Complex energy spectra in reggeon quantum mechanics with cubic plus generalized quartic interactions

We investigate the energy eigenvalue spectra in reggeon quantum mechanics when the hamiltonian contains (non-hermitian) cubic, symmetric quartic and asymmetric quartic interactions. We describe two new methods for finding eigenvalues numerically. When the asymmetric quartic coupling is zero, the energy eigenvalues cross the vacuum state sequentially as predicted by Bronzan as long as r?0.7. For r?0.7 the energy eigenvalues above the ground state pinch together pairwise above the energy axis, leaving the ground state to oscillate about the vacuum. The addition of an asymmetric quartic term appears to dilute the effects produced by increasing the cubic coupling strength. Quantitative graphs of the functional dependence of the eigenvalues on the parameter are given. An alternative derivation of Bronzan's formula for vanishing eigenvalues is given in the appendix.     

Possibilities of improving the determination of extremely low lead concentrations in marine fish by graphite furnace atomic absorption spectrometry

Summary With the aim to produce reliable analytical data on lead contents in marine fish a multi-stage analytical procedure was developed, in which graphite furnace atomic absorption spectrometry was combined with pre-instrumental chemical sample treatment. The latter consisted of sample decomposition with nitric acid in a closed system under normal pressure, followed by separation and enrichment of lead traces by solvent extraction. For analytical quality assurance purposes the material to be analysed was labelled with practically carrier-free Pb-203 (internal standard) and recovery was controlled by activity measurement. As contamination throughout the analytical procedure represents a main source of systematic error in ultra trace lead analysis, special precautions were taken to hold the size and variability of the analytical blank as small and reproducible as possible.The practically obtainable detection ability of the method was demonstrated in an exemplary study of some specimens of marine fish (cod and plaice) from the North Sea. Results obtained for muscle tissue (range 0.5–4.1 ng g^–1=2.4–20 nmol kg^–1 wet weight) were extremely low and considerably below the most data published up to now in the literature.

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Möglichkeiten zur Verbesserung der Bestimmung extrem niedriger Bleikonzentrationen in Seefischen durch Graphitrohrofen-Atomabsorptionsspektrometrie

Zusammenfassung Mit dem Ziel, zuverlässige analytische Daten über Bleigehalte von Seefischen zu ermitteln, wurde ein mehrstufiges Analysenverfahren entwickelt, in dem Graphitrohrofen-Atomabsorptionsspektrometrie mit vorgeschalteter Probenaufbereitung verbunden wurde. Letztere bestand aus Probenaufschluß mit Salpetersäure in einem geschlossenen System unter Normaldruck, dem sich Abtrennung und Anreicherung der Bleispuren durch Solvent-Extraktion anschlossen. Zum Zwecke der analytischen Qualitätssicherung wurde das Untersuchungsmaterial mit praktisch trägerfreiem Pb-203 markiert (interner Standard) und mittels Aktivitätsmessung die Ausbeute überprüft.Da Kontaminationen während der analytischen Prozedur eine Hauptursache für systematische Fehler bei der extremen Bleispurenanalytik darstellen, wurden besondere Maßnahmen getroffen, um Größe und Schwankungsbreite des Blindwertes so klein und reproduzierbar wie möglich zu halten.Das praktisch erreichbare Nachweisvermögen der Methode wurde beispielhaft an Hand der Untersuchung einiger Fische (Kabeljau und Scholle) aus der Nordsee gezeigt. Die ermittelten Gehalte für Muskelfleisch-Frischsubstanz (Schwankungsbreite 0,5–4,1 ng g^–1=2,4–20 nMol kg^–1) lagen extrem niedrig und erheblich unter den meisten bisher in der Literatur publizierten Daten.

     

X-ray diffraction studies of two azametallatranes. Peculiarities of structures of N,N′,N″-tris(trimethylsilyl)azametallatranes using DFT calculations

Single crystal structures of N(CH₂CH₂NSiMe₃)₃Si-Vinyl (1) and N(CH₂CH₂NSiMe₃)₃Si-n-Butyl (2) were determined by X-ray diffraction studies: both compounds show weak transannular N_ax→M interactions (1, d(N_ax→Si)=2.712(1) Å, 2, d(N_ax→Ge)=2.743(3) Å). General trends for molecular structures of the group 14 elements (Si, Ge, Sn) azametallatranes are discussed with also included DFT calculations data.     

Evidence for heavy leptons from anomalous μe production in e+e− annihilation

Events of the type $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→μ}{}^{\mathrm{\pm }}\text{+e}{}^{\mathrm{?}}\text{+}\text{“nothing”}$ have been observed in the magnetic detector PLUTO at the storage ring DORIS at DESY. The data support the hypothesis of the pair production of heavy leptons, and allow to determine decay parameters. Decay rates into muons and electrons are equal within error, and argue for a new lepton number of the heavy lepton.     

Efficient Syntheses of Novel Fluoro‐Substituted Pentacenes and Azapentacenes: Molecular and Solid‐State Properties

Non‐symmetrical 6,13‐disubstituted pentacenes bearing trifluoromethyl and aryl substituents have been synthesized starting from pentacenequinone. Diazapentacenes with a variety of fluorine substituents were prepared either via a Hartwig–Buchwald aryl amination route or by a S_NAr strategy. As a result of a non‐symmetric substitution pattern containing electron‐donating substituents in combination with electron‐accepting fluorine substituents, the synthesized compounds feature distinct molecular dipoles. All compounds are analyzed regarding their optoelectronic properties in solution with special focus on the frontier orbital energies as well as their molecular packing in the crystal structures. The analyses of isolated molecules are complemented by thin‐film studies to examine their solid‐state properties. A precise comparison between these and the molecular properties gave detailed insights into the exciton binding energies of these compounds, which are explained by means of a simple model considering the molecular packing and polarizabilities.     

Die Kristallstrukturen einer Serie von Verbindungen mit Kationen des Typs [R3PNH2]+, [R3PN(H)SiMe3]+ und [R3PN(SiMe3)2]+

Crystal Structures of a Series of Compounds with Cations of the Type [R₃PNH₂]⁺, [R₃PN(H)SiMe₃]⁺, and [R₃PN(SiMe₃)₂]⁺ The crystal structures of a series of compounds with cations of the type [R₃PNH₂]⁺, [R₃PN(H)SiMe₃]⁺, and [R₃PN(SiMe₃)₂]⁺, in which R represents various organic residues, are determined by means of X‐ray structure analyses at single crystals. The disilylated compounds [Me₃PN(SiMe₃)₂]⁺I^–, [Et₃PN(SiMe₃)₂]⁺I^–, and [Ph₃PN(SiMe₃)₂]⁺I₃^– are prepared from the corresponding silylated phosphaneimines R₃PNSiMe₃ with Me₃SiI. [Me₃PNH₂]Cl (1): Space group P2₁/n, Z = 4, lattice dimensions at –71 °C: a = 686.6(1), b = 938.8(1), c = 1124.3(1) pm; β = 103.31(1)°; R = 0.0239. [Et₃PNH₂]Cl (2): Space group Pbca, Z = 8, lattice dimensions at –50 °C: a = 1272.0(2), b = 1147.2(2), c = 1302.0(3) pm; R = 0.0419. [Et₃PNH₂]I (3): Space group P2₁2₁2₁, Z = 4, lattice dimensions at –50 °C: a = 712.1(1), b = 1233.3(2), c = 1257.1(2) pm; R = 0.0576. [Et₃PNH₂]₂[B₁₀H₁₀] (4): Space group P2₁/n, Z = 4, lattice dimensions at –50 °C: a = 809.3(1), b = 1703.6(1), c = 1800.1(1) pm; β = 96.34(1)°; R = 0.0533. [Ph₃PNH₂]ICl₂ (5): Space group P1, Z = 2, lattice dimensions at –60 °C: a = 825.3(3), b = 1086.4(3), c = 1241.2(4) pm; α = 114.12(2)°, β = 104.50(2)°, γ = 93.21(2)°; R = 0.0644. In the compounds 1–5 the cations are connected with their anions via hydrogen bonds of the NH₂ groups with 1–3 forming zigzag chains. [Me₃PN(H)SiMe₃][O₃S–CF₃] (6): Space group P2₁/c, Z = 8, lattice dimensions at –83 °C: a = 1777.1(1), b = 1173.6(1), c = 1611.4(1) pm; β = 115.389(6)°; R = 0.0332. [Et₃PN(H)SiMe₃]I (7): Space group P2₁/n, Z = 4, lattice dimensions at –70 °C: a = 1360.2(1), b = 874.2(1), c = 1462.1(1) pm; β = 115.19(1)°; R = 0.066. In 6 and 7 the cations form ion pairs with their anions via NH … X hydrogen bonds. [Me₃PN(SiMe₃)₂]I (8): Space group P2₁/c, Z = 8, lattice dimensions at –60 °C: a = 1925.4(9), b = 1269.1(1), c = 1507.3(4); β = 111.79(3)°; R = 0.0581. [Et₃PN(SiMe₃)₂]I (9): Space group Pbcn, Z = 8, lattice dimensions at –50 °C: a = 2554.0(2), b = 1322.3(1), c = 1165.3(2) pm; R = 0.037. [Ph₃PN(SiMe₃)₂]I₃ (10): Space group P2₁, Z = 2, lattice dimensions at –50 °C: a = 947.7(1), b = 1047.6(1), c = 1601.6(4) pm; β = 105.96(1)°; R = 0.0334. 8 to 10 are built up from separated ions.     

N‐Chlortriphenylphosphanimin und seine Anwendung als Edukt zur Synthese asymmetrischer PNP‐Kationen. Kristallstrukturen von Ph3PNCl und [Ph3PNPEt3]Cl

N‐chlorotriphenylphosphaneimine and its Application as an Educt for the Synthesis of Asymmetric PNP Cations. Crystal Structures of Ph₃PNCl and [Ph₃PNPEt₃]Cl Ph₃PNCl ( 1 ) originates in good yield as pale yellow crystals from the reaction of Ph₃PNSiMe₃ with phenyliodine dichloride. According to the crystal structure analysis 1 has a monomeric molecular structure without perceptible intermolecular contacts with distances P–N of 161.0 pm, N–Cl of 175.9 pm, and with a PNCl bond angle of 110.31°. 1 reacts with phosphines PR₃ forming asymmetric PNP salts [Ph₃PNPR₃]Cl. This was tested by reactions with PEt₃ and bis‐diphenyl phosphano ferrocene (DPPF). The crystal structure analysis of [Ph₃PNPEt₃]Cl ( 2 ) shows an almost symmetric PNP bridge with distances PN of 158.6 and 157.0 pm, and with a bond angle of 145.9°.     

Triethylphosphanimin-Komplexe der Acetate von Kupfer(II) und Zink. Kristallstrukturen von [Zn(O2C–CH3)2(HNPEt3)], [Cu5(O2C–CH3)10(HNPEt3)2] und [Cu(O2C–CH3)2(HNPEt3)2]

Triethylphosphanimine Complexes of the Acetates of Copper(II) and Zinc. Crystal Structures of [Zn(O₂C–CH₃)₂(HNPEt₃)], [Cu₅(O₂C–CH₃)₁₀(HNPEt₃)₂], and [Cu(O₂C–CH₃)₂(HNPEt₃)₂] The title compounds originate from the anhydrous acetates of zinc and copper(II) with trimethylsilyl-triethylphosphanimine, Me₃SiNPEt₃, in the presence of water in dichloromethane. They form colourless ( 1 ), bluish-green ( 2 ), and blue ( 3 ), respectively, single crystals, which were characterized by IR spectroscopy and by crystal structure analyses. [Zn(O₂C–CH₃)₂(HNPEt₃)] ( 1 ): Space group P 4 2₁c, Z = 8, lattice dimensions at –83 °C: a = b = 1709.6(2), c = 982.4(1) pm, R = 0.0551. 1 has a polymeric chain structure in which the zinc atoms are μ₂-bridged via the oxygen atoms of one of the two acetato groups, while the second acetato group and the phosphanimine are bonded terminally. [Cu₅(O₂C–CH₃)₁₀(HNPEt₃)₂]( 2 · 4 CH₂Cl₂): Space group P2₁/c, Z = 8, lattice dimensions at –80 °C: a = 1761.18(13), b = 4074.5(2), c = 1733.34(15) pm, β = 91.383(10)°, R = 0.0413. 2 consists of the two structural units [Cu₂(O₂C–CH₃)₄] and [Cu₃(O₂C–CH₃)₆(HNPEt₃)₂], which are connected via two of the acetato groups of the Cu₃-unit along the crystallographic a-axis to form three crystallographically independent polymeric strands. [Cu(O₂C–CH₃)₂(HNPEt₃)₂] ( 3 ): Space group P2₁/n, Z = 2, lattice dimensions at 20 °C: a = 695.49(8), b = 1217.85(10), c = 1380.05(7) pm, β = 96.451(7)°, R = 0.0291. 3 forms monomeric, centrosymmetric molecules with a square planar environment at the Cu atoms.