Asymmetric NMR spectra of weakly coupled nuclei: A common characteristic in the 13C NMR spectra of [U-13C]-labeled molecules and in natural abundance protoncoupled 13C spectra

Typically encountered proton-decoupled spectra of [U-¹³C]-labeled molecules or proton-coupled spectra of natural abundance or singly labeled molecules contain many nuclei which satisfy the weak coupling approximation. The spectra of such nuclei are frequently highly asymmetric and often appear to exhibit the skewed intensity distribution characteristic of strongly coupled spins. Analysis of typical cases indicates that such effects arise in the presence of at least one moderately strong coupling interaction in the spin system (Jδν ～ 1/3), and the apparent intensity asymmetry reflects small differences in the spacing of unresolved components of the observed resonance. This effect is analogous to the case of ‘virtual coupling’ in which weakly coupled spins cannot be analyzed as first order spectra; however; the ABX spin system which generally serves as a model for such systems does not predict the existence of spectral asymmetry for the X resonances. Prediction of this asymmetry requires a spin system of at least four spins with at least ABMX complexity, and can be treated generally using the effective Hamiltonian approach of Poeple and Schaefer.     

Evidence for hexadecapole vibrations in A ≈ 170 deformed nuclei; New results for 168Yb

Dominating proton structure has been identified in the K^π=3⁺ band of ¹⁶⁸Yb, contrasting with neutron structure in the corresponding band of ¹⁷²Yb. A region of low-lying K^π=3⁺ bands is now established, with N=98?104, Z=68?72. For all stable nuclei in this region, the I^πK=4⁺3 state is excited by inelastic deutron scattering.     

The reaction π−p → K0Σ0 up to 2375 MeV/c

Differential cross-section and polarization measurements for the reaction π^?p → K⁰Σ⁰ are presented from 1395 to 2375 MeV/c incident beam momentum. The polarization data from an earlier experiment, from thershold to 1334 MeV/c, have been re-analysed by an improved method leading to a substantial reduction in the errors.     

Techniques,computations, and conjectures for semi-topological <Emphasis Type="Italic">K</Emphasis>-theory

We establish the existence of an Atiyah-Hirzebruch-like spectral sequence relating the morphic cohomology groups of a smooth, quasi-projective complex variety to its semi-topological K-groups. This spectral sequence is compatible with (and, indeed, is built from) the motivic spectral sequence that relates the motivic cohomology and algebraic K-theory of varieties, and it is also compatible with the classical Atiyah-Hirzebruch spectral sequence in algebraic topology. In the second part of this paper, we use this spectral sequence in conjunction with another computational tool that we introduce — namely, a variation on the integral weight filtration of the Borel-Moore (singular) homology of complex varieties introduced by H. Gillet and C. Soulé – to compute the semi-topological K-theory of a large class of varieties. In particular, we prove that for curves, surfaces, toric varieties, projective rational three-folds, and related varieties, the semi-topological K-groups and topological K-groups are isomorphic in all degrees permitted by cohomological considerations. We also formulate integral conjectures relating semi-topological K-theory to topological K-theory analogous to more familiar conjectures (namely, the Quillen-Lichtenbaum and Beilinson-Lichtenbaum Conjectures) concerning mod-n algebraic K-theory and motivic cohomology. In particular, we prove a local vanishing result for morphic cohomology which enables us to formulate precisely a conjectural identification of morphic cohomology by A. Suslin. Our computations verify that these conjectures hold for the list of varieties above.Mathematics Subject Classification (2000): 19E20, 19E15, 14F43The first author was partially supported by the NSF and the NSAThe second author was supported by the Helen M. Galvin Fellowship of Northwestern UniversityThe third author was partially supported by the NSF and the NSA