Lie-group theoretic method for analyzing interaction of discontinuous waves in a relaxing gas

A Lie group of transformations method is used to establish self-similar solutions to the problem of shock wave propagation through a relaxing gas and its interaction with the weak discontinuity wave. The forms of the equilibrium value of the vibrational energy and the relaxation time, varying with the density and pressure are determined for which the system admits self-similar solutions. A particular solution to the problem has been found out and used to study the effects of specific heat ratio and ambient density exponent on the flow parameters. The coefficients of amplitudes of reflected and transmitted waves after the interaction are determined.     

Fine-hyperfine structures ofc\bar c andb\bar b systems in a non-relativistic Hulthen plus linear potentialsystems in a non-relativistic Hulthen plus linear potential

The heavy mesons of the charmonium and upsilon family are described in an alternative static potential model chosen in a combination of Hulthen and linear potential. We find that the quark-confining potential in the form of an equal admixture of vector and scalar parts successfully explains the fine-hyperfine structures of \(c\bar c\) and \(b\bar b\) systems in a flavour-independent manner. The leptonic decay widths of the vector mesons ofψ and γ families are calculated taking into account the Poggio-Schnitzer correction. We obtain some of the bound states of the yet-to-be observed \(t\bar t\) system for thet-quark mass ranging from 50 to 200 GeV.     

Rotational-diffusion anomalies in dye solutions from transient-dichroism experiments

Subnanosecond transient-dichroism experiments have been performed to investigate the rotational diffusion of dyes in solution. Dyes and solvents were chosen in a way to obtain information on the influence of size, shape and hydrogen-bonding abilities either of the solute or the solvent molecules. One finds slow orientational relaxation of di-anionic xanthene dyes in alcohols, while oblate cationic dyes rotate faster in spite of their comparable size. The rotational diffusion times for alcohol solutions exceed the theoretical values predicted by the Debye-Einstein model except for prolate molecules. For a solute molecule with internal mobility the rotational diffusion exhibits a partial slip behaviour. It is shown that the deviations from the Debye-Einstein model are restricted to alcohols since for other solvents either with or without strong hydrogen-bonding abilities the experimental values agree with the hydrodynamic model including the stick-boundary condition. Experiments on erythrosine B reveal the influence of size and shape of the attached solvent molecules.     

Orientational aspect of transient absorption in solutions

In picosecond spectroscopy transient absorption methods are utilized to measure ground-state repopulation kinetics. Since linearly polarized light pulses from mode-locked lasers are used, the transient absorption characteristics in solutions are governed by the rotational diffusion of the absorbing molecules, too. The theory for isotropic diffusion is given and compared to a measurement on the rhodamine 6G molecule dissolved in solvents of different viscosity using a novel pulse spectrophotometer.     

Anomalous behavior of atomic hydrogen interacting with gold clusters

The change in the electronic structure of Au(n)- clusters induced by the exchange of an Au atom by hydrogen is studied using photoelectron spectroscopy. Au anion clusters react with one hydrogen atom but not with molecular hydrogen. The spectra of Au(n)- and Au(n-1)H- clusters show almost identical features for n > 2 suggesting that hydrogen behaves as a protonated species by contributing one electron to the valence pool of the Au(n)- cluster. This behavior is in sharp contrast to that of the commonly understood electronic structure of hydrogen in metals; namely, it attracts an electron from the conduction band of the metal and remains in an "anionic" form or forms covalent bonding. We discuss the influence of the unique electronic structure of H on the unusual catalytic behavior of Au clusters.     

Separation of rotational diffusion and level kinetics in transient absorption spectroscopy

Transient absorption spectroscopy on electronic levels of molecules in the liquid phase is governed by population kinetics as well as rotational diffusion. The goal of transient absorption experiments has been the true level kinetics free of rotation. Moreover, to extract the rotational time from transient photodichroism experiments the knowledge of true population kinetics is instrumental. Three methods for separating rotational and level kinetics are described theoretically, and one of them is performed experimentally using a repetitive picosecond spectrometer for the measurement of rotational behaviour of fluorescein 27 in solvents of different viscosity.     

Cluster calculations of the interactions of μ+ with lattice defects in Li

Using the Hartree-Fock Roothaan scheme we have carried out molecular cluster calculations to study the interaction of positive muon with host metal atoms and intrinsic lattice defects in lithium. The total ground state energies of the clusters are calculated selfconsistently for various assumed impurity-host configurations. From the minimum in the total energy curve, we are able to determine the equilibrium lattice constant, the relaxation of first near neighbors around the impurity, the binding energy of the muon to a lattice trap and the activation energy for muon diffusion. Extension of the present method to treat ⁺-defect complexes in other metallic hosts are discussed.     

Structural and electronic properties of compound metal clusters

The equilibrium geometries, relative stabilities, and vertical ionization potentials of compound clusters involving Li _n , Na, Mg, and Al atoms have been calculated using ab initio self-consistent field linear combination of atomic orbitals — molecular orbital (SCF-LCAO-MO) method. The exchange energies are calculated exactly using the unrestricted Hartree-Fock (UHF) method whereas the correlation correction is included within the framework of configuration interaction involving pair excitations of valence electrons. While the later correction has no significant effect on the equilibrium geometries of clusters, it is essential for the understanding of relative stabilities. Clusters with even numbers of electrons are found to be more stable than those with odd numbers of electrons regardless of their charge state and atomic composition. The equilibrium geometries of homo-nuclear clusters can be significantly altered by replacing one of its constituent atoms with a hetero-nuclear atom. The role of electronic structure on the geometries and stabilities of compound clusters is discussed.     

The method of infinite ascent applied on A 4 ± nB 3 = C 2

Each of the Diophantine equations A ⁴ ± nB ³ = C ² has an infinite number of integral solutions (A,B,C) for any positive integer n. In this paper, we will show how the method of infinite ascent could be applied to generate these solutions. We will investigate the conditions when A, B and C are pair-wise co-prime. As a side result of this investigation, we will show a method of generating an infinite number of co-prime integral solutions (A,B,C) of the Diophantine equation aA ³ +cB ³ = C ² for any co-prime integer pair (a, c).