Algebraic Model for Quantum Scattering. Reformulation, Analysis and Numerical Strategies

The convergence problem for scattering states is studied in detail within the framework of the Algebraic Model, a representation of the Schrodinger equation in an L^2 basis. The dynamical equations of this model are reformulated featuring new "Dynamical Coefficients", which explicitly reveal the potential effects. A general analysis of the Dynamical Coefficients leads to an optimal basis yielding well converging, precise and stable results. A set of strategies for solving the equations for non-optimal bases is formulated based on the asymptotic behaviour of the Dynamical Coefficients. These strategies are shown to provide a dramatically improved convergence of the solutions.Comment: 31 pages, 41 postscript figure

Fundamental and applied aspects of the chemistry of acetylenylquinones

In addition to the reported synthetic routes for the acetylene derivatives of quinones, a detailed analysis of the fundamental chemical, physicochemical, and biological properties of this class of compounds is presented herein. The advantages of Pd- and Cucatalyzed cross-coupling of terminal alkynes with iodarenes via the Sonogashira reaction to produce new acetylenylquinones with predetermined properties are examined. Here, combining quinoid and acetylene residues into one molecule gives the resulting compounds chemical specificity, as demonstrated by several reported examples of non-trivial transformations. In particular, the presence of the quinoid cycle significantly increases the electrophilicity of the triple bond and determines the range of transformation possibilities. Moreover, acetylenylquinones have heightened sensitivity to both external (such as the reaction temperature and the nature of the solvent) and internal (e.g., the structure of substituents in the nucleus and the acetylene fragment) factors. For example, regioselective cleavage of a strong triple bond under the action of amines is possible in the absence of a metal catalyst. Peri-substituted acetylenyl-9,10-anthraquinones are most suited for the synthetic route because of the proximity of the acetylene and carbonyl groups. Mechanisms of reactions of selective alkynylquinones are described

Algebraic Model for scattering in three-s-cluster systems. I. Theoretical Background

A framework to calculate two-particle matrix elements for fully antisymmetrized three-cluster configurations is presented. The theory is developed for a scattering situation described in terms of the Algebraic Model. This means that the nuclear many-particle state and its asymptotic behaviour are expanded in terms of oscillator states of the intra-cluster coordinates. The Generating Function technique is used to optimize the calculation of matrix elements. In order to derive the dynamical equations, a multichannel version of the Algebraic Model is presented.Comment: 20 pages, 1 postscript figure, submitted to Phys. Rev.

Algebraic Model for scattering of three-s-cluster systems. II. Resonances in the three-cluster continuum of 6He and 6Be

The resonance states embedded in the three-cluster continuum of 6He and 6Be are obtained in the Algebraic Version of the Resonating Group Method. The model accounts for a correct treatment of the Pauli principle. It also provides the correct three-cluster continuum boundary conditions by using a Hyperspherical Harmonics basis. The model reproduces the observed resonances well and achieves good agreement with other models. A better understanding for the process of formation and decay of the resonance states in six-nucleon systems is obtained.Comment: 8 pages, 10 postscript figures, submitted to Phys. Rev.

Monopole and quadrupole polarization effects on the alpha-particle description of 8^{8}Be

We investigate the effect of monopole and quadrupole modes on the elastic alpha-alpha resonance structure of $^{8}$Be. To this end we make a fully microscopic coupled channels calculation with three coupled channels, using the Algebraic Model. The continuum spectrum and wave functions are analyzed in terms of the individual channels to understand the nature of the resonances. It is shown that both monopole and quadrupole modes have a non-negligible effect on the resonances in the alpha-alpha continuum.Comment: 20 pages, 4 figures. submitted to Phys.Rev.

Resonances in three-claster continuum of 5H nucleus

The resonance structure of 5H is investigated within a three-cluster microscopic model. Hyperspherical Harmonics are used to characterize the channels of the three-cluster continuum and to implement the appropriate boundary conditions. The model predicts the energy and width of the 5H resonance states well and allows for a detailed channel analysis

A netron halo in 8He

The structure of $^8$He is investigated within a three-cluster microscopic model. The three-cluster configuration $\alpha+^2n+^2n$ was used to describe the properties of the ground state of the nucleus. The obtained results evidently indicate the existence of a neutron halo in $^8$He.Comment: 14 pages, 6 postscript figures, submitted to Phys. Atom. Nuc