Effective Hamiltonian for polyatomic linear molecules

The leading terms of an effective Hamiltonian for a linear molecule in a given vibrational state are presented up to κ¹⁰T_v order of magnitude, whereby higher-order l-dependent terms such as $\text{H}\text{?}{}_{12.0}$, $\text{H}\text{?}{}_{8.0}$, and $\text{H}\text{?}{}_{8.2}$ have been neglected because in spectroscopic application they are of minor importance. This Hamiltonian therefore includes all those l-type interactions which could contribute to the fitting procedure, within a vibrational state where one or more bending vibrations are excited.     

Molecular constants for the ã 3A2 state of formaldehyde

The 0⁺–0 and 1⁺–0 bands of the ā ³A₂X? ¹A₁ transition of formaldehyde have been reinvestigated using higher resolving power than was available in the earlier work of Raynes. The rotational analyses have been considerably extended, and improved molecular constants for the ā ³A₂ state have been obtained with the aid of a new triplet—singlet computer programme.^sSR branches of the K′ = 7K″ = 5 and K′ = 5K″ = 3 subbands have been observed in the 0⁺–0 band using 7m atm of absorbing gas. These results provide the first example of the observation of ΔK = ±2 transitions in triplet—singlet bands of a polyatomic molecule. The “perpendicular” transition moment is found to be about 10% of the “parallel” transition moment.     

Self-consistent-field theory for one-electron properties

The SCF-formalism is modified to include as constraints in the variational procedure physical quantities defined by one-electron operators. Introducing empirical values for the expectation values of these operators, pseudo-eigenvalue equations are obtained whose solution will lead to self-consistent orbitals which are constrained to achieve the chosen empirical values.

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Zusammenfassung Die SCF Methode ist abgewandelt, um als Nebenbedingung in der Variationsmethode physikalische Eigenschaften einzuschließen, die durch Ein-Elektron-Operatoren definiert sind. Durch Einführung von empirischen Werten für die Erwartungswerte dieser Operatoren erhält man Pseudo-Eigenwert-Gleichungen, deren Lösung zu SCF-Orbitalen führt, die die gewählten empirischen Werte geben.

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Résumé On a modifié le formalisme de champ auto-cohérent à fin de pouvoir introduire les valeurs de propriétés physiques comme conditions sécondaires dans la méthode de variation. La solution des équations à valeurs propres, qu'on y obtient, permet d'obtenir des orbitales qui donnent les valeurs empiriques choisies.

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This work has been supported in part by the National Research Council of Canada.     

Anreicherung von Spuren Seltener Erden aus Mineralwässern durch Ionenaustausch

In the described analysis of mineral waters, after the throughflow of the sample through a column with Dowex 50 WX 12 in H⁺ form, the main cations are first eluted by 1.6 N HCl and then the rare earths by 6 N HCl. The latter are separated by ion-exchange chromatography on Dowex 50WX8 in NH₄ ⁺ form, the elution being performed with ammonium citrate pH 4.19. The presence of rare earths in the eluate was ascertained spectrophotometrically by means of their reaction with xylenol orange in the presence of cetylpyridinium bromide. In mineral waters from the West-Bohemian spa region it was possible to find traces of trivalent La, Ce, Pr, Nd, Sm + Gd, Y, Dy, Ho, Er, Tm, Yb and Lu.     

A multi-technique study of compact and hydrous Au oxide growth in 0.1 M sulfuric acid solutions

The growth and reduction of compact (α-) and overlying hydrous (β-) oxide films on polycrystalline Au electrodes in aqueous 0.1 M H₂SO₄ solutions have been investigated using potentiostatic, cyclic voltammetry, ellipsometric and quartz crystal microbalance (QCMB) techniques. All α-oxide films, formed with time at constant potentials up to 2.6 V, or by multicycling of the potential, are non-hydrated in nature, even when covered by a thick β-oxide film. The α-oxide film composition is suggested to be AuO below 1.5 V, and a mixture of AuO+Au₂O₃ at potentials above this, becoming predominantly Au₂O₃ at very high potentials. Up to three monolayers of Au₂O₃ can be formed. When formed at constant potential, the β-oxide film becomes increasingly hydrated as it thickens with time of growth, with a mass to charge ratio and refractive index consistent with Au₂O₃·H₂O and later with Au₂O₃·2H₂O. In contrast, the β-oxide film formed by multicycling has a higher mass overall, and becomes less hydrated as it thickens with time, with a mass and refractive index consistent with Au₂O₃·10H₂O at short times, ranging to Au₂O₃·2H₂O as the film thickens.     

Upper and lower bounds to eigenvalues

The variational method based on the Temple-Kato formulae is applied to the determination of bounds for some ^1,3 P(1s np) states of He.

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Zusammenfassung Die Variationsmethode, die auf der Temple-Kato Formel beruht, wird angewandt zur Bestimmung der Grenzen für einige ^1,3 P(1s np)-ZustÄnde des He.

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Résumé La méthode variationnelle basée sur la formulation de Temple-Kato est appliquée à la détermination de limites pour certains états ^1,3 P(1s np) de He.

     

The kinetics of charging and discharging of iridium oxide films in aqueous and non-aqueous media

Cyclic voltammetry and chronocoulometry have been used to investigate the kinetics of oxidation and reduction of electrochenucally generated Ir oxide films in H₂SO₄(aq), basic aqueous LiClO₄ solutions and LiClO₄ + acetonitrile solutions. In acidic aqueous solutions, the scan rate at which the main anodic peak potential begins to shift positively in cyclic voltammetry experiments has been used as a parameter to assess the charging and discharging kinetics of Ir oxide films grown under various conditions. In acidic and basic aqueous solutions, chronocoulometric measurements indicate that electron transport through the oxide is rate limiting for the main redox wave, whereas ion transport probably limits the charging/discharging kinetics in LiClO₄ + CH₃CN solutions. In this non-aqueous medium, it appears that ca. 35% of the oxide sites charge and discharge approximately an order of magnitude more rapidly than the remaining sites.     

Gamma-ray bursts from evaporating primordial black holes

It is believed that the detection of gamma-ray bursts from evaporating primordial black holes is highly improbable in the near future since the expected photon flux, consisting mainly of photons with energies ? GeV, is too low. Contrary to this point of view, we show that a large fraction of the black hole power at the final stage of evaporation (the last 10³ s) can be liberated as a burst of soft γ-ray emission of duration 10^?1–10³ s and luminosity 10²⁸–10³¹ erg/s in the energy range 0.1–1 MeV. According to our calculations of the black hole evaporation rate (within the Standard Model of elementary particles), when the black hole temperature exceeds approximately 10 GeV, the charged particle outflow from a black hole forms a well-defined plasma and can be described in the hydrodynamic approximation. In this case more than half of the rest energy of a black hole can be converted into soft gamma-rays due to the presence of the magnetic field with energy density comparable to that of charged particles. We consider various mechanisms leading to such transformation and estimate their efficiency. It is shown that, at least, some of the gamma-ray bursts detected by BATSE can be associated with evaporating black holes.     

Analytische Aspekte der Oxydation organischer Stickstoffverbindungen mit Chromsäure. IV

Zusammenfassung Die schon früher vorgeschlagene Halbmikromethode zur Bestimmung der N-N-Gruppierung wurde an einer Reihe aromatischer Azoverbindungen erprobt. Sie beruht auf der Oxydation der Substanz mit einem Chromsäure-Schwefelsäure-Gemisch in einer geschlossenen Apparatur. Die Azogruppen werden als elementarer Stickstoff abgespalten, der im Azotometer gesammelt und gemessen wird. Durch die Rücktitration der unverbrauchten Chromsäure kann außerdem die Oxydationszahl der untersuchten Substanz bestimmt werden.

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Summary The semimicro method previously suggested for the determination of the N-N-grouping was tested on a number of aromatic azo compounds. It is based on oxidation of the sample with a chromic-sulfuric acid mixture in a closed apparatus. The azo groups are split off as elementary nitrogen which is collected in an azotometer and measured. In addition the oxidation number of the material being studied can be found by backtitration of the unconsumed chromic acid.

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Résumé On a mis à l'épreuve la semimicrométhode déjà préconisée auparavant, pour le dosage du groupe N-N, sur une série de composés azo-aromatiques. Elle repose sur l'oxydation de la substance par un mélange d'acide chromique et d'acide sulfurique, en système clos. Les groupes azoïques se trouvent dissociés à l'état d'azote élémentaire que l'on récupère et que l'on dose dans l'azotomètre. On peut déterminer, de plus, l'indice d'oxydation de la substance étudiée par titrage en retour de l'acide chromique non consommé.

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III. Mitteilung siehe 1.     

Multivector analysis I: A comparison with tensor algebra

A comparison of the procedures used in crystal physics to accommodate physical tensors with those appropriate to multivector analysis involves, in the first instance, a consideration of tensor analysis. This is achieved by the imposition of a carefully chosen sequence of constraints. In a companion paper (II), a corresponding comparison with vector analysis is presented.