Self-consistent models of collective and single-particle structures and their test by inelastic scattering: The case of 54Fe

Generator coordinate wave functions built from angular momentum and particle number projected Hartree-Fock-Bogoliubov states that were constrained to different quadrupole deformations and allowing two-quasiparticle excitations are tested by their use in analyses of inelastic proton scattering. Transitions to low-lying states in ⁵⁴Fe are used as the specific examples and comparisons are made with appropriate, albeit smaller basis, shell-model predictions.     

An estimate of giant resonance effects in (α,p) transitions

A comparison of transition amplitudes for the¹⁶O(α, p)¹⁹F^* (1/2^?, 110keV) reaction suggests the utility of such reactions in the study of isoscalar giant resonances.     

Semi-infinite matter and the nuclear surface

The surface energy and thickness of semi-infinite nuclear matter are calculated by Swiatecki's variational method. Smooth, effective two-body interactions are used to study the relationship between the characteristics of each interaction and the predicted bulk surface properties. Both local and non-local Gaussian interactions are considered and are adjusted to either saturate infinite nuclear matter or to fit two-nucleon (singlet-even) phase shifts. Purely local potentials are found to give an excessively large surface energy ( ), whereas potentials having some non-locality (even if the non-locality is confined to short distances) reduce the surface energy to a reasonable value of (20–30) . The separate potential and kinetic energy contributions are examined in detail and are used to explain how the character of each interaction affects the surface properties. This model calculation shows that the surface energy is greatly influenced by non-locality. Also, we find that the predicted surface thickness tends to be too large (t ≈ 3.5 fm) for potentials that are adjusted to saturate and too small (t ≈ 1.8 fm) for potentials that are fitted to two-nucleon phase-shifts.     

Construction theorems for polytopes

Certain construction theorems are represented, which facilitate an inductive combinatorial construction of polytopes. That is, applying the constructions to ad-polytope withn vertices, given combinatorially, one gets many combinatoriald-polytopes—and polytopes only—withn+1 vertices. The constructions are strong enough to yield from the 4-simplex all the 1330 4-polytopes with up to 8 vertices.     

Electric and magnetic properties of CO,HF, HCI,and CH3F

Electric multiple moments polarizabilities and magnetizabilities of CO, HF, HCI, and CH₃F are calculated using SCF wavefunctions and coupled Hartree-Fock perturbation method. The A and G tensors are also calculated and discussed in relation to electric-induced differential scattering and electric-field-gradient-induced birefringence in these gases.     

Perturbative Approach to the Inner Structure of a Rotating Black Hole

This is the first in a series of papers analyzing the inner structure of a generic rotating black hole. The black hole is assumed to evolve from the gravitational collapse of an isolated rotating object in an empty asymptotically-flat universe. This paper covers the first stages of the evolution: from the gravitational collapse and the formation of a black hole, up to the stage where the black hole settles down to Kerr. We shall discuss the generalization of Price's analysis (regarding the latetime asymptotic decay of perturbations outside the black hole) from Schwarzschild to Kerr, and present preliminary results. We then consider these external small perturbations as initial data for the evolution of perturbations inside the black hole. We demonstrate that an important region inside the black hole, which we call the late-time region (and which extends up to the inner horizon) experiences (arbitrarily) small initial perturbations. This, we argue, justifies the attempt to apply the small-perturbation approach to the black hole's interior. We discuss the physical significance of this late-time region. We shall also outline the strategy we use for evolving the perturbations from the event horizon to the inner horizon.     

On weakly neighborly polyhedral maps of arbitrary genus

A weakly neighborly polyhedral map (w.n.p. map) is a 2-dimensional cell-complex which decomposes a closed 2-manifold without boundary, such that for every two vertices there is a 2-cell containing them. We lay the foundation for an investigation of the w.n.p. maps of arbitrary genus. In particular we find all the w.n.p. maps of genus 0, we prove that for everyg> the number of w.n.p. maps of genusg (orientable or not) is finite, and we find an upper bound for the number of vertices in a w.n.p. map of genusg>0. This upper bound grows as (4g(^2/3) wheng→∞.     

An expedient synthesis of substituted indoles

Condensation of carboxylic acid esters with organodilithium reagents derived from N-trimethylsilyl-o-toluidine or N-trimethylsilyl-o-ethyl aniline affords substituted indoles.     

Multicomponent linchpin couplings. Reaction of dithiane anions with terminal epoxides, epichlorohydrin, and vinyl epoxides: efficient, rapid, and stereocontrolled assembly of advanced fragments for complex molecule synthesis

The development, application, and advantages of a one-flask multicomponent dithiane linchpin coupling protocol, over the more conventional stepwise addition of dithiane anions to electrophiles leading to the rapid, efficient, and stereocontrolled assembly of highly functionalized intermediates for complex molecule synthesis, are described. Competent electrophiles include terminal epoxides, epichlorohydrin, and vinyl epoxides. High chemoselectivity can be achieved with epichlorohydrin and vinyl epoxides. For vinyl epoxides, the steric nature of the dithiane anion is critical; sterically unencumbered dithiane anions afford S(N)2 adducts, whereas encumbered anions lead primarily to SN2' adducts. Mechanistic studies demonstrate that the SN2' process occurs via syn addition to the vinyl epoxide. Integration of the multicomponent tactic with epichlorohydrin and vinyl epoxides permits the higher-order union of four and five components.