Synthesis, properties, and reactions of a series of stable dialkyl-substituted silicon-chalcogen doubly bonded compounds

The first dialkyl-substituted silicon-chalcogen doubly bonded compounds [R2Si=X; R2=1,1,4,4-tetrakis(trimethylsilyl)butane-1,4-diyl, X = S (4), Se (5), and Te (6)]were synthesized by the reactions of an isolable dialkylsilylene R2Si: (3) with phosphine sulfide, elemental selenium, and elemental tellurium, respectively. Systematic changes of characteristics of silicon-chalcogen double bonds are elucidated by X-ray analysis, UV-vis spectroscopy, and DFT calculations. In the solid state, the unsaturated silicon atom in 4-6 adopts planar geometry and the extent of the shortening of Si=X double bonds from the corresponding Si-X single bonds decreases in the order 4 > 5 > 6. In the absorption spectra of 4-6, pi -->pi* transition bands are observed distinctly in addition to n -->pi* transition bands. Both the n -->pi* and pi -->pi* transitions are red-shifted in the order 4 < 5 < 6, and the difference between the energies of the two transitions is kept almost constant among 4-6. The tendency is explained using the qualitative perturbation theory and is reproduced by the DFT calculations for model silanechalcogenones. Addition reactions of water, methanol, and isoprene to 4-6 are reported.     

Electromagnetic moments of short lived β emitters 21F, 23Mg, 27Si and 39Ca

The β-NMR spectra of ²¹F, ²³Mg, ²⁷Si and ³⁹Ca which were produced in heavy ion collisions and implanted in various crystals have been observed. The magnetic moments of ²¹F and ²⁷Si were determined to be |μ(²¹F)| = 3.9194 ± 0.0012 μ_N and |μ(²⁷Si)| = 0.8653 ± 0.0003 μ_N, respectively. The electric quadrupole coupling constants were determined for the first time to be |eqQ(²¹F in MgF₂)/h|= 9.94 ± 0.09 MHz, |eqQ(²³Mg in MgF₂)/h|= 1.96 ± 0.06 MHz, |eqQ(²⁷Si in Al₂O₃)/h|= 1.90 ± 0.12 MHz, |eqQ(³⁹Ca in CaCO₃)/h|= 0.60 ± 0.04 MHz. From the present eqQ/h, the Q moments were deduced as |Q(²¹F)|= 110 ± 22 mb, |Q(²³Mg)|= 114 ± 3 mb, |Q(²⁷Si)|= 60 ± 13 mb and |Q(³⁹Ca)|= 36± 7 mb. The present data were compared with the theoretical values obtained by the OXBASH shell model code. This revised version was published online in August 2006 with corrections to the Cover Date.     

Optimal measurements for general quantum systems

We give a general formulation of the theory of optimal quantum measurements, based on Gudder's [8] convex structure approaches to axiomatic quantum mechanics, which includes the case of Holevo's formulation [14] and operational quantum mechanics [3]. Simple and general conditions for existence of Bayes optimal measurements are obtained by a method without operator valued measure techniques. For this purpose, a representation of convex prestructures and a characterization of a class of loss functions are obtained. Finally, an application of the results to Wald's theory of statistical decision functions is shown.     

Polymer foil applicable to the tilted foil technique

A polymer foil of polyethylene-terephthalate was successfully used for the tilted foil to create nuclear polarization of beta-emitters. The foil was carefully prepared to produce atomic flatness on the surfaces. The resultant smoothness was confirmed with beta-NMR measurements on¹²B and found to be as good as those of carbon foils used previously in the measurements.     

Mosaic and Principal Functions of log-hyponormal Operators

The purpose of this paper is to introduce mosaic and principal functions of log-hyponormal operators associated with Aluthge transformation and discuss determining sets.     

Exponential decay of solutions to nonlinear elliptic equations with potentials

Exponential decay estimates are obtained for complex-valued solutions to nonlinear elliptic equations in where the linear term is given by Schr?dinger operators H = − Δ + V with nonnegative potentials V and the nonlinear term is given by a single power with subcritical Sobolev exponent in the attractive case. We describe specific rates of decay in terms of V, some of which are shown to be optimal. Moreover, our estimates provide a unified understanding of two distinct cases in the available literature, namely, the vanishing potential case V = 0 and the harmonic potential case V(x) = |x|². Dedicated to Professor Jun Uchiyama on the occasion of his sixtieth birthday Received: May 4, 2004     

Coulomb dissociation of 8B and the low-energy cross section of the 7Be(p,gamma)8B solar fusion reaction

An exclusive measurement of the Coulomb breakup of 8B into 7Be+p at 254A MeV allowed the study of the angular correlations of the breakup particles. These correlations demonstrate clearly that E1 multipolarity dominates and that E2 multipolarity can be neglected. By using a simple single-particle model for 8B and treating the breakup in first-order perturbation theory, we extract a zero-energy S factor of S17(0)=18.6+/-1.2+/-1.0 eV b, where the first error is experimental and the second one reflects the theoretical uncertainty in the extrapolation.