Lines tangent to

We show that for there are complex common tangent lines to general spheres in and that there is a choice of spheres with all common tangents real.

     

Three-body problem in a dilute bose-Einstein condensate

We derive the explicit three-body contact potential for a dilute condensed Bose gas from microscopic theory. The three-body coupling constant exhibits the general form predicted by Wu [Phys. Rev. 115, 1390 (1959)]] and is determined in terms of the amplitudes of two- and three-body collisions in vacuum. In the present form, the coupling constant becomes accessible to quantitative studies which should provide the crucial link between few-body collisions and the stability of condensates with attractive two-body forces.     

Saturation of gauge-invariant Schwinger-model correlation functions by instantons

We draw some conclusions from the saturation of QED₂ correlation functions by non-quasiclassical instantons.     

13C NMR spectra of diazastilbenes. I—trans-styryldiazines

The ¹³C NMR spectra of all trans-styryldiazines, methyldiazines and trans-styrylpyridines have been fully assigned. Empirical shift increments were obtained for the chemical shifts of the carbon atoms; these are discussed in the light of theoretical considerations.     

From uncharged to decacationic molecules: syntheses and spectroscopic properties of heteroarenium-substituted pyridines

Nucleophilic substitutions on pentachloropyridine with 4-(dimethylamino)pyridine, 4-aminopyridine, and 4-(pyrrolidin-1-yl)pyridine give mono-, tri- and pentacationic pyridine-hetarenium salts. The mono-, tri- and pentacationic 4-aminopyridine derivatives can be deprotonated to neutral compounds in solution, or protonated to di-, hexa- and decacationic pyridine derivatives, respectively. Successive substitutions with different heteroaromatic nucleophiles give pyridines with two distinct types of heteroarenium substituents.     

Highly stretched single polymers: atomic-force-microscope experiments versus ab-initio theory

Experimental single-molecule stretching curves for three backbone architectures (single-stranded DNA, various types of peptides, polyvinylamine) are quantitatively compared with corresponding quantum-chemical (zero-temperature) ab-initio calculations in the high-force range of up to two nanonewtons. For high forces, quantitative agreement is obtained with the contour length of the polymers as the only fitting parameter. For smaller forces, the effects of chain fluctuations are accounted for by using recent theoretical results for the stretching response of a freely-rotating-chain model.     

Spontaneous dissociation of long-range Feshbach molecules

We study the spontaneous dissociation of diatomic molecules produced in cold atomic gases via magnetically tunable Feshbach resonances. We provide a universal formula for the lifetime of these molecules that relates their decay to the scattering length and the loss rate constant for inelastic spin relaxation. Our universal treatment as well as our exact coupled channels calculations for 85Rb dimers predict a suppression of the decay over several orders of magnitude when the scattering length is increased. Our predictions are in good agreement with recent measurements of the lifetime of 85Rb(2).     

Polarity matching of radical trapping: high yielding 3-exo and 4-exo cyclizations

A catalyzed synthesis of cyclopropanes and cyclobutanes via radical chemistry is described. The method that generally proceeds in high yields uses epoxides as radical precursors and titanocene(III) complexes as the electron transfer catalysts (see scheme). The key to the success of the transformation is constituted by the chemoselectivity of radical reduction. Electrophilic enol radicals generated through cyclization are reduced rapidly whereas their precursors, nucleophilic alkyl radicals, remain unaffected.