Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

Electron transfer reactions of nickel(III) and nickel(IV) complexes

This review narrates the electron transfer reactions of various nickel(III) and nickel(IV) complexes reported during the period 1981 until today. The reactions have been categorized mainly with respect to the type of nickel complexes. The reactivity of nickel(III) complexes of macrocycles, 2,2′-bipyridyl and 1,10-phenanthroline, peptides and oxime–imine, and of nickel(IV) complexes derived from oxime–imine, oxime and miscellaneous ligands with various organic and inorganic electron donors have been included. Kinetic and mechanistic features associated with such interactions have been duly analyzed. The relevance of Marcus cross-relation equations in the delineation of the electron transfer paths has also been critically discussed.     

The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons

In many metrics of physical interest, the gravitational field can be represented as an optical medium with an effective index of refraction. We show that, in such a metric, the orbits of both massive and massless particles are governed by a variational principle which involves the index of refraction and which assumes the form of Fermat's principle or of Maupertuis's principle. From this variational principle we derive exact equations of motion of Newtonian form which govern both massless and massive particles. These equations of motion are applied to some problems of physical interest.     

A Two‐Dimensional Coordination Compound as a Zinc Ion Selective Luminescent Probe for Biological Applications

A 2D coordination compound {[Cu₂(HL)(N₃)]?ClO₄}_∞ ( 1 ; H₃L=2,6‐bis(hydroxyethyliminoethyl)‐4‐methyl phenol) was synthesized and characterized by single‐crystal X‐ray diffraction to be a polymer in the crystalline state. Each [Cu₂(HL)(N₃)]⁺ species is connected to its adjacent unit by a bridging alkoxide oxygen atom of the ligand to form a helical propagation along the crystallographic a axis. The adjacent helical frameworks are connected by a ligand alcoholic oxygen atom along the crystallographic b axis to produce pleated 2D sheets. In solution, 1 dissociates into [Cu₂(HL)₂(H₃L)]?2H₂O ( 2 ); the monomer displays high selectivity for Zn²⁺ and can be used in HEPES buffer (pH 7.4) as a zinc ion selective luminescent probe for biological application. The system shows a nearly 19‐fold Zn²⁺‐selective chelation‐enhanced fluorescence response in the working buffer. Application of 2 to cultured living cells (B16F10 mouse melanoma and A375 human melanoma) and rat hippocampal slices was also studied by fluorescence microscopy.     

Kinetics and mechanism of the reaction oftrans-cyclohexane-1,2-diamine-N N N' N'-tetra-acetatomanganate(III) with substituted thioureas in aqueous medium

Summary The kinetics of reduction of [Mn^III(cydta)]^– (where H₄cydta=trans-cyclohexane-1,2-diamine-N N N' N'-tetraacetic acid) by some thiourea reductants have been studied in aqueous solution by stopped-flow techniques in the pH ranges 2.5–4.5 and 9.2–10.2. An initial increase in absorbance followed by a steady decrease indicated the formation of a precursor complex prior to the electron transfer step. The reactions are first order in both oxidant and reductant. The observed increase in rate in going from low to high pH is attributed to the difference in reactivities of the aqua and hydroxo species of the Mn^III complex; the higher reactivity of the latter is consistent with the formation of a ligand-bridged activated species prior to electron transfer. The reactivity order for the thiourea derivatives follows the order of their reported substituent effects.     

Separation of molybdenum from tungsten with di(2-ethylhexyl)-phosphoric acid ac extractant

The use of di(2-ethylhexyl)phosphoric acid (HDEHP) as an extractant for the separation of molybdenum from tungsten was examined with the help of molybdenum-99 and tungsten-187 as radiotracers. Effective separation was obtained when the aqueous phase contained phosphoric acid at pH 0.8–2 or pH 3–3.5, depending on the amounts of metal. The method is applicable to both tracer and milligram amounts of molybdenum. The structure of the extracted species was examined by infrared spectroscopy.     

Studies on the polymerization of ethyl acrylate. II. Chain transfer studies

Transfer constants for different solvents representing hydrocarbons, halogenated compounds, alcohols, ketones, acids, and esters were determined in the thermal polymerization of ethyl acrylate at 80°C and they are compared with the available data on methyl acrylate and ethyl methacrylate. It was observed from the values of transfer constants that ethyl acrylate radicals are a little more effective than methyl acrylate or ethyl methacrylate in abstracting hydrogen atom from hydrocarbons and alcohols. In acetic and n-butyric acid media, it has been found, by the aid of endgroup analysis, that the derived solvent radicals from transfer reactions are not too efficient to start a new chain.