Detailed nuclear structure studies far from stability

State-of-the-art spectroscopy of nuclei far from stability has achieved an extraordinary level of sophistication and detail in the last ten years. In principle, if a state can be populated, it can be characterized by its energy, spin, parity, and major decay paths. Sometimes its lifetime can be measured. In practice, one is confronted with enormous complexity. To convert raw spectroscopic data into nuclear structure data involves a complex process of disentangling gamma rays and conversion electrons into decay schemes. Specifically, coincidence techniques, especially coincidence intensities, play a crucial role in this process. Recent examples and methods from work done at UNISOR are presented.     

Cyclic trihydroxamic acid derivatives

In the crystal structures of two cyclic trihydroxamic acid derivatives containing the same substructure unit, viz. 1,3,5‐trihydroxy‐1,3,5‐triazinane‐2,4,6‐trione dihydrate, C₃H₃N₃O₆·2H₂O, (I), and 1,3,5‐benz­yloxy‐1,3,5‐triazinane‐2,4,6‐trione, C₂₄H₂₁N₃O₆, (II), there is no significant difference in the geometric parameters. In (I), there are 11 hydrogen bonds of the O—H⋯O type inter­connecting the mol­ecules in a three‐dimensional network, while in (II) there are only two weak C—H⋯O hydrogen bonds. The results of IR spectroscopic analysis are in good agreement with the crystallographic study.     

Mercury(II) complex with terpyridine: structure of the 2∶1 solvate of [Hg(terpy)2](CF3SO3)2 with acetone

[Hg(terpy)₂](CF₃SO₃)₂·0.5(CH₃)₂CO crystallizes in the triclinic space group witha=14.631(6),b=15.258(4),c=18.785(7) Å, =69.66(2), =70.72(1), =88.55(1)°. The crystal structure consists of two independent [Hg(terpy)₂]²⁺ cations, four trifluoromethanesulfonate anions and an acetone molecule in the asymmetric unit. Each mercury atom is coordinated by two tridentate terpyridine ligands forming an irregular six-coordination polyhedron. The Hg–N bond lengths range from 2.27(2) to 2.53(2) Å.     

Direct Potentiometric Study of Cationic and Nonionic Surfactants in Disinfectants and Personal Care Products by New Surfactant Sensor Based on 1,3-Dihexadecyl−1H-benzo[d]imidazol−3-ium

A novel, simple, low-cost, and user-friendly potentiometric surfactant sensor based on the new 1,3-dihexadecyl−1H-benzo[d]imidazol−3-ium-tetraphenylborate (DHBI–TPB) ion-pair for the detection of cationic surfactants in personal care products and disinfectants is presented here. The new cationic surfactant DHBI-Br was successfully synthesized and characterized by nuclear magnetic resonance (NMR), Fourier transform infrared (FTIR) spectrometry, liquid chromatography–mass spectrometry (LC–MS) and elemental analysis and was further employed for DHBI–TPB ion-pair preparation. The sensor gave excellent response characteristics for CTAB, CPC and Hyamine with a Nernstian slope (57.1 to 59.1 mV/decade) whereas the lowest limit of detection (LOD) value was measured for CTAB (0.3 × 10⁻⁶ M). The sensor exhibited a fast dynamic response to dodecyl sulfate (DDS) and TPB. High sensor performances stayed intact regardless of the employment of inorganic and organic cations and in a broad pH range (2−11). Titration of cationic and etoxylated (EO)-nonionic surfactant (NSs) (in Ba²⁺) mixtures with TPB revealed the first inflexion point for a cationic surfactant and the second for an EO-nonionic surfactant. The increased concentration of EO-nonionic surfactants and the number of EO groups had a negative influence on titration curves and signal change. The sensor was successfully applied for the quantification of technical-grade cationic surfactants and in 12 personal care products and disinfectants. The results showed good agreement with the measurements obtained by a commercial surfactant sensor and by a two-phase titration. A good recovery for the standard addition method (98–102%) was observed.     

The Langlands classification for non-connected -adic groups II: Multiplicity one

For a non-connected reductive -adic group, we prove that the Langlands subrepresentation appears with multiplicity one in the representation parabolically induced from the corresponding Langlands data.

     

Tl-based superconducting films prepared by aerosol spray deposition and thallinated in an open system

Superconducting Tl-based films were prepared on a LaAlO₃ single crystal substrate. Spray pyrolysis of Ba, Ca and Cu nitrate solutions was used for deposition of the precursor films. They were subsequently ex-situ thallinated in flowing oxygen (open system). While the superconducting Tl-2212 phase formed at an annealing temperature of 880°C, thallination at 900°C led to the formation of a Tl-2223 /Tl-2212 mixture. The amount of Tl-2223 increased with prolonged thallination, whereas the Tl-2212 phase progressively disappeared. Films prepared in such a manner were c-oriented and contained only low amounts of non-superconducting impurities. The resulting samples were characterized by XRD and SEM and their T _C values were determined by resistive four-point measurements. They showed critical temperatures in the range of T _ON = 125–135 K, T _C0 = 91–93 K. Differences between the composition and properties of the obtained films and those thallinated in closed systems under 50 kPa of oxygen are discussed in this paper. Results show that the Tl-2212 → Tl-2223 transformation proceeds at a slower rate under flowing oxygen than in a closed system. Presented at 5-th International Conference Solid State Surfaces and Interfaces, November 19–24, 2006, Smolenice Castle, Slovakia.     

Hydrolysis and retro‐aldol cleavage of ethyl threo‐2‐(1‐adamantyl)‐3‐hydroxybutyrate: competing reactions

The hydrolysis of ethyl threo‐2‐(1‐adamantyl)‐3‐hydroxybutyrate ( 1 ) and the parent ester ethyl 3‐hydroxybutyrate ( 4 ) has been studied experimentally and computationally. In the hydrolysis of threo‐ester 1 with 2 M NaOH, predominantly retro‐aldol product was observed, whereas the hydrolyzed product was present in a minor amount. When the reaction is carried out under the same conditions with the parent ester ethyl 3‐hydroxybutyrate ( 4 ), hydrolyzed product is exclusively observed. The competitive pathways, namely hydrolysis and the retro‐aldol reaction for 1 and 4 were investigated using DFT calculations in the both gas and solvent phase. The calculated results in the solvent phase at B3LYP/6–31 + G* level revealed that the formation of retro‐aldol products is kinetically preferred over the hydrolysis of threo‐ester 1 in the presence of a base. However, the parent ester 4 showed that the retro‐aldol process is less favored than the hydrolysis process under similar conditions. The steric effect imposed by the bulky adamantyl group to enhance the activation barriers for the hydrolysis of the ethyl threo‐2‐(1‐adamantyl)‐3‐hydroxybutyrate ( 1 ) was further supported by the calculations performed with tert‐butyl group at the α‐carbon atom of ethyl 3‐hydroxybutyrate ( 7 ). Copyright © 2010 John Wiley & Sons, Ltd.     

Requirements in mathematics textbooks: a five-dimensional analysis of textbook exercises and examples

Mathematics textbooks play a very important role in mathematics education and textbook tasks are used by students for practice to a large extent. Since the nature of the tasks may influence the way students think it is important that the textbooks provide a balance of a variety of tasks. The analyses of the requirements in textbook tasks contain the usual dimensions of content, cognitive demands, question type and contextual features. The aim of this study is to embed a new fifth dimension into the framework: mathematical activities. This addresses the question of what a student should do in a particular textbook task: to represent, to compute, to interpret or to use argumentation. The analysis encompassed more than 22,000 tasks from the most commonly used Croatian mathematics textbooks in the 6th, 7th and 8th grade. The results show that the textbooks do not provide a full range of task types. There is an emphasis on computation, while argumentation and interpretation activities, reflective thinking and open answer tasks are underrepresented. The study revealed that incorporating mathematical activities into the multidimensional framework of textbook tasks may help to better understand the opportunities to learn which are afforded students by using mathematics textbooks.