Showing papers by "Tata Institute of Fundamental Research published in 1974"

Electromagnetic fields in spatially dispersive media

Abstract: The structure of the electromagnetic field in a spatially dispersive model medium occupying a plane parallel slab is obtained, free of several customary ad hoc assumptions made in other theories. The model medium is characterized by a dielectric response function appropriate to the neighborhood of an isolated-exciton transition frequency. The exact mode expansion for the electromagnetic field in the slab is derived and it is found that, unlike in the case of an unbounded medium, a single plane wave cannot be generated in the slab. An elementary solution (a single mode) is found to consist, in general, of six plane waves (four transverse and two longitudinal ones), coupled by two linear relations. These relations are shown to be equivalent to two nonlocal boundary conditions (of the form encountered in connection with the Ewald-Oseen extinction theorem in molecular optics), which the nonlocal contribution to the induced polarization must satisfy on the faces of the slab. This result resolves a long-standing controversy about the nature of the so-called additional boundary conditions that are generally believed to be required for solving problems of interaction of an electromagnetic field with a spatially dispersive medium. The results are applied to the problem of refraction and reflection on a spatially dispersive model medium occupying a half-space and a generalization of the classic formulas of Fresnel are obtained. The behavior of the reflected and transmitted waves as functions of the angle of incidence and of the frequency are illustrated by several figures. Our results are shown to differ from those obtained by Pekar in a well-known paper. The difference is traced to the nature of the additional boundary conditions postulated by Pekar; they are found to be inconsistent with the additional boundary conditions that we derive as an exact consequence of Maxwell's theory. Comparisons with several other theories, especially with those of Sein and Birman and of Maradudin and Mills are also made.

Semigroups of Measures on Lie Groups

Abstract: Let G be a locally compact Hausdorff topological group. By a weakly continuous convolution semigroup of positive probability measures on G.

Thomas-Fermi and Thomas-Fermi-Dirac calculations for atoms in a very strong magnetic field

Abstract: A statistical model for atoms in a very strong magnetic field (${10}^{12}$-${10}^{14}$ G) may be built, starting from the assumption that the Coulomb motion of the atomic electrons is adiabatically slow with respect to their magnetic motion. Within this framework, the binding energies and radii, as well as the ionization energies of singly and doubly ionized atoms, are computed for atomic numbers $5\ensuremath{\le}Z\ensuremath{\le}100$ in the Thomas-Fermi case, and for $5\ensuremath{\le}Z\ensuremath{\le}70$ in the Thomas-Fermi-Dirac case. Possible astrophysical implications may concern the emission of electrons and ions from the surface of pulsars, the abundances of the elements in the cosmic radiation, and the properties of the condensed matter forming the outer crust of magnetic neutron stars.

High energy radiation from white holes

Abstract: COMPARED to black holes, their time-reversed versions, white holes have attracted little attention from theoreticians. Here we point out possible ways in which white holes may be useful to high energy astrophysics.

Biochemical genetics of Coenorhabditis elegans

Abstract: A new method of isolating mutants of the free-living nematode Caenorhabditis elegans is described. This method utilises the fluorescence of the nematode as the phenotype. 15 mutants belonging to four genes obtained using this technique have been characterised. Mutants in two of these genes are shown to have blocks in tryptophan catabolism. It is suggested that this method could be used to obtain mutants corresponding to blocks in other metabolic pathways with fluorescent end products.

Multiplicity Formulae for Discrete Series.

Abstract: In a series of papers [20, 211 and [22], Schmid obtained several important results on the discrete series for semisimple Lie groups. The purpose of this paper is to prove Schmid's results by somewhat different methods and to relax as much as possible the restriction imposed on the regularity of the parameters of discrete classes. Though the basic line is similar to Schmid's, the main difference is that our methods do not rely upon complex analysis on the non-compact flag manifold G/T as developed in [20] and [21]. Rather, we just rely on some elementary differential calculus on the symmetric space G/K. This difference gives rise to less restrictive assumptions since the results on the vanishing of L2-cohomologies in the symmetric space situation seem to be sharper, so far. Our work also leads to some interesting results concerning the multiplicity formula of discrete classes in L 2 (/' \ G). In our development, we shall give an alternative proof of the key fact (Theorem 1, w 4) which is obtained in [20] using the complex analysis on G/T. Our proof, given in w 5, will be carried out directly in the symmetric space situation, and some standard theory of sheaf cohomology centering the Borel-WeilBott theorem on the compact flag manifold KIT will be used as in [20]. In this proof, our methods seem to be quite elementary. We now give a more precise description of the contents of the paper. Let G be a non-compact real semisimple Lie group with discrete series g2 4= qS. Assume, for simplicity throughout the paper, that G is a connected real form of a simply connected complex semisimple Lie group G e. Harish-Chandra 1-7] showed that there exists a compact Cartan subgroup T of G and that, if one denotes by T' the set of regular characters of T, there exists a distinguished surjection co: T'---, g2. We fix T and a maximal compact subgroup K containing T once and for all. Let ge, t e denote the complexifications of the Lie algebras g, t of G, T respectively. In considering the discrete class co (A) for a given regular character A e T', we always choose a positive root system P for the pair (go, t~) such that A is regular dominant with respect to 19, i.e., P = {~; (A, c0>0 }. Here as

Spatial configuration of single-stranded polynucleotides. Calculations of average dimensions and Nmr coupling constants.

Abstract: The probability distributions of the torsional angles (Φ', ω', ω, Φ, and ψ), which fix the structure of nucleotide backbone, have been calculated using the results of energy calculations based on extended Huckel theory (EHT), complete neglect of differential overlap (CNDO), perturbative configuration interaction using localized orbitals (PCILO), and classical potential functions (CPF) methods. Statistical average values of the vicinal 1 H 1 H, 1 H 31 P, and 13 C 31 P nmr coupling constants J have been calculated from the generalized Karplus relations using the probability distribution in the Φ', Φ, and ψ space. Experimental J values for polyribouridylic acid (polyU) support the theoretical predictions for these torsional angles. Using Monte Carlo technique, random coils of single-stranded polynucleotides have been simulated and the mean-square end-to-end distance r 2 has been calculated. Molecular orbital methods (EHT, CNDO, and PCILO) suggest considerable flexibility around OP bonds, leading to fairly small values for the characteristic ratio (C ∞ ~4). Observed values of the unperturbed characteristic ratio for polynucleotides are quite large (C ∞ ~18) suggesting a relatively rigid nucleotide backbone. The results based on molecular orbital calculations can be reconciled with the experimental values by introducing an additional stabilization of ~2 kcal mol -1 for the predicted minimum energy ragion (Φ' ~240°, ω' ~290°, ω 290°, Φ 180°, and ψ 60°). Such a stabilization may arise from the association of water molecules and metal ions with the phosphate group and (or) Coulomb interaction between neighboring phosphate groups. The calculations provide a semiquantitative estimate of torsional rigidity in the nucleotide backbone.

Energy dependence of multiplicity in proton-nucleus collisions and models of multiparticle production

Abstract: This is a continuation of our earlier investigation (Gurtuet al 1974Phys. Lett. 50 B 391) on multiparticle production in proton-nucleus collisions based on an exposure of emulsion stack to 200 GeV/c beam at the NAL. It is found that the ratioR em = 〈n s〉/〈n ch〉, where 〈n ch〉 is the charged particle multiplicity in pp-collisions, increases slowly from about 1 at 10 GeV/c to 1·6 at 68 GeV/c and attains a constant value of 1·71 ± 0·04 in the region 200 to 8000 GeV/c. Furthermore,R em = 1·71 implies an effectiveA-dependence ofR A =A 0.18,i.e., a very weak dependence. Predictions ofR em on various models are discussed and compared with the emulsion data. Data seem to favour models of hadron-nucleon collisions in which production of particles takes place through adouble step mechanism,e.g., diffractive excitation, hydrodynamical and energy flux cascade as opposed to models which envisage instantaneous production.

Study of molecular motions in liquids by electron spin-lattice relaxation measurements, I: Semiquinone ions in hydrogen bonding solvents

Abstract: The electron spin-lattice relaxation times (T 1) of a variety of semiquinone ions in hydrogen bonding solvents have been measured by the pulsed saturation recovery technique as a function of temperature (T) and viscosity (η) of the solvent. Also linewidths (ΔH) have been measured in suitable cases in such solvents at low radical concentrations (∼10−4 M). It is observed that (i) the temperature and viscosity dependence ofT 1 can be fitted to an equation of the form 1/T 1=A(T/η)+Bexp(-ΔE/RT) whereA andB are constants and ΔE is an activation energy of the order of 1 kcal mole−1 for these systems; (ii)T 1 is essentially independent of the radical concentration within the range 10−3 to 5×10−2 M; (iii) the concentration independent part of the linewidth (ΔH) increases linearly with (η/T) at sufficiently low temperatures, and (iv) the (η/T) dependent part ofT 1 is sensitive to the size of the semiquinone as well as that of the solvent molecule, whereas the linewidth which is proportional to (η/T) at high viscosity, low temperature region is not sensitive to the size of the semiquinone and that of the solvent. Based on these observations, it is postulated that in hydrogen bonding solvents, three types of motion contribute significantly to electron spin relaxation: The fact thatT 1 is not sensitive to the concentration of the radicals, is ascribed to the formation of the solvent cage that prevents the close approach of radicals, thereby rendering radical-radical interactions to be weak mechanisms for relaxation, even at relatively high radical concentrations.

On the Relativistic Electronic States of a Monatomic and a Diatomic One‐Dimensional Lattice

Abstract: A new method has been developed to obtain directly wave functions and relations between the energy and momentum of an electron in a linear array of δ-potentials obeying the Dirac equation, both for a monatomic and a diatomic one-dimensional lattice. Es wird eine neue Methode fur die direkte Bestimmung von Wellenfunktionen entwickelt, und es werden Beziehungen zwischen der Energie und dem Impuls eines Elektrons in einer linearen Anordnung von δ-Potentialen, die der Dirac-Gleichung genugen, sowohl fur ein einatomares als auch fur ein zweiatomares eindimensionales Gitter erhalten.

Crystal field effects on the saturation magnetic moment of Sm3+ ion in ferronagnetic samarium compounds

Abstract: The effects of cubic crystal fields on the saturation magnetic moment of Sm3+ ion in ferromagnetic compounds have been investigated. In samarium compounds with magnetic elements, the exchange fieldH ex acting on Sm3+ ion is taken to be proportional to the sublattice magnetization of the magnetic element, while in compounds with nonmagnetic elementsH ex is taken to be proportional to the spin average of the Sm3+ ion and is determined self-consistently. In both types of compoundsH ex is assumed to be along [001] direction. The saturation magnetic moment is calculated by taking into account the admixture of excited (J=7/2 andJ=9/2) levels into the ground (J=5/2) level of Sm3+ ion by crystal fields and exchange fields. It is shown that depending upon the strength, the crystal fields quench or enhance the magnetic moment from the free ion value, and in some cases force Sm3+ ion to behave effectively like an (L+S) ion rather than an (L−S)ion. The crystal fields may have important bearing on the performance of samarium compounds as permanent magnet materials.

Microwave spectrum and dipole moment of pentafluorobenzene

Abstract: With the idea of evaluating the dipole moment of pentafluorobenzene from a lowJ transition, its microwave spectrum was investigated in the frequency region of 8,000 to 12,400 MHz. The spectrum had been earlier observed by the authors in the 12,400 to 18,000 MHz region which needs reassignment in the light of present investigations. The rotational constants areA=1480·856±0·003 MHz,B=1030·066±0·003 MHz andC=607·496±0·002 MHz. The dipole moment is 1·44±0·05 D.