The S-matrix for abstract scattering systems

Let S() be the S-matrix at energy for an abstract scattering system. We derive a bound, in terms of the interaction, on integrals of the form h () S()- _HS ² d, where denotes the Hilbert-Schmidt norm.Supported by the Swiss National Science Foundation.     

Contents of Volume 7 (2004)

Volume Contents

Contents of Volume 7 (2004)     

The Farrell-Jones Isomorphism Conjecture for finite covolume hyperbolic actions and the algebraic -theory of Bianchi groups

We prove the Farrell-Jones Isomorphism Conjecture for groups acting properly discontinuously via isometries on (real) hyperbolic -space with finite volume orbit space. We then apply this result to show that, for any Bianchi group , , , and vanish for .

     

The carbenoid approach to peptide synthesis

A different approach to the synthesis of dipeptides is described based on the formation of the NHCHR1CONH-CHR2CO bond by carbenoid N-H insertion, rather than the formation of the peptide bond itself. Thus decomposition of triethyl diazophosphonoacetate catalysed by rhodium(II) acetate in the presence of N-protected amino acid amides 8 gives the phosphonates 9. Subsequent Wadsworth-Emmons reaction of 9 with aldehydes in the presence of DBU gives dehydro dipeptides 10. The reaction has been extended to a simple two-step procedure, without the isolation of the intermediate phosphonate, for conversion of a range of amino acid amides 11 into dehydro dipeptides 12 and to an N-methylamide 11 h, and for conversion of a dipeptide to tripeptide (13-->14). Direct conversion, by using methyl diazophenylacetate, of amino acid amides to phenylglycine-containing dipeptides 19 proceeds in good chemical yield, but with poor diastereoselectivity.     

Stability Criteria for the Weyl m-Function

This paper presents a new approach to spectral theory for theSchrödinger Operator on the half-line. Solutions of nonlinearRiccati-type equations related to the Schrödinger equation at realspectral parameter are characterised by means of their clusteringproperties as is varied. A family of solutions exhibiting aso-called -clustering property is shown to imply precise estimatesfor the complex boundary value of the Weyl m-function and thespectral measure, and leads to an analysis of the absolutely continuouscomponent of the spectral measure in terms of stability criteria for thecorresponding Riccati equations.     

Synthesis of a key precursor for orienticin C and model study on ruthenium-mediated macrocyclization

A tripeptido--arene--ruthenium complex was prepared as a key precursor for the projected synthesis of orienticin C, demonstrating that the cyclopentadienylruthenium moiety can be attached to a chloroarene in the presence of multiple functionality. The ruthenium-mediated intramolecular SNAr reaction for formation of the required diaryl ether linkage was successfully tested on a model system.     

Molecular fragmentation driven by ultrafast dynamic ionic resonances

The authors time resolve molecular motion in bound state, ionic potentials that leads to bond cleavage during the interaction with intense, ultrafast laser fields. Resonances in molecular ions play an important role in dissociative ionization with ultrafast laser fields, and the authors demonstrate how these resonances evolve in time to produce dissociation after initial strong-field ionization. Exploiting such dynamic resonances offers the possibility of controlled bond breaking and characterizing time-dependent molecular structure.     

Precision branching ratio measurement for the superallowed beta+ emitter 62Ga and isospin-symmetry-breaking corrections in A>or=62 nuclei

A high-precision branching ratio measurement for the superallowed beta+ decay of 62Ga was performed at the Isotope Separator and Accelerator radioactive ion beam facility. Nineteen gamma rays emitted following beta+ decay of 62Ga were identified, establishing the dominant superallowed branching ratio to be (99.861+/-0.011)%. Combined with recent half-life and Q-value measurements, this branching ratio yields a superallowed ft value of 3075.6+/-1.4 s for 62Ga decay. These results demonstrate the feasibility of high-precision superallowed branching ratio measurements in the A>or=62 mass region and provide the first stringent tests of the large isospin-symmetry-breaking effects predicted for these decays.