for Sm A, the difference being that the essential T 1 dispersion observed with our technique occurs at much lower frequencies, namely below about 100 kHz. As a consequence, the relaxation dispersion for both smectic phases looks very similar. It can be described quantitatively in terms of relaxation by "nematic-like" order fluctuations, self-diffusion, and by a third molecular mechanism with (for simplicity) Debve-like power spectrum, which is possibly a second type of order fluctuation or a molecular rotation about the short axis. The analysis reveals surprisingly far going parallels between the spin relaxation of simple smectics and that of high-temperature nematics like PAA.

By means of X-ray scattering and ultrasonic experiments, the structure of different melts of the Cd-Ga system was investigated. The structure factors S (q) obtained for the pure elements agree well with those reported by other authors. The concentration dependence of the structure factors shows no special features. From the structure factors, the total pair-distribution functions were calculated by a Fourier transformation. The nearest-neighbour distances, obtained from the total pair-distribution functions, amount to 3.04 Å for pure Cd and 2.83 Å for pure Ga and are nearly constant for all alloys. The concentration dependence of the experimental nearest-neigh-bour distances and coordination numbers was determined and is compared with statistical distribution and macroscopic segregation models. These comparisons tend to indicate a preference for like-atom neighbours. From the long-wavelength limit S(0) of the structure factors of Cd and Ga, the isothermal compressibilities were calculated. These show a satisfactory agreement with those calculated from adiabatic sound velocity data. The anomalous ultrasonic absorption of a single melt with nearly critical concentration indicates the existence of concentration fluctuations. This result is in agreement with those obtained by X-ray smallangle scattering experiments which are described in Part 2 of this work [1].

X-ray small-angle scattering experiments were performed on nine melts of the Cd-Ga system at different temperatures up to 440°C. Evaluation of the data follows the Ornstein-Zernike theory of critical scattering, thus yielding correlation lengths ξ of concentration fluctuations and the long-wavelength limit Sec (0) of the Bhatia-Thornton structure factor. Studies of the concentration and temperature dependence of ξ and S CC (0) indicate that the critical point occurs at c c = 50.0 ± 1-0 at % Ga and T c - 295.2 ± 0-1° C. For a melt with the critical concentration, S CC (0) increases up to 3500 times the ideal S 1d CC (0)= C A C B -This indicates a strong segregation tendency. In the vicinity of the critical point of the Cd-Ga system, experimental correlation lengths ξ > 100 A were obtained. The critical-point exponents ν and γ were determined. It follows that the behaviour of a critical Cd-Ga melt satisfies the prediction of the classical mean-field theory for higher temperatures, whereas, within experimental accuracy, the lattice-gas predictions are satisfied upon approaching the critical temperature.

Phase, pulse and steady-state measurements of ethanolic solutions of 4-methylumbelliferone with various water and hydrochloric acid contents were performed. A kinetic model is proposed and some parameters are determined.

The Na + tracer diffusion coefficient and the 27 Al NMR spin lattice relaxation time in Na β-alumina display an anomalous temperature dependence near 470 K. These phenomena are related to absorption of water which takes place when the temperature is decreased below 470 K. Water absorption processes in pure and partially substituted β-aluminas are studied by thermogravimetric analysis. Their effects upon conductivity are qualitatively discussed.

Molecular chemiluminescence spectra from selected alkali-halogen reactions are presented using a beam-gas arrangement operating with pressures between 10 -1 mtorr (single collision conditions) up to 10 mtorr in the reaction zone. Spectra are presented for the chemiluminescent reactions M 2 + X 2 ->MX* + MX, where M 2 = K 2 , Na 2 and X 2 = Cl 2 , Br 2 , I 2 . The MX* emitter is identified by comparison with previous absorption and emission studies of these molecules. The sodium reaction with I 2 as well as all lithium reactions with different halogens (Cl 2 , Br 2 , I 2 ) do not yield appreciable molecular emission. The differences in molecular chemiluminescence intensities among this type of reactions can be understood in terms of the Landau-Zener formalism for an electron jump and turn out to be consistent with the results from measurements on absorption, emission and dissociation.

The analysis of X-ray reflections allows for the determination of the grain dimension in the direction of the bisector of the incident and scattered radiation. It is shown that correct results will be obtained only as long as the grain dimensions perpendicular to this direction are sufficiently large. The possible errors are estimated. The conditions for the determination of the shape anisotropy are discussed.

Starting with a linear partial differential operator for a certain system of transition amplitudes associated to a state |a> with baryon number ρ(a) we derive an equation in the ρ(a)-sector of the Functional space which provides the state |a> with an effective potential caused by the polarization cloud. With regard to the needs of n-body scattering we then undertake a cluster decomposition of the effective potential. In particular, we derive the relativistic analoga of Lippmann-Schwinger-and Faddeev equations.

Low index structure potentials of silicon were determined by convergent beam electron diffraction (Kossel-Möllenstedt technique) from very small crystal areas of about 100 Å in diameter. The values of 111, 222, 220, 113 and 004, determined to an accuracy of ±0.03 volts, are in excellent agreement with the accurate X-ray results of Aldred and Hart (see [6], p. 239). Heavy arsenic or phosphorous doping was found to cause a shift of 0.15 volts in the 111 structure potential. Absorption potentials were also determined and found to be 1/3 of the theoretical values published by Radi [20].

Recent results concerning the structure of microparacrystals established in different melts are reported. In spite of structural differences among the investigated samples the reduced density is always the same. This approach is possibly a first step towards a correlation between the hard sphere concept of statistical mechanics and our refined structural analysis.

The binding energy shifts of the Is levels of nitrogen atoms in 15 different bonding situations are calculated by the self-consistent charge molecular orbital (SCC-MO) method employing an electrostatic potential model in the point charge approximation. The standard deviation of the obtained correlation is ~ 0.5 eV, which is substantially better than the earlier CNDO/2 GPM and RPM results. The scatter of the correlated values is diminished to roughly 1/3 of the previous CNDO/2 results. The merits and shortcommings of the electrostatic potential model are briefly discussed. It is concluded that the present approach provides a useful tool for studying ESCA shifts in large molecules of biochemical interest.

A closer look at the off-diagonal elements of the density matrix of a thermal gas phase molecular ensemble reveals, that they lead to a contribution to thermal radiation which increases in power proportional to the number of particles. A quantitative comparison of this contribution to the one originating from spontaneous emission is given.

Elementary Derivation of the Dirac Equation. IV This paper attempts to make evident the basic ideas behind the alternative electrodynamic model of the hy-drogen atom.