Retarded Boson-Fermion interaction in atomic systems

The retarded interaction between an electron and a spin-0 nucleus, that has been derived from electro-dynamical perturbation theory is discussed here. A brief account of the derivation is given. The retarded form is correct through order v ²/c ². Use of the relative coordinates leads to an effective one-electron operator that can be used through all orders of perturbation theory. A few unitary transformations give rise to the interaction that is valid in the non-relativistic limit.     

Ab-initio nonrelativistic and relativistic Hartree-Fock calculations for both closed- and open-shell molecules using GTO basis

Computer programs forab-initio Hartree-Fock and Dirac-Hartree-Fock calculations on closed- and open-shell atoms and molecules have been indigenously developed. Sample results of high quality are given for Li, Be, LiH and Be₂. As a byproduct of these calculations the importance of considering relativistic effects in the investigation of the elusive bound-state structure of Be₂ is clearly indicated.     

Propagation of dust-acoustic waves in weakly ionized plasmas with dust-charge fluctuation

For an unmagnetized partially ionized dusty plasma containing electrons, singly charged positive ions, micron-sized massive negatively charged dust grains and a fraction of neutral atoms, dispersion relations for both the dust-ion-acoustic and the dustacoustic waves have been derived, incorporating dust charge fluctuation. The dispersion relations, under various conditions, have been exhaustively analysed. The explicit expressions for the growth rates have also been derived. International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore, India.     

A simple route to enantiopure bis-lactones: synthesis of both enantiomers of epi-nor-canadensolide, nor-canadensolide, and canadensolide

A simple strategy has been developed for the synthesis of both enantiomers of nor-canadensolide, epi-nor-canadensolide, and an intermediate to canadensolide. An orthoester Claisen rearrangement of an appropriately constructed allyl alcohol derivative prepared from R-(+)-2,3-di-O-cyclohexylidine glyceraldehyde followed by epoxidation of the resulting unsaturated esters produced hydroxy-lactones, which on oxidation gave keto-lactones. Stereoselective reduction of the keto-carbonyl using either a chelation controlled or a non-chelation controlled process led to the natural or the epi-series, respectively. The interplay of the electronic effect between the polar groups and the steric effect of the β-substituent during reduction of the keto-lactones turned out to be the key factors in deciding the stereochemical outcome. Regeneration of the aldehyde functionality latent in the ketal moiety of the hydroxy-lactones provided the lactols, which on oxidation gave the bis-lactones.     

Parameśvara's rule for the circumradius of a cyclic quadrilateral

The expression for the circumradius of a cyclic quadrilateral in terms of its sides, usually attributed to L'Huilier in 1782, was known in India to Parame?vara (circa 1430). The present paper contains the original Sanskrit text of the rule, its English translation, and a discussion of its derivation as given by Sankara Váriar in his Kriy$\text{a}$kramakar$\text{i}$ (16th Century) along with relevant historical remarks.     

Dielectric relaxation,ac and dc conductivities in the fullerenes C60 and C70

The complex conductivity in polycrystalline C₆₀ and C₇₀ has been investigated for frequencies 20 Hz≤ν≤10⁶ Hz and temperatures 10 K≤T≤750 K. The high-frequency dielectric constants ε_α= 2.6±0.1(C₆₀) and ε_∞= 4.6±0.1 (C₇₀) were deduced from these experiments. The observed low temperature relaxation process in C₆₀ fits well into the relaxation dynamics of the C₆₀ molecules as determined by many other experimental techniques operating on very different time scales. In addition to the study of the dipolar relaxation process, the dc and ac conductivities were determined. From the temperature dependence of the dc conductivities energy barriers of E_G=1.75±0.1 eV (C₆₀) and E_G=1.7±0.1 eV (C₇₀) were estimated. In C₇₀ we found indications for small polaron tunneling.     

Complexes of ruthenium(II) and -(III) with dimethylsulphoxide—III. Bis-iodo-tetrakis- dimethylsulphoxide ruthenium(II) and some other iodo complexes of ruthenium(II)

The ruthenium(II) complex [RuI₂(Me₂SO)₄] was synthesized and characterized. The Me₂SO ligands are all S-bonded. Reactions of RuI₂(Me₂SO)₄ with ligands containing P, N and S donor atoms have been carried out and the complexes obtained were characterized using different physical methods. [RuI₂L₄] (L= CH₃CN, Me₂SO and py), [RuI₂(CH₃CN)₂(PPh₃)₂] and [RuI₂(CS)(PPh₃)₃] have been synthesized using RuI₃ as the source material and characterized as above.     

Theoretical study of the effective electron mass in ternary chalcopyrite semiconductors in the presence of crossed electric and magnetic fields

An attempt is made to investigate theoretically the effective electron mass in ternary chalcopyrite semiconductors at low temperatures on the basis of a newly derived dispersion relation of the conduction electrons under cross fields for the more generalized case which occurs from the consideration of the various types of anisotropies in the energy spectrum. It is found, taking degeneraten-CdGeAs₂ as an example, that the effective electron mass at the Fermi level along the direction of magnetic quantization depends on both the Fermi energy and the magnetic quantum number due to the combined influence of the crystal field splitting parameter and the anisotropic spin-orbit splitting parameter respectively, resulting in different effective masses at the Fermi level corresponding to different magnetic sub-bands. It is also observed that the same mass at the Fermi level in the direction normal to both magnetic and electric fields also varies both with Fermi energy and magnetic sub-band index, and the characteristic feature of cross-fields is to introduce the index-dependent oscillatory mass anisotropy. The theoretical results are in good agreement with the experimental observations as reported elsewhere.     

Oscillatory free convection flow of a second order fluid from a vertical plate

This paper investigates the problem of free convection flow of a second order liquid in the boundary layer from a semi-infinite vertical plate in which the mean surface temperature varies as a function of the distance from the leading edge of the plate. Study of the oscillatory flow is restricted to small amplitudesε only. Several graphs have been drawn and tables have been presented to depict the effect of elasticity of the liquid and Prandtl number on the velocity and temperature distributions and Nusselt number.