A characterization of the \Sigma_1-definable functions of KP\omega + (uniform\; AC)

The subject of this paper is a characterization of the -definable set functions of Kripke-Platek set theory with infinity and a uniform version of axiom of choice: . This class of functions is shown to coincide with the collection of set functionals of type 1 primitive recursive in a given choice functional and . This goal is achieved by a G?del Dialectica-style functional interpretation of and a computability proof for the involved functionals. Received October 9, 1996     

Conformal field algebras with quantum symmetry from the theory of superselection sectors

According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors—i.e. different irreducible representations of the observable algebra—are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central chargec=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid groupB which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hilbert space of physical states. It obeys local braid relations in an appropriate weak sense.     

Ab initio calculations of small hydrides including electron correlation

Five different structures of CH₅ ⁺ and one structure of CH₅ ^– are calculated using a gaussian basis both in the SCF approximation and with the inclusion of electron correlation in the independent electron pair approximation (IEPA). While on SCF level the C _sstructure of CH₅ ⁺ has to lowest energy, the energy difference between the C _sand C _2vstructures becomes negligible if correlation is included. In contrast to this the approach of a proton to CH₄ at large and intermediate distances is most favorable towards a corner of the CH₄ tetrahedron which means a structure. The decomposition of CH₅ ⁺ into CH₃ ⁺ and H₂ requires 20kcal/mol on SCF level and 40 kcal/mol if correlation is included.     

Perhalogenmethylmercapto-heterocyclen, (VII) [1] konkurrenzreaktionen elektronenarmer,substituierter aromaten um die halogenmethylmercapto- BZW. Chlorgruppe von Cl3-nFnCSCl in starken saeuren

Electron-deficient aromatics, such as 2,5-bis(trifluoromethylmercapto)thiophene ($\text{1a}$) or (trifluoromethylmercapto)benzene ($\text{8a}$), react with F₃CSCl in the presence of F₃CSO₃ as a catalyst to give mainly 3-chloro-2,5-bis(trifluoromethylmercapto)thiophen ($\text{3a}$) and 1-chloro-4- or 2-(trifluoromethylmercapto)benzene ($\text{10}$, respectively. This reaction competes with the one expected to result in 2,3,5-tris(trifluoromethylmercapto)thiophene ($\text{2a}$) and 1,4- and 1,2-bis(trifluoromethylmercapto)benzene ($\text{9}$,$\text{9′}$), respectively. Further reactions of deactivated aromatics with Cl_3-nF_nCSCl show that the chlorine substitution is in general catalysed by strong acids. Reaction mechanisms are proposed for both Substitutions. The Cl_3-nF_nCS group in aromatics exerts a -M-effect in the case of an attack of a positive ion, e.g. H^⊕, the well-known +M-effect in the case of reactions with positively polarized molecules, e.g. CF₃S^β+Cl^β-.     

The direct determination of Brueckner orbitals with application to the H2 molecule

An iterative procedure is presented which allows for the direct determination of approximate Brueckner orbitals for small atomic and molecular systems. Starting from the Hartree-Fock determinant one first determines pair natural orbitals (PNOs) of independent electron pairs in the HF-field of the remaining electrons. The use of the generalized Brillouin-theorem then leads to an approximate Brueckner orbital for each electron pair. This procedure must be repeated up to self-consistency which is reached generally after 4–5 macroiterations. Applications to the ground state of H₂ show how important the use of Brueckner orbitals is to get good expectation values of one-electron operators and the correct asymptotic behaviour of the potential energy curve for large internuclear distances.

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Zusammenfassung Es wird eine Iterationsmethode beschrieben, die eine direkte Bestimmung genäherter Bruecknerorbitale für kleine atomare und molekulare Systeme gestattet. Ausgehend von der Hartree-Fock-Determinante bestimmt man zunächst Paar-NOs (PNOs) der unabhängigen Elektronenpaare im HF-Feld der übrigen Elektronen des Systems. Mit Hilfe des verallgemeinerten Brillouin-Theorems erhält man dann ein genähertes Bruecknerorbital für jedes Elektronenpaar. Dies Verfahren muß bis zur Selbstkonsistenz wiederholt werden, die man im allgemeinen nach 4–5 solcher Makroiterationen erreicht. Anwendung auf den Grundzustand des H₂-Moleküls zeigt, wie wichtig die Benutzung von Bruecknerorbitalen ist, wenn man gute Erwartungswerte von Einelektronenoperatoren und das richtige asymptotische Verhalten der Potentialkurve bei großen Abständen erhalten will.

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Résumé On propose un schéma itératif qui permet le calcul direct des orbitales de Brueckner approchées pour les atomes et les petites molécules. Partant du déterminant Hartree-Fock on calcule d'abord les PNO (pair natural orbitals) des paires indépendantes d'électrons dans le champ effectif des autres électrons dans l'approximation Hartree-Fock. Ensuite le théorème de Brillouin généralisé permet de calculer les orbitales de Brueckner approchées pour chaque paire d'electrons. On recommence le calcul des PNO, la self-consistance de cette méthode itérative s'établit en général au bout de 4 ou 5 macroitérations. Les applications à la molécule H₂ démontrent que l'utilisation d'orbitales de Brueckner s'impose si l'on s'intéresse à des bonnes valeurs moyennes d'opérateurs monoélectroniques ou au comportement asymptotique correct des courbes de potentiel aux grandes distances.

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Dedicated to the memory of Prof. K. H. Hansen.     

Ultraviolet Bremsstrahlung spectroscopy

Recent experimental progress has introduced Bremsstrahlung spectroscopy especially in the isochromat mode as a new surface analytical tool. Bremsstrahlung production may be regarded as radiative capture by solids and is therefore the inverse process to the well known photoemission. In contrast to photoemission which probes occupied electronic states at solid surfaces, Bremsstrahlung spectroscopy opens up the possibility to investigate unoccupied electronic states including the important region between Fermi- and vacuum energy. Measurements on polycrystalline materials will be discussed on the basis of an isotropic three step model for Bremsstrahlung emission. More recent experiments on single crystals with electrons of well defined energy and initial momentum $\text{k}\text{}$ have demostrated that $\text{k}\text{}$-resolved spectroscopy provides energy versus momentum dispersion relations for unoccupied bands. Application of spin polarized electron beams has advanced $\text{k}\text{}$-resolved Bremsstrahlung spectroscopy to a state of maturity comparable to spin polarized angle resolved photoemission. This paper attempts to review the development and summarize the present state of ultraviolet Bremsstrahlung isochromat spectroscopy.     

Preferred dimerization of tetra-tolyl- and tetra-tosylurea derivatives of flexible and rigidified calix[4]arenes

The dimerization of tetratolyl- and tetratosyl-urea derivatives 1 and 2, derived from a tetrapentoxy calix[4]arene in the cone conformation and of the corresponding tetra-urea derivatives 3 and 4, in which the cone conformation is rigidified by the two crown-3 tethers, have been studied. All six possible equimolar mixtures were examined by 1H NMR using CDCl3 and CD2Cl2 as solvents. While no heterodimers are found for the combinations 1/3 and 2/4 in either solvent, all remaining combinations lead to the (exclusive) formation of heterodimers in CD2Cl2. In CDCl3 heterodimers are only observed for the combinations of 3 with 2 or 4. These results are discussed in terms of entropic and enthalpic contributions and compared with MD-simulations in a box of chloroform solvent molecules.     

Electroexcitation of nucleon resonances

In these lectures the status of electromagnetic excitation of nucleon resonances is reviewed and some of the open problems of the structure and spectroscopy of light-quark baryons are discussed. The basic formalism for describing electromagnetic processes is introduced but not derived.Lecture given at the 8th Summer School on Intermediate-Energy Physics: Hadron Dynamics at Low and Intermediate Energies, Prague, July 10–14, 1995.     

Asymptotic behavior of -semigroups in Banach spaces

We present optimal estimates for the asymptotic behavior of
strongly continuous semigroups in terms of growth abscissas of the resolvent function of the generator . In particular we give Ljapunov's classical stability condition a definite form for (infinite dimensional) abstract Cauchy problems: The abscissa of boundedness of equals the growth bound of the classical solutions of .