On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Solvent extraction of microamounts of strontium from water into nitrobenzene by using cesium dicarbollylcobaltate in the presence of 15-crown-5

Extraction distribution of microamounts of strontium in the water-CsCl-15-crown-5 (15C5,L)-nitrobenzene-cesium dicarbollylcobaltate system has been investigated. The equilibrium data have been explained assuming that the CsL⁺, CsL₂ ⁺ and SrL₂ ²⁺ complexes are extracted into the organic phase. The values of extraction and stability constants of the species in nitrobenzene saturated with water have been determined.     

Threshold electron impact excitation of Cl2

A high resolution electron impact threshold spectroscopy technique was used to examine the excitation of Cl₂ in the 2–14 eV region. This study complements previous photon absorption and emission measurements, because it is capable of detecting transitions which are optically forbidden. In the region up to 7.5 eV, broad dissociative structures are correlated with optically active valence states, although relative intensities in the threshold spectrum differ considerably and indicate a substantial contribution from the optically forbidden transitions. At 7.46 eV a series of 5 equidistant sharp peaks is detected and interpreted as arising from the² π _g Feshbach resonance, which differs from the ground state positive ion Cl ₂ ⁺ by a pair of Rydberg electrons: (4sσ)². The decay channels responsible for the appearance of the resonance in a threshold spectrum are discussed and it is suggested that they include several valence states of the (2431) and (2341) configurations, whose potential energy curves cross the Cl ₂ ^? ,²π_g curve in the region of energy at which the resonance state is formed. At higher incident electron energies and up to ionisation, Rydberg states predominate, starting with (2430) 4s^3,1 π _g states detected for the first time. The absence of broad peaks above 8 eV and the irregular appearance of Rydberg bands is consistent with the strong Rydberg-valence configuration mixing proposed by Peyerimhoff and Buenker. Where our resolution permits comparison, good general agreement is found with recent synchrotron radiation absorption measurements of optically allowed transitions.     

Analytische Bestimmung von Niob,Tantal, Phosphor,Chlorid und 2,2-Dipyridyl in einigen Komplexverbindungen

Zusammenfassung Die analytische Bestimmung der Metalle, des Dipyridyls und der Chloride in Oxo-chloro-alkoxo-dipyridyl-Komplexverbindungen des Niobs und Tantals wurde beschrieben. Eine modifizierte Methode der Dipyridylanalyse, wie auch der Chloridbestimmung in Gegenwart von Dipyridyl wurde angegeben. Die radiometrische Metallbestimmung in Extraktionsverbindungen von Niob und Tantal mit Di-oktyl-methylenbis-phosphonsäure wurde dargelegt.

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Summary The analytical determination of metals, dipyridyl and chlorides in oxochloro-alkoxo-dipyridyl complex compounds of niobium and tantalum is described. A modified procedure of the dipyridyl analysis and also of the determination of chloride in the presence of dipyridyl is given. The radiometric determination of the metals in extraction compounds of niobium and tantalum with di-octyl-methylene-bis-phosphonic acid is discussed.

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Résumé On décrit le dosage des métaux, du dipyridyle et des chlorures dans les composés complexes oxo, chloro, alcoxo, dipyridyle, du niobium et du tantale. On indique une méthode modifiée pour le dosage de dipyridyle ainsi que pour la détermination des chlorures, en présence de dipyridyle. On décrit le dosage radiométrique des métaux dans les produits d'extraction du niobium et du tantale par l'acide di-octyl-méthylène-bis-phosphonique.

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Vorgetragen beim Symposium für analytische Chemie in Graz, 29. September bis 1. Oktober 1965.     

Kinetic determination of ultramicro amounts of copper

A new catalytic reaction is proposed and a kinetic method developed for the determination of ultramicro amounts of Cu(II) on the basis of its catalytic activity in oxidation of the 2-thiosemicarbazone of sodium 1,2-naphthoquinone-4-sulphonate by hydrogen peroxide in the presence of ascorbic acid. Under optimal conditions the sensitivity of the method is 0.25 ng/ml. The relative error is 4.8-18.2% for the concentration range 5-0.8 ng/ml. Most foreign ions do not change the rate of the catalysed reaction. Co(2+) and I(-) catalyse the reaction, Ni(2+) extensively inhibits it, and in the presence of EDTA only the uncatalysed reaction takes place.     

Extraction of barium picrate into nitrobenzene in the presence of benzo-15-crown-5

From extraction experiments with ¹³³Ba as a tracer, the extraction constant corresponding to the equilibrium Ba²⁺(aq) + 2A^-(aq) + 2L(nb) BaL₂ ²⁺(nb) + 2A^-(nb) in the two-phase water-nitrobenzene system (A^- = picrate, L = benzo-15-crown-5; aq = aqueous phase, nb = nitrobenzene phase) was evaluated as log K _ex (BaL₂ ²⁺, 2A^-) = 5.7. Furthermore, the stability constant of the benzo-15-crown-5 - barium complex in nitrobenzene saturated with water was calculated: log b_nb (BaL₂ ²⁺) = 14.6.     

Eine kennzeichnende Eigenschaft der Zykel der Galileischen Ebene

Ohne Zusammenfassung     

Extraction and DFT study on the complexation of the methylammonium cation with a hexaarylbenzene-based receptor

In methods for quantification of ⁶³Ni, in e.g. reactor coolant water, a chemical separation is required due to ⁶³Ni being a pure beta emitter with limited means of quantification. ⁶⁰Co, a common radionuclide in reactor coolant water, is not completely separated with the commonly used separation procedure, and it is not resolved from ⁶³Ni in the beta spectrum. The separation method discussed in this work consists of TRU resin (Eichrom) and Ni resin (Eichrom). After running the separation procedure, depending on the initial activity of ⁶⁰Co, there may still remain enough ⁶⁰Co to interfere in the measurement of ⁶³Ni. The ⁶⁰Co interference is corrected for via a gamma spectrometric measurement. This correction may, depending on the ⁶³Ni/⁶⁰Co ratio, introduce a large contribution to the measurement uncertainty. The aim of this work was to evaluate the possibility to reduce the measurement uncertainty of ⁶³Ni measurements by adding a second Ni separation to the method. Double Ni separations were performed on reactor coolant water having a ⁶⁰Co activity much higher than the ⁶³Ni activity (⁶³Ni/⁶⁰Co = 0.01), in order to decrease the radioactivity of ⁶⁰Co in the sample. The measurement uncertainty of the ⁶³Ni measurement result was reduced by a factor of about three.     

Effect of the size of experimental channels of the lead slowing-down spectrometer SVZ-100 (Institute for Nuclear Research, Moscow) on the moderation constant

Lead slowing-down (LSD) spectrometers have a low energy resolution (about 30%), but their luminosity is 10³ to 10⁴ times higher than that of time-of-flight (TOF) spectrometers. A high luminosity of LSD spectrometers makes it possible to use them to measure neutron cross section for samples of mass about several micrograms. These features specify a niche for the application of LSD spectrometers in measuring neutron cross sections for elements hardly available in macroscopic amounts—in particular, for actinides. A mathematical simulation of the parameters of SVZ-100 LSD spectrometer of the Institute for Nuclear Research (INR, Moscow) is performed in the present study on the basis of the MCNPX code. It is found that the moderation constant, which is the main parameter of LSD spectrometers, is highly sensitive to the size and shape of detecting volumes in calculations and, hence, to the real size of experimental channels of the LSD spectrometer.