Strong binding and shrinkage of single and double nuclear systems (K?pp,K?ppn,K?K?p and K?K?pp) predicted by Faddeev-Yakubovsky calculations

Non-relativistic Faddeev and Faddeev-Yakubovsky calculations were made for K⁻pp, K⁻ppn, K⁻K⁻p and K⁻K⁻pp kaonic nuclear clusters, where the quasi bound states were treated as bound states by employing real separable potential models for the K⁻-K⁻ and the K⁻-nucleon interactions as well as for the nucleon-nucleon interaction. The binding energies and spatial shrinkages of these states, obtained for various values of the interaction, were found to increase rapidly with the interaction strength. Their behaviors are shown in a reference diagram, where possible changes by varying the interaction in the dense nuclear medium are given. Using the Λ(1405) ansatz with a PDG mass of 1405 MeV/c² for K⁻p, the following ground-state binding energies together with the wave functions were obtained: 51.5 MeV (K⁻pp), 69 MeV (K⁻ppn), 30.4 MeV (K⁻K⁻p) and 93 MeV (K⁻K⁻pp), which are in good agreement with previous results of variational calculation based on the Akaishi-Yamazaki coupled-channel potential. The K⁻K⁻pp state has a significantly increased density where the two nucleons are located very close to each other, in spite of the inner NN repulsion. Relativistic corrections on the calculated non-relativistic results indicate substantial lowering of the bound-state masses, especially of K⁻K⁻pp, toward the kaon condensation regime. The fact that the recently observed binding energy of K⁻pp is much larger (by a factor of 2) than the originally predicted one may infer an enhancement of the interaction in dense nuclei by about 25% possibly due to chiral symmetry restoration. In this respect some qualitative accounts are given based on “clearing QCD vacuum” model of Brown, Kubodera and Rho.     

Synthesis and characterization of 4‐arm star side‐chain liquid crystalline polymers containing azobenzene with different terminal substituents via ATRP

4‐Arm star side‐chain liquid crystalline (LC) polymers containing azobenzene with different terminal substituents were synthesized by atom transfer radical polymerization (ATRP). Tetrafunctional initiator prepared by the esterification between pentaerythritol and 2‐bromoisobutyryl bromide was utilized to initiate the polymerization of 6‐[4‐(4‐methoxyphenylazo)phenoxy]hexyl methacrylate (MMAzo) and 6‐[4‐(4‐ethoxyphenylazo)phenoxy]hexyl methacrylate (EMAzo), respectively. The 4‐arm star side‐chain LC polymer with p‐methoxyazobenzene moieties exhibits a smectic and a nematic phase, while that with p‐ethoxyazobenzene moieties shows only a nematic phase, which derives of different terminal substituents. The star polymers have similar LC behavior to the corresponding linear homopolymers, whereas transition temperatures decrease slightly. Both star polymers show photoresponsive isomerization under the irradiation with UV–vis light. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3342–3348, 2007     

Gravitational collapse of a susy star

The evidence for a positive vacuum energy in our universe suggests that we might be living in a false vacuum destined to ultimately decay to a true vacuum free of dark energy. At present the simplest example of such a universe is one that is exactly supersymmetric (susy). It is expected that the nucleation rate of critically sized susy bubbles will be enhanced in regions of high density such as in degenerate stars. The consequent release of energy stored in Pauli towers provides a possible model for gamma ray bursts. Whether or not all or any of the currently observed bursts are due to this mechanism, it is important to define the signatures of this susy phase transition. After such a burst, due to the lifting of degeneracy pressure, the star would be expected to collapse into a black hole even though its mass is below the Chandrasekhar limit. Previous studies have treated the star as fully releasing its stored energy before the collapse. In this article we make an initial investigation of the effects of the collapse during the gamma ray emission.     

Influence of strong magnetic field on β decay in the crusts of neutron stars

βdecay in the strong magnetic field of the crusts of neutron stars is analysed by an improved method. The reactions ⁶⁷ Ni(β^-)⁶⁷ Cu and ⁶² Mn\beta ^-62 Fe are investigated as examples. The results show that a weak magnetic field has little effect on βdecay but a strong magnetic field (B>10¹²G) increases β decay rates obviously. The conclusion derived may be crucial to the research of late evolution of neutron stars and nucleosynthesis in r-process.     

The acircuitic directed star arboricity of subcubic graphs is at most four

A directed star forest is a forest all of whose components are stars with arcs emanating from the center to the leaves. The acircuitic directed star arboricity of an oriented graph G (that is a digraph with no opposite arcs) is the minimum number of arc-disjoint directed star forests whose union covers all arcs of G and such that the union of any two such forests is acircuitic. We show that every subcubic graph has acircuitic directed star arboricity at most four.     

Several remarks on star-shaped sets

Questions related to the properties of unions and intersections of star-shaped compact subsets of finite-dimensional spaces are considered. Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 511–519, April, 1999.     

Bruijning—Nagata and Hashimoto—Hattori characteristics of covering dimension revisited

New dimension functions for topological spaces are introduced in the spirit of Nagata’s approach. Expressions for the new functions in terms of covering dimension include the Bruijning—Nagata and Hashimoto—Hattori formulas.     

On a fluid model of neutron star

We consider an initial boundary value problem for the equations of a fluid spherical model of neutron star considered by Lattimer et al. We estimate the asymptotic decay of the solution, which may serve as a crude estimate of a “thermalization time” for the system.