Exceptional points of a Hamiltonian and phase transitions in finite systems

For a model Hamiltonian which describesN interacting Fermions and which is typical for systems that undergo phase transitions it is shown that for finiteN the transitional point is associated with exceptional points of the Hamiltonian. In the limit of largeN these singularities move down to the real axis. The nature of the limit turns out to be quite different depending on whether it is taken for interaction strengths smaller or larger than the critical value.     

Selfconsistent calculation of the 11- and 33-amplitude in the low-energy π-N-scattering

A self-consistent calculation of the masses of the nucleon and the 33-resonance, theπN-coupling constant and the resonance width is made. By using a simplified version of theN/D-method the consistency equations are reduced to algebraic equations. Therefore selfconsistency can be obtained at once for both partial waves. In order to suppress the high energy contributions a second subtraction at threshold is made. The thereby introduced subtraction constants are connected with the 11- and 33-scattering lengths which are known from experiment.     

Two channelN/D calculation of the p11 partial wave of πN scattering at low energies

Thep ₁₁-phase shift of πN scattering is calculated by a two-channel matrixN/D method using the reaction σN→σN as second channel. The calculated amplitude has the two main features of the p₁₁ partial wave at low energies: the nucleon pole and the zero of the phase near the inelastic threshold.     

Triaxial octupole deformations and shell structure

Manifestations of pronounced shell effects are discovered when non-axial octupole deformations are added to a harmonic oscillator model. The degeneracies of the quantum spectra are in good agreement with the corresponding main periodic orbits and winding number ratios which are found by classical analysis. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 525–530 (25 April 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Determination of the isomerization rate constant HOCH2CH2CH2CH(OO·)CH3 →HOC·HCH2CH2CH(OOH)CH3. Importance of intramolecular hydroperoxy isomerization in tropospheric chemistry

The rate constant of the title reaction is determined during thermal decomposition of di-n-pentyl peroxide C₅H₁₁O( )OC₅H₁₁ in oxygen over the temperature range 463–523 K. The pyrolysis of di-n-pentyl peroxide in O₂/N₂ mixtures is studied at atmospheric pressure in passivated quartz vessels. The reaction products are sampled through a micro-probe, collected on a liquid-nitrogen trap and solubilized in liquid acetonitrile. Analysis of the main compound, peroxide C₅H₁₀O₃, was carried out by GC/MS, GC/MS/MS [electron impact EI and NH₃ chemical ionization CI conditions]. After micro-preparative GC separation of this peroxide, the structure of two cyclic isomers (3S*,6S*)3α-hydroxy-6-methyl-1,2-dioxane and (3R*,6S*)3α-hydroxy-6-methyl-1,2-dioxane was determined from ¹H NMR spectra. The hydroperoxy-pentanal OHC( )(CH₂)₂( )CH(OOH)( )CH₃ is formed in the gas phase and is in equilibrium with these two cyclic epimers, which are predominant in the liquid phase at room temperature. This peroxide is produced by successive reactions of the n-pentoxy radical: a first one generates the CH₃C·H(CH₂)₃OH radical which reacts with O₂ to form CH₃CH(OO·)(CH₂)₃OH; this hydroxyperoxy radical isomerizes and forms the hydroperoxy HOC·H(CH₂)₂CH(OOH)CH₃ radical. This last species leads to the pentanal-hydroperoxide (also called oxo-hydroperoxide, or carbonyl-hydroperoxide, or hydroperoxypentanal), by the reaction HOC·H(CH₂)₂CH(OOH)CH₃+O₂→O()CH(CH₂)₂CH(OOH)CH₃+HO₂. The isomerization rate constant HOCH₂CH₂CH₂CH(OO·)CH₃→HOC·HCH₂CH₂CH(OOH)CH₃ (k₃) has been determined by comparison to the competing well-known reaction RO₂+NO→RO+NO₂ (k₇). By adding small amounts of NO (0–1.6×10¹⁵ molecules cm⁻³) to the di-n-pentyl peroxide/O₂/N₂ mixtures, the pentanal-hydroperoxide concentration was decreased, due to the consumption of RO₂ radicals by reaction (7). The pentanal-hydroperoxide concentration was measured vs. NO concentration at ten temperatures (463–523 K). The isomerization rate constant involving the H atoms of the CH₂( )OH group was deduced: or per H atom: The comparison of this rate constant to thermokinetics estimations leads to the conclusion that the strain energy barrier of a seven-member ring transition state is low and near that of a six-member ring. Intramolecular hydroperoxy isomerization reactions produce carbonyl-hydroperoxides which (through atmospheric decomposition) increase concentration of radicals and consequently increase atmospheric pollution, especially tropospheric ozone, during summer anticyclonic periods. Therefore, hydrocarbons used in summer should contain only short chains (<C₄) hydrocarbons or totally branched hydrocarbons, for which isomerization reactions are unlikely. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 875–887, 1998     

Analysis of isotopic signals in the Danube River water at Tulln,Austria, based on daily grab samples in 2012

Results of stable isotope measurements (δ²H, δ¹⁸O) of daily grab samples, taken from the Danube River at Tulln (river km 1963) during 2012, show seasonal and short-term variations depending on the climatic/hydrological conditions and changes in the catchment area (temperature changes, heavy rains and snow melt processes). Isotope ratios in river water clearly reflect the isotopic composition of precipitation water in the catchment area since evaporation influences play a minor role. Average δ²H and δ¹⁸O values in 2012 are?78‰ and?11.0‰, respectively, deuterium excess averages 10‰. The entire variation amounts to 1.8‰ in δ¹⁸O and 15‰ in δ²H. Quick changes of the isotopic composition within a few days emphasise the necessity of daily sampling for the investigation of hydrological events, while monthly grab sampling seems sufficient for the investigation of long-term hydro-climatic trends. ³H results show peaks (half-width 1–2 days, up to about 150 TU) exceeding the regional environmental level of about 9 TU, probably due to releases from nuclear power plants.     

Ammonium ion binding with pyridine-containing crown ethers

Dipyrido[24]crown-8 (DP24C8) has been synthesized and shown to form [2]pseudorotaxanes spontaneously with dibenzylammonium ions. These complexes, which have been demonstrated by (1)H NMR spectroscopy to form faster in solution than when the macrocyclic polyether is dibenzo[24]crown-8 (DB24C8), are also stronger than their DB24C8 counterparts. One of the [2]pseudorotaxanes has been used to construct a [2]rotaxane (see above) comprising a dumbbell-shaped component based on a dibenzylammonium ion which is encircled by a DP24C8 macrocycle and terminated by (triphenylphosphonium)methyl stoppers.     

Isomeric hexyl‐ketohydroperoxides formed by reactions of hexoxy and hexylperoxy radicals in oxygen

Isomerization reactions of peroxy radicals during oxidation of long‐chain hydrocarbons yield hydroperoxides, and therefore play an important role in combustion and atmospheric chemistry, because of their action as branching agents in these chain reaction processes. Different formation mechanisms and structures are involved. Three isomeric hexyl‐ketohydroperoxides are formed via isomerization reactions in oxygen of either hexoxy RO or hexylperoxy RO₂ radicals. In the temperature range 373–473 K, 2‐hexoxy (C₆H₁₃O) radical in O₂/N₂ mixtures gives 2‐hexanone‐5‐hydroperoxide via two consecutive isomerizations. The second one is a H transfer from a HC(OH) group occurring via a seven‐membered ring intermediate: Its rate constant has been determined at 453 and 483 K, and the general expression can be written as Hexylperoxy C₆H₁₃O₂ radical, present in n‐hexane oxidation by oxygen/nitrogen mixtures in the temperature range 543–573 K, gives 2‐hexanone‐4‐hydroperoxide, 3‐hexanone‐5‐hydroperoxide, and 2‐hexanone‐5‐hydroperoxide. The first two are formed through an isomerization reaction via a six‐membered ring intermediate, and the last through an isomerization reaction via a seven‐membered ring intermediate. The ratio of the rate constant of the isomerization reactions of RO₂ radicals via a seven‐membered ring intermediate to that via a six‐membered ring is found to be 0.795, and the rate constant expression via a seven‐membered ring intermediate is proposed: The role of these reactions in the formation of radicals in the troposphere is discussed. Other products arising in the reactional path, such as ketones, furans, and diketones, are identified. Identification of these ketohydroperoxides was made using gas chromatography/mass spectrometry with electron impact, and with NH₃ (or ND₃) chemical ionization. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 354–366, 2003