Schwefelverbindungen

Ohne Zusammenfassung     

Quantum chaos triggered by precursors of a quantum phase transition: the dicke model

We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localization-delocalization transition in which a macroscopic superposition is generated. We also describe the classical analogs of this behavior.     

Synthesis of ketomethylene analogs of dipeptides

A convenient method of synthesizing ketomethylene dipeptides by using homoallylic Grignard reagents as amino acid analog synthons is described.     

A universal tunnelling coefficient for step- and graded-index multimode fibres

A single expression is presented for the power transmission coefficient of both step- and graded-index fibres, which is uniformly valid for all weakly tunnelling and refracting rays. Its accuracy is demonstrated in a comparison of the corresponding power attenuation coefficient for the step-index fibre with solutions to the electromagnetic boundary value problem.     

The low-energy pion-nucleus interaction

We discuss the low-energy pion-nucleus interaction within the framework of the optical model. We find that a consistent expansion of the πN amplitude in momentum is required in order that the low-energy pion-nucleus interaction is physically compatible with a simple compositie picture of the nuclear sacttering process. This introduces an energy-dependent component into the usual local part of the Ericson-Ericson optical potential stemming from the πN s-wave effective range. The size of this component is estimated and the corresponding pion-nucleus effective ranges and volume parameters are determined for uniformly dense nuclei. Finally a modified extrapolation to the bound state energies is considered in the light of these large effective ranges.     

Natural abundance nitrogen-15 n.m.r. spectroscopy. Spin–lattice relaxation in organic compounds

The small negative magnetogyric ratio (γ) of the ¹⁵N nucleus decreases the efficiency of ¹⁵N? ¹H dipole-dipole relaxation to about 25% of that for an analogous ¹³C nucleus. This may lead to greater competition from other relaxation mechanisms in ¹⁵N n.m.r. and consequent partial or total quenching of the negative nuclear Overhauser effect (NOE). In unfavorable circumstances nulling of the ¹⁵N resonance can occur. Previous ¹⁵N relaxation studies have examined isotopically enriched, low molecular weight compounds. The present study examines several small to intermediate size organic compounds containing nitrogen at natural isotopic abundance. In contrast to some of the earlier studies, ¹⁵N? ¹H dipolar relaxation was found to be dominant for protonated nitrogen atoms, even for two tertiary nitrogens (the tertiary amine nitrogen in 1,2,3,4,6,7,12,12b-octahydroindolo[2,3-a] quinolizine and the oxime nitrogen in 3-methyl-2-pentanone ketoxime). The magnitude of the NOE and the moderate value of T₁ indicate effective dipolar relaxation from neighboring but not directly bonded protons in these cases. Nitro groups were found, as expected, to have predominant contributions from non-dipolar mechanisms, and in one case (2-methyl-2-nitro-1, 3-propanediol) signal nulling (NOE of η = ?1) was observed. The effect of paramagnetic impurities was demonstrated for ethanolamine, which contains a basic nitrogen. In this case T₁^DD(¹⁵N? ¹H) = 4·3 s; added Ni(acac)₂ at 1 × 10^?4 Molar reduced the ¹⁵N T₁ to 0·065 s and consequently the NOE to η = 0.