Towards finite density QCD with Taylor expansions

Convergence properties of Taylor expansions of observables, which are also used in lattice QCD calculations at non-zero chemical potential, are analyzed in an effective Nf=2+1$N_f=2+1$ flavor Polyakov quark–meson model. A recently developed algorithmic technique allows the calculation of higher-order Taylor expansion coefficients in functional approaches. This novel technique is for the first time applied to an effective Nf=2+1$N_f=2+1$ flavor Polyakov quark–meson model and the findings are compared with the full model solution at finite densities. The results are used to discuss prospects for locating the QCD phase boundary and a possible critical endpoint in the phase diagram.     

Studying pion effects in the quark propagator

Within the framework of Schwinger-Dyson and Bethe-Salpeter equations we investigate the importance of pions for the quark-gluon interaction. To this end we choose a truncation for the quark-gluon vertex that includes intermediate pion degrees of freedom and adjust the interaction such that unquenched lattice results for various current quark masses are reproduced. After extrapolation to the physical point we find a considerable contribution of the pion back reaction to the quark mass function as well as to the chiral condensate.     

E0 andM1 excitations in56Ni

The centroid energy and the decay width of the giant monopole resonance in the unstable nucleus⁵⁶Ni are predicted. The resulting 0⁺, ΔT=0 strength distribution, including the escape and the spreading width, displays a structure centered at around 18 MeV with the total width of about 5 MeV. We also study theM1 response in this nucleus which shows a strong isovector transition at 9.6 MeV and a weak isoscalar one at 7.5 MeV.     

Korbförmige wirtmoleküle: : Tetrahydrofuran-Einschluss und Gast-selektive Katalyse des H/D-Austauschs in saurer Lösung

Macropolycyclic molecules ($\text{6a}$,$\text{b}$, $\text{7}$ and $\text{11}$) with an extended basket-shaped skeleton including a benzene ring, which acts as a floor plate, have been synthesized for the first time. The cavity of the hydrochloride of $\text{7}$ retains tetrahydrofuran even in water solution. The host $\text{6a}$ strongly accelerates guest-selective H/D exchanges in aromatic 1,3-diols.     

Gamow-Teller resonance in hot nuclei and astrophysical applications

A formalism based on thermo field dynamics is described. It allows the effect of the temperature on the strength distribution of charge-exchange transitions in hot nuclei to be taken into account. Numerical calculations with the pair correlations in the BCS approximation and the schematic στ interaction are carried out for Gamow-Teller transitions in the ⁵⁶Fe nucleus. The electron capture and β^? decay rates are calculated for this nucleus at temperatures and densities corresponding to the advanced stage of the evolution of massive stars.     

Understanding what a proof is: a classroom-based approach

Being unaware of the assumptions underlying a deductive argument is widespread among learners and is a major stumbling block to their understanding of proof. Thus, the basic idea of the present paper is that at some points in the course of secondary education there should be classroom-based interventions addressing this difficulty and making the axiomatic organization of mathematics a theme. Students should be made aware that there are axioms in mathematics, what their role is and how mathematicians come to agree about which axioms should be accepted. An axiom which is not yet accepted is simply a hypothesis. A hypothesis is evaluated by deductively drawing consequences and by investigating whether these consequences agree with experience or should be accepted for other reasons. The teaching intervention discussed in this paper exemplifies this idea by way of the example of ancient attempts at modelling the path of the sun, the so-called “anomaly of the sun”. It is investigated to what extent the teaching intervention fostered students’ understanding of the conditionality of mathematical/astronomical statements, that is, of the fact that the truth of these statements is dependent on the initial hypotheses.     

The medium modification of hadrons

The spectral properties of hadrons in hot and dense matter are discussed with focus on spontaneously broken chiral symmetry in the vacuum and its restoration in the medium.