Synthesis and characterization of fluorene end‐labeled polystyrene with atom transfer radical polymerization

Fluorene end‐labeled polystyrene was prepared by atom transfer radical polymerization with 9‐bromofluorene as the initiator. Reactions were carried out in bulk or tetrahydrofuran solutions at temperatures of 80 °C or above. Analysis by gel permeation chromatography indicated that the polymers formed had low polydispersities with molecular weights consistently 2–5 times higher than calculated based on monomer‐to‐initiator ratios. Coupling of two fluorenyl radicals, formed by activation of the 9‐bromofluorene, was found to compete with initiation, leading to the higher‐than‐expected molecular weight values while giving rise to a fluorene dimer. UV–vis spectrometry indicated near‐quantitative fluorene labeling of the polystyrene. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2657–2665, 2005     

Self-consistent symmetries of the Hartree-Fock-Bogoliubov equations in a rotating frame

The self-consistent symmetries σ_x (reflection through the yz plane) and TR_z(π) and their eigenfunctions are employed to reduce the dimension of the Hartree-Fock-Bogoliubov equations in a rotating frame by a factor of two. In the canonical or BCS representation, σ_x, maps each single-particle orbital into itself.     

Missing Gamow-Teller strength in mass 42

The reaction ⁴²Ca(p,n)⁴²Sc at E_p = 160 MeV is used to measure the Gamow-Teller (GT) strength function. Normalization of the dominant peak in the (p,n) spectrum to B(GT) determined from the analogous transition in the beta decay of ⁴²Ti renders the strength function absolute, and the total measured stregth is about half of the minimum value required for a T = 1 nucleus. Shell model calculations are presented which reproduce the shape of the strength function, but overpredict the absolute measured strength by about a factor of two. Evidently the missing strength has been moved out of the region of nucleon particle-hole excitations, and quenching, due possibly to Δ₃₃ coupling, is indicated. Symmetry implications of an observed strong suppression of the T_> component of the GT strength are discussed.     

Pion small-angle multiple scattering at energies spanning the (3,3) resonance

The small-angle multiple scattering of positive and negative pions has been measured for C, Al, Cu and Pb targets throughout an energy range spanning the (3, 3) resonance. The measurements were made using two-dimensional multiwire proportional counters placed in the pion beam. All previous multiple scattering data for electrons and protons as well as these new data for pions are used to recalculate the empirical terms in the Moliere theory of multiple scattering. A second-order Born approximation multiple scattering theory has been devised for spin zero particles. Modified Moliere theory gives a better fit to the experimental data than the second-order Born calculation. Because the updated Moliere theory contains much simpler equations and gives closer agreement with experiment, it is recommended in place of the more sophisticated theory for the interpretation of new experimental data.     

Sufficient conditions for a graph to be Hamiltonian

Three sufficient conditions for a graph to be Hamiltonian are given. These theorems are in terms of subgraph structure and do not require the fairly high global line density which is basic to the Pósa-like sufficiency conditions. Line graphs of both Eulerian graphs and Hamiltonian graphs are also characterized.     

Model of the interaction potential of an atom with a hard corrugated surface incorporating a stationary potential well

We propose a new atom-surface interaction potential model which is designed for use in the recent exact theory for the elastic scattering of an atom by a hard corrugated surface model which incorporates a stationary attractive potential well [N. García, F.O. Goodman, V. Celli and N.R. Hill, Phys. Rev. B (1979)]. The model parameters are adjusted to obtain a best-fit to all available experimental data on atom-surface bound-state energies, and comparisons are also made with the latest theoretical data, with satisfactory results.     

Finite-temperature HFB theory

The finite-temperature Hartree-Fock-Bogoliubov (FTHFB) equations are derived. For the pairing hamiltonian FTHFB simplifies to finite-temperature BCS (FTBCS). The solution of the FTBCS equations for the degenerate model displays a temperature-dependent pairing “phase transition”.     

Response-function theory of laser-stimulated desorption of atoms from solid surfaces

Laser-stimulated desorption fiom solid surfaces is studied as a special case of the theory of linear response functions. For many problems, for example calculation of the minimum intensity of the laser radiation field necessary for desorption, it is shown that the only dynamical property of the host system (lattice) which is required is the Laplace transform of the “response function” of the atom of the host lattice to which the adsorbed atom is attached. The results for one-dimensional host lattices with N atoms are compared with similar results obtained recently, using a quite different approach, by Murphy and George, Surface Sci. 102 (1981) L46. Effects of dimensionality of the host lattice are discussed, and an explicit comparison is presented of the results for simplified one- and three-dimensional host lattice models. Applications of the work to calculation of frequencies of normal modes of the adsorbed systems which are localized at the adsorbates (“localized modes”) are discussed and compared with previous analyses.