On the geometric structure underlying the eikonal equation

Given the eikonal equation _i=1 ³ (/x ⁱ ) ² =n ², we investigate the geometric structure that underlies the law of propagation of the wavefronts (x ¹,x ²,x ³) —ct=0. It turns out that Huygens' principle for the propagation of wavefronts is given in terms of a contact structure. Wavefronts are carried into wavefronts by contact transformations. As regards the wave-particle duality principle that arises in quantum mechanics, there is a natural geometric structure, a symplectic manifold (M ²ⁿ , ), which unifies Fermat's principle and the eikonal equation (Huygens' principle).On leave of absence from Institut für Angewandte Mathematik, Fachbereich Mathematik der Universität Mainz, Mainz, German Federal Republic.     

Direct calculation of ionization potentials of closed-shell atoms and molecules

Vertical ionization potentials, electron affinities and information about quasi-particles can be obtained by using the technique of the single-particle propagator. The expansion of the self-energy part up to third order perturbation theory can be evaluated numerically, but does not lead, in most cases, to satisfying results. A theoretical and numerical analysis of the diagrammatic expansion of the self-energy part requires the introduction of a renormalized interaction and renormalized hole and particle lines.     

The electronic structure of molecules by a many-body approach

The vertical valence ionization potentials of cyclopropane, ethylene oxide and ethylene imine are calculated by a many-body Green's function method. For C₃H₆ the ordering of the ionization potentials is 2e(), 1e(), 2a₁(), 1a₂(), 1e(). The assignment of the 2a₁ and the 1a₂ ionization potentials which has been controversial is thus clarified. The ordering is in agreement with the result obtained via Koopmans' theorem. For ethylene oxide and ethylene imine Koopmans' theorem fails in predicting the correct order of ionic states. For C₂H₄O the ordering of the ionization potentials is 2b ₁(), 4a ₁, 1a ₂(), 2b ₂,3a ₁, 1b ₁(), 1b ₂, 2a ₁ and for C₂H₅N 6a, 5a, 3a, 2a, 4a, 3a, 1a, 2a. The agreement of the computed ionization potentials with the experimental values is very satisfactory.     

AlSiP3, a compound with a novel wurtzite-pyrite intergrowth structure

AlSiP₃ is formed by heating aluminum and silicon powder with red phosphorus and adding small amounts of iodine or AlCl₃. Small, black crystals with metallic lustre grow at 1200°K. The compound crystallizes in the orthorhombic space group Pmnb (No. 62) with a = 987.2 pm, b = 586.1 pm, c = 608.8 pm and four formula units. In the structure isolated P atoms as well as P₂ pairs are present (PP = 218.2 pm). Silicon is tetrahedrally bonded (SiP = 224.2 ? 228.2 pm) whereas aluminum has octahedral coordination (AlP = 244.2 – 260.8 pm). The structure can be described as an intergrowth structure of wurtzite and pyrite type.     

Cathodoluminescence Depth Profiling in SiO2:Ge Layers

 For investigation of the luminescent center profile cathodoluminescence measurements are used under variation of the primary electron energy E ₀ = 2…30 keV. Applying a constant incident power regime (E ₀·I ₀ = const), the depth profiles of luminescent centers are deduced from the range of the electron energy transfer profiles dE/dx. Thermally grown SiO₂ layers of thickness d = 500 nm have been implanted by Ge⁺-ions of energy 350 keV and doses (0.5–5)10¹⁶ ions/cm². Thus Ge profiles with a concentration maximum of (0.4 – 4) at% at the depth of d_m≅240 nm are expected. Afterwards the layers have been partially annealed up to T _a = 1100 °C for one hour in dry nitrogen. After thermal annealing, not only the typical violet luminescence (λ = 400 nm) of the Ge centers is strongly increased but also the luminescent center profiles are shifted from about 250 nm to 170 nm depth towards the surface. This process should be described by Ge diffusion processes, precipitation and finally Ge nanocluster formation. Additionally, a Ge surface layer is piled-up extending to a depth of roughly 25 nm.     

In-situ HEED structure analysis of AlNx films grown by the simultaneous use of a radical beam source and ICB technique

A reactive ionized cluster beam technique (RICB) which was composed of a conventional ICB source and a radical beam source has been used to deposit stable and metastable polycrystalline AlN_x (0≤x≤1) films. Using in-situ high energy electron diffraction (HEED) at grazing incidence geometry, crystallographic properties such as structure, preferred orientation and interplanar dspacing values were determined and the relation to deposition parameters investigated. It could be shown that the simultaneous use of the ICB technique and a radical beam source to separately control the kinetic energy of the Al ions and the dissociation rate of molecular nitrogen, allows AlN films to be deposited with variable composition and crystal structures. In-situ HEED used in the transmission mode is an effective tool to investigate the crystallography of growing compound films such as AlN_x.     

Piperaceae alkaloids: Part IV. Structure and Synthesis of Cyclostachine A,Cyclostachine B and Cyclopiperstachine

Three new alkaloids designated as cyclostachine A (2), cyclostachine B (7) and cyclopiperstachine (10) have been isolated from Piper trichostachyon C. DC. Their structures have been derived on the basis of spectral and degradative studies and confirmed by synthesis. The ¹H- and ¹³C-NMR. spectra of these compounds are discussed.     

Autocollimation spectroscopy for fast hydrogenic ions

We propose a new experimental method (Autocollimation Spectroscopy), which provides a strong suppression of systematic error contributions in the laser resonance spectroscopy of broad resonances. Using a bidirectional laser beam with a fixed wavelength in connection with high current pulsed ion beams an accuracy ofΔE _Exp/Γ≈5·10^?5 (Γ: resonance width) for the resonance energy seems to be achievable. Applying this technique to 2S-Lamb shift (LS) measurements on medium heavy ions would yield a precision ofΔE _Exp/E _LS≈1·10^?5, i.e. an improvement by a factor up to 100 as compared to present experiments.     

Pseudopotential calculations on Rb+2, Cs+2, RbH+, CsH+ and the mixed alkali dimer ions

Semi-empirical pseudopotentials are used in calculating the ground-state potentials curves for single valence-electron molecular ions. Very accurate results are obtained and a number of predictions given. The ionization energies of the neutral dimers are evaluated. A spectroscopic rule enables us to estimate the A ¹Σ⁺ state of KRb and RbCs.     

Infrared spectra of gas-phase V(+)-(benzene) and V(+)-(benzene)(2) complexes

The organometallic ions V+-(benzene) and V+-(benzene)2 are produced by laser vaporization in a pulsed nozzle source. They are trapped and mass selected in an ion-trap/time-of-flight mass spectrometer, and their infrared spectra are measured with resonance-enhanced multiphoton photodissociation (IR-REMPD) spectroscopy with a tunable free-electron laser. Vibrational bands in the 600-1800 cm-1 region are characteristic of the benzene molecular moiety perturbed by the metal cation bonding. Experimental data are compared to the IR spectra derived from density functional calculations. Vibrational patterns in V+-(C6H6) indicate that the metal is bound in an eta6 pi-bonding configuration, while V+-(C6H6)2 is a sandwich. Trapped-ion IR-REMPD is a general method to access the vibrational spectroscopy of organometallic ions and their clusters.