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.     

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.     

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.     

Thermogravimetric analysis of cobalt sulfate

Morpholine is a base of moderate strength, comparable with that of ammonia, and capable of forming -onium-type salts. Extensive studies [1,2] have been made on the thermal stability of ammonium perchlorate because of its technological use as an oxidant in solid state rocket propellants. The preparation, characterization and thermal behaviour of morpholinium perchlorate are reported in this note. The study was followed by XRD, IR, TG, DTA and mass spectral techniques.     

Zeolite-mediated photochemical charge separation using a surface-entrapped ruthenium-polypyridyl complex

Employing the strategy of quaternization of the 2,2' N atoms of the conjugated bipyridine ligand 1,4-bis[2-(4'-methyl-2,2'-bipyrid-4-yl)ethenyl]benzene (L), a polypyridyl complex of ruthenium(II) was tethered on the surface of zeolite Y. Electrochemical and spectroscopic properties of the complex suggest that, upon visible photoexcitation of the MLCT band, the electron is localized on the conjugated ligand rather than the bipyridines. Electron transfer from the surface complex to bipyridinium ions (methyl viologen) within the zeolite was observed. Visible light photolysis of the ruthenium-zeolite solid ion-exchanged with diquat and suspended in a propyl viologen sulfonate solution led to permanent formation of the blue propyl viologen sulfonate radical ion in solution. The model that is proposed involves intrazeolitic charge transfer to ion-exchanged diquat followed by interfacial (zeolite to solution) electron transfer to propyl viologen sulfonate in solution. Because of the slow intramolecular back-electron-transfer reaction and the forward electron propagation via the ion-exchanged diquat, Ru(III) is formed. This Ru(III) complex formed on the zeolite is proposed to react rapidly with water in the presence of light, followed by reaction with the propyl viologen sulfonate, to form pyridones and regeneration of Ru(II), which then continues the photochemical process.     

Conformational effects on vibronic spectra and excited state dynamics of 3-fluorobenzoic acid dimer

Two conformational isomers of 3-fluorobenzoic acid dimer (3-FBA(2)) have been identified in a supersonic jet expansion by use of laser-induced fluorescence excitation (FE), UV-UV hole-burning, and dispersed fluorescence (DF) spectroscopic methods. In the FE spectrum, the S(1) origins of the two isomeric species appear at a frequency gap of only 24 cm(-1), and the vibronic intensities of the redshifted dimer (dimer I) are about two times weaker than those of dimer II. However, ab initio quantum chemistry calculations at the MP2/6-31G(**) level of theory predict that all the isomeric species of 3-FBA(2) have almost the same binding energy (approximately 17 kcal/mol) in the ground state. Furthermore, unlike benzoic acid dimer, the present system shows intense activity for a low-frequency mode in both the FE and DF spectra. With the aid of DFT (B3LYP/6-311G(**)) predicted normal mode frequencies, we have assigned the mode to the in-plane gear (cogwheel) vibration of the cyclic hydrogen-bonded frame of the dimer. The Franck-Condon profiles for vibronic excitation of the mode indicate that the distortion of the cyclic hydrogen bond frame as a result of S(1)<--S(0) excitation is larger for dimer I than dimer II. Moreover, the fluorescence lifetime at the S(1) zero-point level of the former is also significantly smaller than the latter. Using the predictions of configuration interaction singles calculations, we have proposed that the spectral and dynamical differences between the two isomeric species observed in this study are manifestations of the different characteristics of their S(1) surfaces. By measuring FE, DF, and hole-burning spectra of a mixed dimer between 3-fluobenzoic acid and benzoic acid we have shown that the isomeric features in the homodimer spectra are due to two locally excited rotamers of the 3-fluorobenzoic acid moiety.