Weak-coupling expansion of the low-lying energy values in the SU(2) gauge theory on a torus

Relying on analytic results obtained previously, we complete the one-loop computation of the low-lying energy values of the SU(2) gauge theory in an L × L × L periodic box. The expansions are then rewritten in terms of the universal parameter z = M(0⁺) · L (M(0⁺): energy gap in the J^p = 0⁺ sector). We find that the crossover from small-volume to large-volume behaviour is likely to take place at z ? 2. Furthermore, near the crossover, the lowest energy levels (above the ground state) in the 0⁺ sector and the 2⁺ sector are practically degenerate. In each of these sectors there is one more state at about 1.5 · M(0⁺). In the 0^? sector, on the other hand, the lowest energy value is greater than 3 · M(0⁺).     

Ein Algorithmus zur Berechnung der Vielfachheiten von Gewichten

Zusammenfassung Es wird ein Algorithmus zur Berechnung der Vielfachheiten der Gewichte von Darstellungen halbeinfacher Lie-Gruppen angegeben, der auf der Division des Weyl'schen Quotienten für den Charakter beruht. Dabei wird diese Division im Stiefel-Diagramm geometrisch interpretiert.

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This paper is concerned with the multiplicities of the weights of representations of semisimple Lie groups. an algorithm for the calculation of these multiplicities using the division of Weyl's quotient for the character is given. By means of the Stiefel diagram this division is geometrically interpreted.

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Meinem verehrten Lehrer, Professor E. Stiefel gewidmet     

Series of compositions Bi2(M′xM1−x)4O9 (M′, M=Al, Ga, Fe; 0≤x≤1) with mullite-type crystal structure: Synthesis, characterization and O/O exchange experiment

Series of compositions Bi₂(M′_xM_1−x)₄O₉ with x=0.0, 0.1,…, 1.0 and M′/M=Ga/Al, Fe/Al and Fe/Ga were synthesized by dissolving appropriate amounts of corresponding metal nitrate hydrates in glycerine, followed by gelation, calcination and final heating at 800 °C for 24 h. The new compositions with M′/M=Ga/Al form solid-solution series, which are isotypes to the two other series M′/M=Fe/Al and Fe/Ga. The XRD data analysis yielded in all cases a linear dependence of the lattice parameters related on x. Rietveld structure refinements of the XRD patterns of the new compounds, Bi₂(Ga_xAl_1−x)₄O₉ reveal a preferential occupation of Ga in tetrahedral site (4 h). The IR absorption spectra measured between 50 and 4000 cm⁻¹ of all systems show systematic shifts in peak positions related to the degree of substitution. Samples treated in ¹⁸O₂ atmosphere (16 h at 800 °C, 200 mbar, 95% ¹⁸O₂) for ¹⁸O/¹⁶O isotope exchange experiments show a well-separated IR absorption peak related to the M-¹⁸O_c-M vibration, where O_c denotes the common oxygen of two tetrahedral type MO₄ units. The intensity ratio of M-¹⁸O_c/M-¹⁶O_c IR absorption peaks and the average crystal sizes were used to estimate the tracer diffusion coefficients of polycrystalline Bi₂Al₄O₉ (D=2×10⁻²² m²s⁻¹), Bi₂Fe₄O₉ (D=5×10⁻²¹ m²s⁻¹), Bi₂(Ga/Al)₄O₉ (D=2×10⁻²¹ m²s⁻¹) and Bi₂Ga₄O₉ (D=2×10⁻²⁰ m²s⁻¹).     

On the performance of the Prange-Hellinger-Reissner finite element formulation for elasto-plasticity at small strains

This contribution deals with a stress-displacement mixed finite element formulation for elasto-plasticity within the framework of small deformations based on the Prange-Hellinger-Reissner (PHR) functional. The interpolations for the displacements are given by standard Lagrangian shape functions and a 5-parameter discontinuous interpolation is introduced for the stresses which was published by [1]. Based on the principle of maximum plastic dissipation the flow rule and hardening law will be derived by regarding a von Mises yield criterion, see [2]. In contrast to [3], we apply a point-wise enforcement of the flow rule, hardening law and loading/unloading conditions. This work is related to the physically nonlinear mixed finite element based on the Prange-Hellinger-Reissner formulations for elasto-plasticity, [4]. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The K<Superscript>-</Superscript>α scattering length and the reaction dd↦αK<Superscript>+</Superscript>K<Superscript>-</Superscript>

We present predictions for the K^-α scattering length obtained within the framework of the multiple-scattering approach. Evaluating the pole position of the K^-α scattering amplitude within the zero-range approximation, we find a loosely bound K^-α state with a binding energy of E_R = - 2,..., - 7 MeV and a width Γ_R = 11,..., 18 MeV. We propose to measure the K^-α scattering length through the final-state interaction between the α and K^--meson produced in the reaction dd↦αK⁺K^-. It is found that the K^-α invariant-mass distribution from this reaction at energies near the threshold provides a new tool to determine the s-wave K^-α scattering length.     

Annealing studies on the absorption spectrum of 41K-atoms trapped in an argon matrix

Argon crystals were doped with 0.2 ppm of ⁴¹K through the nuclear reaction ⁴⁰Ar (n, β^-) ⁴¹K. The absorption spectrum from 300 nm to 800 nm was measured as a function of the annealing temperature. Absorption ← 4²s_{$\text{1}\text{2}$} transition of the free atom could be bands corresponding to the 4²p_{$\text{1}\text{2}$}, _{$\text{3}\text{2}$} ← 4²s_{$\text{1}\text{2}$} and 5²p_{$\text{1}\text{2}$}, _{$\text{3}\text{2}$} ← 4²s_{$\text{1}\text{2}$} transition of the free atom could be observed. The absorption bands depend strongly on the annealing temperature. An increase in the annealing temperature results in a blue shift of the absorption bands.