On the structure of analytic renormalization

A direct proof is given that analytic renormalization has an additive structure and hence may be implemented by counterterms in the Lagrangian.     

Inelasticα-scattering from100Mo

The level scheme of¹²³Ba has been extended. Bands based on the [523]7/2^? and [402]5/2⁺ Nilsson configurations were established to spins 59/2 (67/2 tentatively) and 29/2, respectively. The first backbend in this region is found to be caused by the alignment of a pair of h_11/2 protons. For the first time in this mass region there is evidence for a second crossing due to the alignment of an h_11/2 neutron pair in a neutron h_11/2 band. The experimental results are compared with self-consistent cranking calculations. A previous suggestion that large γ-deformation is needed to explain the observed bandheads is not supported.     

Statistical mechanics of the nonlinear Schrödinger equation. II. Mean field approximation

We investigate a mean field approximation to the statistical mechanics of complex fields with dynamics governed by the nonlinear Schrödinger equation. Such fields, whose Hamiltonian is unbounded below, may model plasmas, lasers, and other physical systems. Restricting ourselves to one-dimensional systems with periodic boundary conditions, we find in the mean field approximation a phase transition from a uniform regime to a regime in which the system is dominated by solitons. We compute explicitly, as a function of temperature and density (L ² norm), the transition point at which the uniform configuration becomes unstable to local perturbations; static and dynamic mean field approximations yield the same result.     

Mayer coefficients in two-dimensional coulomb systems

We show that, for neutral systems of particles of arbitrary charges in two dimensions, with hard cores, coefficients of the Mayer series for the pressure exist in the thermodynamic limit below certain thresholds in the temperature. Our methods apply also to correlation functions and yield bounds on the asymptotic behavior of their Mayer coefficients.     

Study of the out-of-plane emission of protons and light fragments in symmetric heavy-ion collisions

Midrapidity protons from²⁰⁹Bi+²⁰⁹Bi collisions were measured with the Kaon Spectrometer at SIS at incident energies of E _Lab /A=400, 700 and 1000 MeV. Additionally, light fragments were analysed at 400 MeV. We have investigated the azimuthal emission pattern of the particles relative to the reaction plane as function of transverse momentum, bombarding energy and impact parameter. We observe an enhanced emission of particles perpendicular to the reaction plane at all bombarding energies. The ratio of the number of particles emitted out-of-plane/in-plane increases strongly with the particles transverse momentum. The anisotropy decreases with increasing beam energy. Composite particles show a much stronger effect than protons.     

Pion production in mass- symmetric heavy ion collisions at 0.8–1.8 AGeV

Double differential cross sections of positively charged pions and protons have been measured in nuclear collisions of mass-symmetric systems (Ne+NaF, Ni+Ni, Au+Au, Bi+Pb) at incident energies between 0.8 and 1.8 AGeV as a function of the centrality of the reaction. Using a magnetic spectrometer pions and protons were detected with laboratory angles between 40 and 48 degrees, and with momenta up to about 1400 MeV/c. This setting allows for the study of pions and protons emitted close to midrapidity. The center-of-mass pion spectra deviate from a Boltzmann distribution. The inverse slope parameters of the high-energetic pions are smaller than those of the proton spectra and they exhibit a weaker centrality dependence. A scenario is presented where the shape of the pion spectra reflects the decay kinematics of nucleonic resonances embedded in the thermal and the collective motion of the nucleons in the reaction zone. The number of emitted pions per participating nucleon is higher for light than for heavy mass systems. For a given mass system, the total pion multiplicity increases linearly with the number of participating nucleons, whereas the multiplicity of high-energy pions increases more than linearly. This result is consistent with a scenario where the high-energy pions are produced in multiple energetic baryon-baryon collisions occurring in the high-density phase of the collision.     

Beitrag zur Polymorphic organischer Substanzen

Zusammenfassung Es wurden 15 organische Verbindungen angegeben, bei denen Polymorphie gefunden wurde. 10 davon wurden näher beschrieben, wobei für die Untersuchungen thermomikroskopische, differential- scanning-calorimetrische und IR-spektroskopische Methoden verwendet wurden. Ausführlicher beschrieben wurden 1-Adamantyl-essigsäure, Äthylendiamintetraacetonitril, N-Äthylthioharnstoff, Benzilsäuremethylester, Benzylmalonsäure, Biphenyl-2-carbonsäure, Bis-(cyklohexanon)-oxaldihydrazon, l,4-Bis-[2-(4-methyl-5-phenyl)-oxa-zolyl]benzol, Butyloxycarbonyl-L-alanin-4-nitrophenylester und 3,3-Dimethylglutarsäure.

---

Contribution to the polymorphismn of organic substances

Summary Fifteen organic substances in which polymorphism was found are specified. Ten of these were described in detail. Thermomicroscopic, differential scanning calorimetric and IR spectroscopic methods were used for the investigations. 1-Adamantylacetic acid, ethylene diamine tetracetonitrile, N-ethylthiourea, benzyl acid methyl ester, benzyl malonic acid, biphenyl-2-carbonic acid, bis-(cyclohexanone)-oxaldihydrazone, l,4-bis-2-(4-methyl-5-phenyl)-oxazolyl benzene, butyloxycarbonyl-L-alanine-4-nitrophenylester and 3,3-dimethylglutaric acid are described in more detail.

     

Influence of substituents on regioselectivity of vinyllithium formation with acrylic acid Derivatives

β-Alkoxy, β-dialkylamino, and β-N-alkylacylamino substituents determine the regioselectivity of the vinylic deprotonation of acrylic ester and nitrile derivatives: either α- or β-vinyllithium species may be generated. The corresponding acrylamides or systems with additional α-alkyl or α-methylmercapto substituents are lithiated at β-position.     

Mean field theory of directed polymers with random complex weights

We show that for the problem of directed polymers on a tree with i.i.d. random complex weights on each bond, three possible phases can exist; the phase of a particular system is determined by the distribution of the random weights. For each of these three phases, we give the expression of the free energy per unit length in the limit of infinitely long polymers. Our proofs require several hypotheses on the distribution , most importantly, that the amplitude and the phase of each complex weight be statistically independent. The main steps of our proofs use bounds on noninteger moments of the partition function and self averaging properties of the free energy. We illustrate our results by some examples and discuss possible generalizations to a larger class of distributions, to Random Energy Models, and to the finite dimensional case. We note that our results are not in agreement with the predictions of a recent replica approach to a similar problem.