Few-valence-particle excitations around doubly magic 132Sn

Prompt γ-ray cascades in neutron-rich nuclei around doubly-magic ¹³²Sn have been studied using a ²⁴⁸Cm fission source. Yrast states located in the N = 82 isotones ¹³⁴Te and ¹³⁵I are interpreted as valence proton and neutron particle-hole core excitations with the help of shell model calculations employing empirical nucleon-nucleon interactions from both ¹³²Sn and ²⁰⁸Pb regions.     

Study of spontaneous fission with EUROGAM

Prompt γ radiation following spontaneous fission has been measured using the EUROGAM 2 array. Using these data and newly developed analysis techniques a number of subjects were studied, which are briefly discussed. One of these subjects, shape transition in A≈100 Sr and Zr nuclei is discussed in more detail. Quadrupole moments were determined for rotational bands in the N=58,59,60,62 and 64 Sr and Zr isotopes. Deformation parameters, which increase from β₂ ≈ 0.1 at N=56 to β₂ ≈ 0.4 at N=64, suggest that in strontium and zirconium isotopes shape change happens gradually between N=56 and N=62 and is probably due to an occupancy of three or more deformation-driving orbitals of h_11/2 parentage.     

On extension and refinement of the Poincaré inequality

The aim of this paper is to analyze the heat semigroup ${(\mathcal{N}_{t})_{t >0 } = \{e^{t \Delta}\}_{t >0 }}$ generated by the usual Laplacian operator Δ on ${\mathbb{R}^{d}}$ equipped with the d-dimensional Lebesgue measure. We obtain and study, via a method involving some semigroup techniques, a large family of functional inequalities that does not exist in the literature and with the local Poincaré and reverse local Poincaré inequalities as particular cases. As a consequence, we establish in parallel a new functional and integral inequality related to the Ornstein–Uhlenbeck semigroup.     

Columnar Liquid‐Crystalline Dinaphthoperylenetetracarboxdiimides

Although the double Friedel–Crafts acylation of arenes with ethyl chloroglyoxylate is hindered by the strongly deactivating effect of the first‐entering glyoxylic substituent, the double reaction is successful with the reactive arene perylene under long reaction times and with concomitant ester hydrolysis. The reaction is regiospecific, giving the 3,9‐regioisomer exclusively. This perylenylenediglyoxylic acid is condensed first with o‐bromophenylacetic acid and then with α‐branched alkylamines to yield the title compounds. Whilst the corresponding tetraalkyl esters only show monotropic mesophases, these diimides show enantiotropic columnar mesophases that can be maintained at room temperature if racemically branched alkyl chains of moderate size are used. A palladium‐induced C?C bond migration during the build‐up of the arene system leads to an isomeric side product of reduced symmetry that can be isolated by aggregation‐controlled chromatographic separation. The HOMO and LUMO energies of the title compounds are considerably higher than those of established perylenetetracarboxdiimides.     

A single parameter determines mesophase transitions in Swollen Liquid Crystals

We report how the control of a single parameter, the co-surfactant, determines the phase transitions of oil-in-water swollen liquid crystals (SLCs) prepared with cetyltrimethylammonium bromide (CTAB), from cubic to hexagonal, lamellar, and finally sponge-like structures. SLCs are complex mixtures (surfactant + co-surfactant + water + salt + oil) usually prepared to form hexagonal mesophases, with cell parameters tunable between 3 and 30 nm. These hexagonal mesophases were successfully used as nanoreactors to prepare a broad range of nanostructured materials. Because the potential of these mesophases as adaptive nanoreactors has not been extended to other liquid crystal geometries than the hexagonal, we studied in a first step the structure evolution of SLCs made with CTAB, cyclohexane, pentanol-1, water and different stabilising salts. We used small-angle X-ray scattering (SAXS), polarised light microscopy and Freeze-Fracture TEM to provide a partial phase diagram and list the different mesophases obtained as a function of composition. We report that the adjustment of a single parameter, the co-surfactant (pentanol-1), determines the phase transition between cubic, hexagonal, lamellar, and sponge-like structures, all other parameters such as the nature and concentration of salt, or amount of oil being constant.     

Modified auxiliary boundary conditions method for an ill-posed problem for the homogeneous biharmonic equation

In this paper, we are interested in the inverse problem for the biharmonic equation posed on a rectangle, which is of great importance in many areas of industry and engineering. We show that the problem under consideration is ill-posed; therefore, to solve it, we opted for a regularization method via modified auxiliary boundary conditions. The numerical implementation is based on the application of the semidiscrete finite difference method for a sequence of well-posed direct problems depending on a small parameter of regularization. Numerical results are performed for a rectangle domain showing the effectiveness of the proposed method.     

High-spin states in the neutron rich fission fragments138Xe and139Xe

High-spin structures in the neutron-rich nuclei^138Xe and¹³⁹Xe have been investigated by observing prompt γ -rays from the spontaneous fission of²⁴⁸Cm with the Eurogam spectrometer. The partial level schemes were constructed on the basis of double-, triple- and quadruple-γ coincidences. The ground state band in¹³⁸Xe has been extended up to 5 MeV excitation energy. The structure of the newly observed medium-spin states in¹³⁹Xe is similar to the one of heavier N=85 isotones where vf ₇ ^2/3 , vh_9/2f ₇ ^2/2 and vf ₇ ^2/3 ? 3^? multiplets have been observed.     

Shapes of the neutron-rich 88-94Kr nuclei

Neutron-rich, ^88-94Kr nuclei, populated in spontaneous fission of ²⁴⁸Cm, have been studied with EUROGAM 2, by measuring prompt γ-rays. Many new excited states in even-even Kr isotopes have been identified. For the first time spins and parities were determined experimentally in these nuclei. Our results indicate that the quadrupole deformation of Kr isotopes will appear only above N = 58, as observed in Sr and Zr nuclei. The newly found 3^- level at 1506.4 keV in ⁹⁰Kr suggests the exsistence of a new region of increased octupole correlations, probably associated with the ν(d _5/2 h _11/2) pair of Δl = Δj = 3 orbitals. Received: 18 September 2000 / Accepted: 18 October 2000     

Columnar Liquid‐Crystalline Dibenzopentacenodithiophenes by Photocyclization

The twofold glyoxylic Perkin reaction of perylene‐3,9‐diglyoxylic acid with thiophene‐diacetic acid followed by oxidative photocylization and reaction with α‐branched primary alkylamines yields columnar liquid‐crystalline diimides with two sulfur atoms in the condensed arene system. A broad temperature range of the hexagonal columnar mesophase is induced by racemic doubly branched alkyl chains. The HOMO and LUMO energy levels of these thiophene‐derived diimides qualify them as electron donors with respect to perylene diimides.