The vacuum expectation value of the S-matrix is represented, following HORI, as a functional integral and separated according to Svac=exp( — i W) ∫ D φ exp( —i ∫ dx Lw). Now, the functional integral involves only the part Lw of the Lagrangian without derivatives and can be easily calculated in lattice space. We propose a graphical scheme which formalizes the action of the operator W = f dx dy δ (x—y) (δ/δ(y))⬜x(δ/δ(x)) . The scheme is worked out in some detail for the calculation of the two-point-function of neutral BOSE fields with the self-interaction λ φM for even M. A method is proposed which under certain convergence assumptions should yield in a finite number of steps the lowest mass eigenvalues and the related matrix elements. The method exhibits characteristic differences between renormalizable and nonrenormalizable theories.
Salt domes represent deep geological formations which are under consideration as final repositories for irradiated research reactor fuel elements. For long-term safety aspects the mobilisation of the radionuclides due to a water ingress is intensively investigated. At the Institute of Energy Research (IEF-6), leaching experiments were performed in a hot cell facility with UAlx-Al and U3Si2-Al dispersed research reactor fuel elements in repository-relevant MgCl2-rich salt brines under anaerobic conditions. The fuel plates corroded completely within one year and a Mg-Al-layered double hydroxide (LDH) with chloride as interlayer anion was identified as one crystalline phase component of the corrosion products (secondary phases). This Mg-Al-LDH was synthesized, characterized, and the ability to retard europium by an incorporation process was investigated. Europium, as a representative for lanthanides, was identified to be one of the radionuclides which were found in the corrosion products. We could show that europium was incorporated in the lattice structure. LDHs have high anion exchange capacities that enhance their potential to remove anionic contaminants from aqueous systems.
In this work the sorption behaviour of selenium in the chemical form as selenite (SeO32−) on Mg-Al-LDH and on Mg-Al-Eu-LDH was investigated. Especially the influence of the larger europium-III ion was of interest. It represents in the Mg-Al-Eu-LDH about 10% of the molar aluminium amount. The sorption has been experimentally studied in a wide range of pH, ionic strength, radionuclide and sorbent concentration. Both LDHs with chloride as interlayer anion were synthesized by a coprecipitation method under controlled conditions, and their main physico-chemical properties were analyzed prior to the sorption experiments.
The sorption kinetics of selenite on the LDHs in water and in MgCl2-rich brine were rapid using a LDH concentration of 10 g/L. Equilibrium, indicated by stable pH values, was obtained within 5 h for an initial selenite concentration of 4.28×10−13 mol/L. Selenite in water sorbed quantitatively on both LDHs. In MgCl2-rich brine a different behaviour to water was observed. The sorption was not quantitatively, due to the presence of high amounts of chloride anions. Chloride, as competing anion, affected the sorption behaviour of selenite. Using a LDH concentration of 0.1 g/L, the sorption of selenite was negligible. The effect of pH on selenite sorption was investigated, too. The sorption was relatively constant when the initial pH values were adjusted between 4 and 8, because both LDHs exhibit a high pH buffering capacity. For a selenite concentration range between 5.43×10−14 and 3.24×10−12 mol/L sorption isotherms were obtained and the data could be fitted to Freundlich and Dubinin–Radushkevich equations. The sorption capacities of the LDHs and the energies of sorption were determined. The sorption of selenite occurred via an ion exchange mechanism and the sorption behaviour was similar for both LDHs.
Determination of chloride contents in aqueously isolated chloroplasts from spinach by amperometric titration indicated chloride concentrations of 60 to 100 mmol 1-1 (based on a chloroplast volume of 25 μl mg-1 chlorophyll). However, when analyzed by anion chromatography, chloride contents in chloroplasts were much lower (1-8 mmol 1-1).
In leaf extracts chloride concentrations obtained with both methods were rather similar. Boiling of chloroplast extracts prior to chloride titration reduced indicated chloride contents by a factor of three or four, but did not change results obtained with anion chromatography. It is concluded that chloroplasts contain large amounts of silver complexing agents giving rise to a drastic overestimation of chloroplast chloride concentrations when measured by amperometric titration. Boiling and centrifugation of extracts apparently precipitates these compounds only insufficiently.