Shape coexistence at high spin in187Au

High-spin states in¹⁸⁷Au have been populated in the¹⁷²Yb(¹⁹F, 4n) reaction and studied with in-beam spectroscopic techniques using the “Château de Cristal” 4π-multidetector array. A comprehensive level scheme of¹⁸⁷Au has been established. Experimental band crossing frequencies and gains in alignment were deduced. Shape coexistence in¹⁸⁷Au, well established at low spin, is found to survive up to spin 57/2, and manifests itself through well separated oblate and prolate structures.     

Convergence theory for nonconvex stochastic programming with an application to mixed logit

Monte Carlo methods have extensively been used and studied in the area of stochastic programming. Their convergence properties typically consider global minimizers or first-order critical points of the sample average approximation (SAA) problems and minimizers of the true problem, and show that the former converge to the latter for increasing sample size. However, the assumption of global minimization essentially restricts the scope of these results to convex problems. We review and extend these results in two directions: we allow for local SAA minimizers of possibly nonconvex problems and prove, under suitable conditions, almost sure convergence of local second-order solutions of the SAA problem to second-order critical points of the true problem. We also apply this new theory to the estimation of mixed logit models for discrete choice analysis. New useful convergence properties are derived in this context, both for the constrained and unconstrained cases, and associated estimates of the simulation bias and variance are proposed. Research Fellow of the Belgian National Fund for Scientific Research     

On the Functional Characterization of the Analytic Wave Front Set of an Hyperfunction

We give a characterization of d-dimensional modulation spaces with moderate weights by means of the d-dimensional Wilson basis. As an application we prove that pseudodifferential operators with generalized Weyl symbols are bounded on these modulation spaces.     

On bornologicalC $$\overline V $$ (X) spaces

Archiv der Mathematik -     

High-spin structure in154Er

High spin states in the nucleus¹⁵⁴Er have been reinvestigated using the¹²³Sb(³⁵Cl, 4n) reaction and a variety of spectroscopic techniques including excitation functions,γ-γ coincidences,γ angular distribution and linear polarization measurements. From the measured energies, relative intensities and transition multipolarities a new level scheme has been deduced up to an excitation energy of ～12 MeV and spin 36. An interpretation of the experimental results is given in terms of the deformed Woods-Saxon orbitals. Gigantic backbending (superdeformation) effect is studied theoretically within the cranking model.     

Competition between few nucleon emission andγ-ray deexcitation for the reaction systems65Cu+87Rb and40Ar+110Pd

Bothγ-ray and neutron emission have been studied for the reaction systems⁶⁵Cu(237MeV) +⁸⁷Rb→¹⁵²Dy^* and⁴⁰Ar(158MeV)+¹¹⁰Pd→¹⁵⁰Gd^*. By using a sum spectrometer in coincidence with neutron counters, Ge(Li) or Nal detectors, we have measured the totalγ-ray energy and the average totalγ-multiplicity distributions as well as the neutron spectra for various exit channels. These measurements provide strong evidence for thermal equilibrium in reactions involving a small number of emitted neutrons (i.e.⁸⁷Rb(⁶⁵Cu,n or 2n)) at rather high excitation energy (～54MeV). This statistical emission of only a few neutrons is controlled by very strong y-ray competition: theγ-entry line is found not to be parallel to the yrast line. Instead the energy gap is about 8MeV for J～27? and rises to at least 13MeV for J～36?. There are some indications that the main part of the energy from this gap is removed by statisticalγ-ray cascades. The main features of the experimental data for both entrance channels are well reproduced by statistical model calculations with proper attention to the yrast line position and an adjustement of the dipoleγ-ray normalization coefficient. It is conceivable that the y-ray enhancement that we introduce may be related to a lack of knowledge of the absolute level densities at high energy and spin, or possibly to the presence of new or additional degrees of freedom that may enter into the competition between neutron andγ-ray emission.     

Singlet-triplet excitation ratios in Ne III, Ar III and N II under ion impact

Peculiar properties of ion-atom collision systems, in particular deviations from statistical populations of singlet and triplet levels, can be studied by optical spectroscopy. We have extended earlier studies by VUV spectroscopy of a number of collision systems at various collision energies in the 0.01-MeV/nucleon to 1-MeV/nucleon range, involving H₂ ⁺, H⁺, He⁺, He²⁺, Ne⁺, Ar⁺, and N₂ ⁺ as projectiles and Ne, Ar, and N₂ as target gases. Statistically significant deviations of the relative intensities of singlet and triplet lines from simple ratios are observed in the displaced terms of the valence shell of Ne III, corroborating and extending earlier work. For Ar III, the energy dependences of singlet-to-triplet excitation ratios are very different for different projectiles. For N II, in contrast, all observed line ratios are practically independent of the projectile energy. Received 17 November 2000 and Received in final form 31 January 2001     

Crystallographic relations in the Fe?Zn system

The crystallographic relations between the various Fe Zn compounds have been investigated by means of single-crystal X-ray diffraction techniques. These techniques were applied to primary single crystals of each compound upon which after cooling a single crystalline layer of the neighbouring compound richer in zinc was grown. In this way it has been possible to determine relationships in the sequence α – Γ – Γ₁ – δ: No crystallographic relationship could be established for δ–ζ because it proved impossible to grow a single crystalline layer of ζ on δ. The apparently bad compatibility of the two lattices was reflected in the nucleation problems which were always encountered during efforts to grow ζ on δ. The influence of the relationships on the actually observed textures in the δ and ζ layers of hot dip galvanized specimens is discussed.     

Synthesis and Properties of Partially Saturated Fluorenyl-Derived [n]Helicenes Featuring an Overcrowded Alkene

The straightforward, multigram-scale synthesis of the partially saturated H₆-fluoreno[n]helicenes (n=5 or 7) featuring a central, overcrowded alkene is described. The key cyclization step was based on an intramolecular McMurry reaction from the corresponding 1,5-diketones. Chiral stationary phase HPLC analysis and isomer separation indicate that each helicenic compound is constituted of three diastereoisomers at room temperature, i. e. the configurationally stable (R,R,P)/(S,S,M) pair of enantiomers and an apparently achiral compound resulting from the rapid interconversion between the (R,S,P) and (S,R,M) enantiomers. The partially saturated H₆-fluoreno[n]helicenes are oxidatively aromatized to give an efficient access to the corresponding fluoreno[n]helicenes. The chiroptical properties (vibrational and electronic circular dichroism) of the chiral, enantiopure compounds have been measured and analyzed by quantum-chemical calculations, confirming their helicoidal nature.