Super-allowed beta decay of nuclei at the drip-line

We have investigated the continuous particle spectra following the beta decay of the neutron-rich nuclei that terminate the mass 6, 8, 9 and 11 isobaric chains. Strong beta transitions feeding the very top of the spectrum are found systematically. The favoured states are within a few MeV of the energy of the initial state. This phenomenon seems to be linked to the occurrence of a di-neutron structure or neutron halo in the drip-line nuclei.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

2D quantum spin models and Jordan-Wigner fermions

We apply the 2D Jordan-Wigner fermionization to examine the ground state and thermodynamic properties of the square-lattice s=1/2 anisotropic XY model. We compare our findings with the results of different analytical and numerical approaches.     

Gosset’s figure in a Clifford algebra

This note describes a way to realize a “projective” version of Gosset’s 240-vertex semiregular polytope 421 using the Clifford algebra Cl(8) generated by an 8-dimensional vector space equipped with a non-degenerate quadratic form. The 120 vertices of this projective Gosset figure are also seen to coincide with a particular basis for the Lie algebra      

Interaction of light with subwavelength apertures: a comparison of approximate and rigorous approaches

The interaction of an electromagnetic wave with various classes of subwavelength one dimensional apertures is studied in detail, using several approximate and rigorous approaches. The attention is given to a comparison of the revealing basic physical features of the interaction. Several semi-analytical models which are able to predict the enhanced transmission phenomenon are reviewed, applied, and extended: the one-mode periodic model, the model based on the composite diffracted evanescent wave approach, and the so called combined model. Then, a detailed rigorous modeling is performed, using the finite difference time domain method, to study the parametrical dependencies of all critical parameters (i.e. the parameters of the aperture—diameter and thickness, and also the parameters of the surrounding corrugations). The transmission properties of the subwavelength single apertures and apertures with the supporting corrugations on the input side and on both sides of the structure are compared in detail, and the options for their optimizations are discussed. Finally, the results of approximate models are compared with that from the rigorous finite difference time domain modeling, for the case of two important cases, a periodic array of slits and the slit-groove diffraction problem, i.e. a combination of the aperture and one corrugation.     

Synthese,Strukturen, NMR‐ und EPR‐Untersuchungen der binuklearen Bis(N,N,N‴,N‴‐tetraisobutyl‐N′,N″‐isophthaloylbis(selenoureato))‐Komplexe des NiII und CuII

Synthesis, Structures, NMR and EPR Investigations of Binuclear Bis(N,N,N‴,N‴‐tetraisobutyl‐N′,N″‐isophthaloylbis(selenoureato)) Complexes of Ni^II and Cu^II The synthesis of binuclear Cu^II and Ni^II complexes of the quadridentate ligand N,N,N‴,N‴‐tetraisobutyl‐N′,N″‐isophthaloylbis(selenourea) and their crystal structures are reported. The complexes crystallize monoclinic, P2₁/c (Z = 2). In the EPR spectra of the binuclear Cu^II complex exchange‐coupled Cu^II‐Cu^II pairs were observed. In addition the signals of a mononuclear Cu^II species are observed what will be explained with the assumption of an equilibrium between the binuclear Cu^II‐complex (Cu^II‐Cu^II pairs) and oligomeric complexes with “isolated” Cu^II ions. Detailed ¹³C and ⁷⁷Se NMR investigations on the ligand and the Ni^II complex allow an exact assignment of all signals of the heteroatoms.     

Double Pendulum and θ -Divisor

Summary. The equations of motion of integrable systems involving hyperelliptic Riemann surfaces of genus 2 and one relevant degree of freedom are integrated in the framework of the Jacobi inversion problem, using a reduction to the θ -divisor on the Jacobi variety, i.e., to the set of zeros of the θ -function. Explicit solutions are given in terms of Kleinian σ -functions and their derivatives. The procedure is applied to the planar double pendulum without gravity, but it is worked out for any Abelian integral of first or second kind.     

Characterizing uranium oxide reference particles for isotopic abundances and uranium mass by single particle isotope dilution mass spectrometry

Uranium and plutonium particulate test materials are becoming increasingly important as the reliability of measurement results has to be demonstrated to regulatory bodies responsible for maintaining effective nuclear safeguards. In order to address this issue, the Institute for Reference Materials and Measurements (IRMM) in collaboration with the Institute for Transuranium Elements (ITU) has initiated a study to investigate the feasibility of preparing and characterizing a uranium particle reference material for nuclear safeguards, which is finally certified for isotopic abundances and for the uranium mass per particle. Such control particles are specifically required to evaluate responses of instruments based on mass spectrometric detection (e.g. SIMS, TIMS, LA-ICPMS) and to help ensuring the reliability and comparability of measurement results worldwide. In this paper, a methodology is described which allows quantifying the uranium mass in single micron particles by isotope dilution thermal ionization mass spectrometry (ID-TIMS). This methodology is characterized by substantial improvements recently achieved at IRMM in terms of sensitivity and measurement accuracy in the field of uranium particle analysis by TIMS. The use of monodisperse uranium oxide particles prepared using an aerosol generation technique developed at ITU, which is capable of producing particles of well-characterized size and isotopic composition was exploited. The evidence of a straightforward correlation between the particle volume and the mass of uranium was demonstrated in this study. Experimental results have shown that the uranium mass per particle can be measured via the ID-TIMS method to a relative expanded uncertainty of about 10% (coverage factor k = 2). The availability of reliable and validated methods for the characterization of uranium particles is considered to be essential for the establishment of SI-traceable measurement results. It is therefore expected that the method developed in this study is valuable for the certification of particulate materials in which the isotopic composition and the content of uranium must be accurately known.