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.     

Studies on ion association. Calorimetric study of the formation of monoazido complexes of Ni(II), Zn(II) and Cd(II)

From rehydration experiments the hydrates Ba(OH)₂ · 8 H₂O, Ba(OH)₂ · 3 H₂O β-Ba(OH)₂, · 1 H₂O, and γ-Ba(OH)₂ · 1 H₂O have been found in the system Ba(OH)₂-H₂O. Thermoanalytical measurements (DTA, TG, DTG, high temperature X-ray diffraction, high temperature Raman scattering) on these hydrates are reported. Thermal decomposition of Ba(OH)₂ · 8 H₂O and Ba(OH)₂ · 3 H₂O always results in the formation of β-Ba(OH)₂ · 1 H₂O, the stable form of the monohydrates at ambient temperature. Dehydration of β- and γ-Ba(OH)₂ · 1 H₂O, both of which form anhydrous β-Ba(OH)₂ as the first product of decomposition, starts at 105 and 115°C, respectively. Single crystals of Ba(OH)₂ · 3 H₂O and γ-Ba(OH)₂ · 1 H₂O were prepared from Ba(OH)₂ · 8 H₂O meltings and from ethanolic solutions of Ba(OH)₂ , respectively. The crystal data are: Ba(OH)₂ · 3 H₂O (orthorhombic, Pnma): a = 764.0(2), b = 1140,3(5), c = 596.5(1) pm, Z = 4; γ-Ba(OH)₂ · 1 H₂O (monoclinic, P2₁/m or P2₁): a = 704.9(2), b = 418.4(1), c = 633.3(1) pm, β = 111.45(2)°, Z = 2.     

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.