Volume 30, Issue 11

The NTD-method is a procedure to compute differences of eigenvalues in quantum mechanical problems: ω αβ =λ α -λ β . It is an instruction to transform and truncate an infinite linear system of eigenvalue equations ω τ k = A k m τ m which is derived with the aid of fundamental field equations or corresponding Hamilton-operators, as e.g. with Heisenberg's nonlinear spinor equation. In this paper we want to test the NTD-method for a many-body-model in solid state physics. We elaborate on the physical and mathematical aspects by choosing a suitable transformation τ → φ = C τ to get a new linear 1 system ω φ k = B k k+2iφ k+2i which permits a truncation to evaluate approximation of states. The efficiency of this method is demonstrated by treating a two-body-system in presence of polarisation quanta, known as exciton model

Mittelstaedt has defined the class of quasi-implicative lattices and shown that an ortholattice (orthocomplemented lattice) is quasi-implicative exactly if it is orthomodular (quasi-modular). He has also shown that the quasi-implication operation is uniquely determined by the quasi-implicative conditions. One of Mittelstaedt's conditions, however, seems to lack immediate intuitive motivation. Consequently, this paper seeks to provide a number of reformulations of the quasi-implicative conditions which are more intuitively plausible. Three sets of conditions are examined, and it is shown that each set of conditions is both necessary and sufficient to ensure that an ortholattice is orthomodular, and each set of conditions uniquely specifies the implication operation to be Mittelstaedt's quasi-implication. Various properties of the quasi-implication are then investigated. In particular, it is shown that the quasi-implication fails to satisfy a number of laws associated with the classical material conditional. Various weakenings of these laws, satisfied by the quasi-implication, are also discussed

Functional quantum theory is defined by an isomorphism of the state space H of a conventional quantum theory into an appropriate functional state space D It is a constructive approach to quantum theory in those cases where the state spaces H of physical eigenstates cannot be calculated explicitly like in nonlinear spinor field quantum theory. For the foundation of functional quantum theory appropriate functional state spaces have to be constructed which have to be representation spaces of the corresponding invariance groups. In this paper, this problem is treated for the spinor field. Using anticommuting source operator, it is shown that the construction problem of these spaces is tightly connected with the construction of appropriate relativistic function spaces. This is discussed in detail and explicit representations of the function spaces are given. Imposing no artificial restrictions it follows that the resulting functional spaces are indefinite. Physically the indefiniteness results from the inclusion of tachyon states. It is reasonable to assume a tight connection of these tachyon states with the ghost states introduced by Heisenberg for the regularization of the nonrenormalizable spinor theory

We present approximate representations of the liquid structure function S(k) for Fermi systems in the framework of the renormalized and unrenormalized Jastrow theory. Using short range correlations we study the behavior of S(k) in the range of low momenta and compare our numerical results with the experimental data of the liquid structure function of liquid 3 He. We conclude that the usual Jastrow ansatz Ψ = Π i<i f(rij) Φ for the trial wave function of a dense Fermi system, together with an application of the cluster expansion method developed by Clark and Westhaus, does not sufficiently describe these systems. Improvements are discussed

The splitting of the energy levels of crystal electrons in homogeneous magnetic fields of moderate strength is described in terms of the matrix elements of the LCAO method. The matrix elements are regarded as adjustable parameters connected with the energy structure of the crystal electron without magnetic field. The translational symmetry of the crystal in a magnetic field is exactly taken into account, and the matrix elements contain the symmetry of the point group of the material. The resulting eigenvalue equation is a system of linear difference equations. In analogy to the treatment of a similar one-dimensional difference equation for the differential equation of Mathieu type the eigenvalues result from an investigation of a vector recursion formula. In connection with this method the limiting cases magnetic field and crystal potential approaching zero are discussed in short

The density of states of polaritons in cubic and uniaxial crystals is calculated. It is shown that closed mathematical expressions for the density of states of polaritons may be given. For uniaxial crystals the density of states of ordinary and extraordinary polaritons must be distinguished. With respect to extraordinary polaritons four different cases are possible

According to earlier measurements with the two-aperture method, the brightness of electron guns has sometimes a maximum value near the cut-off potential. This result has been confirmed by means of the lens method. Experiments with well-oriented monocrystalline spherical cathodes lead to the result that a brightness maximum only occurs when the cathode apex has a lower emission density than its environment. In this case, the axial brightness is increased by electrons emitted from the off-axial cathode area which feed the space-charge cloud in front of the cathode. Under space-charge conditions, the cathode adjustment is not very critical, because the axial brightness differs less than the emission densities of different crystal surfaces

Dielectric loss in the 0.3 to 140 GHz range, and to some extent dispersion, of seven selected aliphatic chain molecules, substituted by Cl, Br, and I at both ends have been measured in dilute solutions of n-heptane, benzene, and decalin. Chain length varied from 3 to 10 carbon atoms. For 1,10-dichlorodecane in decalin and mesitylene the temperature was also varied from -30 to + 60 °C. The unsymmetric absorption curves have been resolved in a weak FIR region and a predominant region with a symmetric relaxation time distribution (log. scale) according to Fröhlich. The width of this distribution is shown to be independent of chain length and halogen. Its mean relaxation time increases linearly with chain length, while the dipole moment goes through a minimum for the butyl compounds. Monoderivatives, three chlorides and one bromide, have also been measured in the same solvents at 20 °C. Their absorption curves can be fitted by a predominant absorption region with the same width as for the corresponding di-derivatives and, besides the FIR wing, by another low frequency Debye-region, the weight of which decreases with increasing chain length. The molecular motions related to these three regions are discussed, and the corresponding magnitudes of dipole moments in mono- and di-derivatives are compared for long and short chains

The radiation emitted from a wall stabilized helium-plasma (n e ≈ 3 • 10 22 m -3 , T ≈ 38 000 K, duration of constant discharge current 0.4 ms) was investigated in the wavelength range 300 nm to 650 nm. From the emission coefficients of the continuum radiation Gaunt factors for the state with the principal quantum number 3 and the state 2 3 P were determined. Gaunt factors for the terms 2 1 S, 2 1 P, 2 3 S and 2 3 P were calculated from the transition probalilities of highly excited states. Agreement to within the accuracy of the measurement was found between the experimental results and the Gaunt factors evaluated from the photoionisation cross-sections calculated by Goldberg. The Gaunt factors for the states 2 1 P and 2 3 S according to Anderson and Griem are in good agreement with our results; for the terms 2 3 P and 2 1 S a discrepancy exists. With the Gaunt factors reported here electron densities in a helium-plasma can be determined with a relative uncertainty of 10%. The ξ-factor calculated by Kriener and Schlüter could be confirmed, if Bremsstrahlung of neutral atoms is neglected

A model for the quantum yield of the coloration caused by UV-light in spiropyran layers is described. This model allows to calculate the sensitivity of layers having different compositions. The mechanism concerning the stability of the coloration is essentially clarified. Calculations of the stability for layers of different compositions are possible by a model describing the mechanism approximately

In a system with a non spherically symmetric pressure tensor, the chemical potential of at least one substance in the system has to be a tensor of the same character as the pressure. The necessary generalization of Gibbs' fundamental equations of thermodynamics is presented. Being already of consequence for equilibrium, this extension is more important for non-equilibrium thermodynamics, in particular for the proper thermodynamic formulation of general relaxation phenomena. Reasons are given why the distinction between dynamic and thermodynamic pressure, originating from the incomplete formulation of customary thermodynamics, is erroneous. Finally a tensorial temperature is introduced which can exist under extreme non-equilibrium conditions, e.g. shock waves

The microwave spectra of the following isotopic species of Methyl-chloro-silane: CH 3 SiH 2 Cl, CH 3 SiD 2 and CD 3 SiD 2 Cl have been measured and the rotational spectroscopic constants (rotational constants, centrifugal distortion constants and nuclear quadrupole coupling constants) have been determined

The enthalpies and entropies of fusion and of solid state transitions in Li formate and acetate; Li, Na, K, Rb, Cs propionates; Li, Rb, Cs n.butyrates were determined by differential scanning calorimetry. Supplementary information was provided through conductance measurements on solids. The collected data, together with those from previous papers, allowed to give a picture of the thermal behaviour of the alkali C 1 -n. C 4 alkanoates. Heat capacity data on solid and molten Na formate, acetate and propionate were also determined

The infrared-active lattice vibrations of the orthorombic marcasite (FeS 2 ) have been studied by measuring the reflectivity of different crystal faces at near-normal incidence. A group-theoretical analysis predicts seven infrared-active modes (k = 0). Cartesian symmetry coordinates as well as vibrational modes of the lattice vibrations are constructed

The fluorescence spectra and the decay time of emission bands of pure and anthracene doped 2,3 Dimethylnaphthalin single crystals excited by short light pulses were examined for temperatures of 4 to 300 K. On raising the temperature from 40 to 120 K the decay time and the relative quantum yield of 2,3 DN decreases, the emission is shifted by about 150 cm -1 to higher energies and simultanously the energy transfer to the anthracene impurity molecule increases. A model calculation is presented which allows a theoretical interpretation of the experimental results

The mass spectrum and the ion molecule reactions of phosphirane and of mixtures of phosphirane with NH 3 , NH 2 D, NHD 2 and ND 3 have been studied by ion cyclotron resonance spectrometry. Almost all important product ions are formed by PH-group transfer reactions, where ethene is generated as the neutral particle. Only two of the more abundant ions, the protonated molecule, H 2 P(CH 2 ) 2 + and the ion m/e=63, P 2 H + , are formed via other reaction pathways. Secondary, tertiary and quarternary product ions with the general formula R(PH) n + (R: phosphirane fragment, n-1, 2, 3) have been detected. The molecular ion is proved to have a cyclic structure. Two possible structures of the product ions with two and three phosphorus atoms are discussed: a structure with an open phosphorus chain, leaving the phosphirane ring intact and a ring extended structure, produced by a ring extension reaction of the PH-group. Several rate constants of the ion molecule reactions of the phosphirane molecular ion are given

The results of absorption measurements on aqueous electrolyte solutions (KF, KI and CsF) with high dielectric loss at five frequencies (8.25; 10.015; 11.88; 27.2 and 38.5 GHz) are reported. With the help of statistical data analysis methods the influence of the higher order modes on the accuracy of the data has been investigated. The use of measuring cells whose construction is based upon the theory of time independent, sourcefree ports, in connection with a highly precise amplitude receiver, allows the analysis of attenuation produced by these solutions. Interpretation of the data obtained using transmission techniques shows that the accuracy of such attenuation measurements is limited to 0.1% by higher order modes

Force constants have been calculated for Se 8 (α-monoclinic selenium) after reassigning the literature values of the fundamental frequencies and using a modified Urey-Bradley force field with six force constants. Very good agreement between observed and calculated frequencies was obtained and valence force constants were calculated. A non-linear relationship holds for SeSe stretching force constants and bond distances. Using the Se 8 force constants the fundamental frequencies of the square-planar Se 4 2+ were calculated and compared with the observed values

X-ray photoelectron spectra (XPS) are obtained for Mg in MgO using high quality (purity 99.999%) Mg films prepared and oxidized under pressures of 10 -6 ~ 10 -8 torr and measured on an ESCA-36 spectrometer at a pressure of 10 -8 torr. AlKα line source was used for excitation, and the minimum of Au valence band at 5.0 eV was chosen for calibration. With increased oxidation the valence band shifts about 1.0 eV towards the Fermi level, but with extreme contamination it disappears completely. Accurate measurements of binding energies have been made of Mg in pure Mg, and Mg in MgO. The average shift resulting from oxidation is 1.1 eV for Mg(2s) and 1.5 eV for Mg(2p) core levels. It is also observed that the contamination effect due to oxygen decreases with increasing film thickness. The present results are compared with the previous results, and a new interpretation is offered by postulating the formation of two kinds of oxides, stoichiometric and chemisorbed layers in Mg on oxidation

The contact contribution to the nuclear spin-spin coupling constant in HD is evaluated variationally by using the nonsingular contact spatial part fm(r,a) =exp(-r/a)/2 a 3 , a=O (10 -6 ) a.u. J HD is calculated to be 39 Hz and is independent of the sharp short-range part of the trial firstorder wavefunction to the order O (a)

A comparison is given between hydrogen-like and Hartree-Fock calculated and experimental absorption data for Silicon. Some values omitted in an earlier paper are added

The Knight shifts of the potassium isotopes 39 K and 41 K were determined with high accuracy: K (39) = 0.2 7 4 35(10)% and K (41) =0.274 93(12)%. The relative isotope effect ΔK/K = -0.210 (20)% is in agreement with the hyperfine structure anomaly 39 Δ 41

The conductivity of aqueous and non-aqueous liquid electrolyte solutions was determined in a low frequency region where no dispersion due to dielectric relaxation of the solvent-solute system can be found. The values of the equivalent conductance of concentrated alkali chloride and nitrate solutions were obtained by measurements in a special cell with high cell constant

An ab initio procedure is described with a basis set of localized orbitals of the fragments. The method was tested on three molecular systems. The results are in agreement with the results of LCAO calculations

A model of liquid germanium is proposed based on two near neighbour distances. The observed interference function at 1047 °C is reproduced, within experimental error, by the superposition of only two different partial interference functions which are approximated by hard sphere interference functions of packing density 0.41 and diameters 2.07 and 2.70 Å