Two Convenient Syntheses of 2-Aryl-1-Cyano-1-Propenes From Quaternary Ammonium Salts

Two readily available and different quaternary ammonium salts have been prepared by the alkylation of vinamidinium salt reduction products. These salts have been successfully converted to 2-aryl-1-cyano-1-propenes and this methodology represents a clean and efficient procedure for the construction of such systems.     

Protection of A 2,6-Dialkylaniline: Synthesis of 4-Dimethylmethoxysilyl-2,6-Diethylaniline

The synthesis of 4-dimethylmethoxysilyl-2,6-diethylani-line (1) from 2,6-diethylaniline (2) is described. An intermediate in the process, disilazane 5 appears to be the first 2,6-dialkylaniline to be protected with 1,1,5,5-tetramethyl-1,4-dichlorodisilethylene (4).     

Z = 50 shell gap near 100Sn from intermediate-energy Coulomb excitations in even-mass 106-112Sn isotopes

Rare isotope beams of neutron-deficient 106,108,110Sn from the fragmentation of 124Xe were employed in an intermediate-energy Coulomb excitation experiment. The measured B(E2,0(1)(+)-->2(1)(+)) values for 108Sn and 110Sn and the results obtained for the 106Sn show that the transition strengths for these nuclei are larger than predicted by current state-of-the-art shell-model calculations. This discrepancy might be explained by contributions of the protons from within the Z = 50 shell to the structure of low-energy excited states in this region.     

Magnetic-field effects on the size of vortices below the surface of NbSe2 detected using low energy beta-NMR

A low energy radioactive beam of polarized 8Li has been used to observe the vortex lattice near the surface of superconducting NbSe2. The inhomogeneous magnetic-field distribution associated with the vortex lattice was measured using depth-resolved beta-detected NMR. Below Tc, one observes the characteristic line shape for a triangular vortex lattice which depends on the magnetic penetration depth and vortex core radius. The size of the vortex core varies strongly with the magnetic field. In particular, in a low field of 10.8 mT, the core radius is much larger than the coherence length. The possible origin of these giant vortices is discussed.     

Second-order superintegrable quantum systems

A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n ? 1 functionally independent constants of the motion that are polynomial in the momenta, the maximum number possible. If these constants of the motion are all quadratic, then the system is second-order superintegrable, the most tractable case and the one we study here. Such systems have remarkable properties: multi-integrability and separability, a quadratic algebra of symmetries whose representation theory yields spectral information about the Schrödinger operator, and deep connections with expansion formulas relating classes of special functions. For n = 2 and for conformally flat spaces when n = 3, we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here, we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension.