• Volume 23, Issue 4

      October 1984,   pages  433-539

    • Gauge fields, space-time geometry and gravity

      Tulsi Dass

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      A general framework for the gauge theory of the affine group and its various subgroups in terms of connections on the bundle of affine frames and its subbundles is given, with emphasis on the correct gauging of groups including space-time translations. For consistency of interpretation, the appropriate objects to be identified with gravitational vierbeins in such theories are not the translational gauge fields themselves, but their pull backs,via appropriate bundle homomorphisms, to the bundle of frames. This automatically solves the problems usually encountered in constructing a gauge theory of the conventional sort for groups containing translations. We give a consistent formulation of the Poincare gauge theory and also of the theory based on translational gauge invariance which, in the absence of matter fields with intrinsic spin, gives a local Lorentz invariant theory equivalent to Einstein gravity.

    • Symmetry groups of mathematical physics

      P Rudra

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      Recent work on Lie’s method of extended groups to obtain symmetry groups and invariants of differential equations of mathematical physics is surveyed. As an essentially new contribution one-parameter Lie groups admitted by three-dimensional harmonic oscillator, three-dimensional wave equation, Klein-Gordon equation, two-component Weyl’s equation for neutrino and four-component Dirac equation for Fermions are obtained.

    • Quasi invariants and generalized killing vectors

      B R Sitaram Ram K Varma

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      The connection between quasi-invariants (invariants of a Hamiltonian system defined only on a single constant energy hypersurface) and generalized Killing vector fields associated with the corresponding Jacobi metric is investigated. The results are used to deduce a generalised form of the classical Whittaker problem in two degrees of freedom.

    • Analysis and merit of the constrained-component variation in dirac theory

      Sambhu N Datta S Jagannathan

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      It is shown that the constrained-component variation generally suggested by Rosicky and Mark is very fundamental, has consistent variational features and reproduces, as a special case, earlier variational results for atomic systems obtained by Drake and Goldman. Numerical merits and demerits of this method are qualitatively assessed.

    • Zeros of the helicity amplitudes of Σ-p and Λ-p elastic scattering

      S Mohanty J K Mohapatra

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      The forces of interaction as reflected in the cosθ plane analytic structures of the helicity amplitudes of Σ-p and Λ-p scattering are optimally exploited using the conformal mapping technique of Cutkosky and coworkers. A suitable parametrization of these amplitudes in the mapped variable is then chosen so that it can see the zeros better. These zeros are then located by making a good fit to the differential scattering cross-section curves. The effect of these zeros upon the cross-sections is discussed. Values for the phase shifts and coupling parameters between channels of fixedJ values are also computed.

    • Refractive indices and related properties of some potential mixed crystals

      D K Ghosh L K Samanta G C Bhar

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      The high frequency refractive indices of some binary, ternary and quaternary mixed crystals have been evaluated from the knowledge of plasmon energy and the lowest gap energy of the crystals for their applications in heterojunctionled and solar cells. The Fermi energy screening factor correction has been applied to effect accuracy in prediction. The model has been used to study the temperature and pressure dependence of refractive index. The calculated value agrees with experiment (within a few percent) justifying the validity of the model.

    • Elastic scattering of 36 MeV alpha particles from197Au

      S Kailas S K Gupta S Bhattacharya S N Chintalapudi Y P Viyogi

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      Angular distribution for the elastic scattering of 36 MeV alpha particles from gold target has been measured fromϑ ∼ 10–56°. The cross-section data have been analyzed in terms of the optical model. The real part of the optical model potential (VR) has been deduced by two prescriptions: (i) combining the volume integral, the radius at whichVR=2.4 MeV and the slope at this radius (1/VR) (dVR/dr) (ii) combining the volume integral, the root mean square radius and the equivalent sharp radius systematics. The imaginary potential depth has been searched to fit the data. The prediction using (i) for the real potential fits the data the best.

    • Ion acoustic subharmonic excitation in a plasma

      R S Chhabra

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      Ion acoustic subharmonic excitation in a plasma, with ion-neutral collision frequency greater than the frequency of excitation, is theoretically investigated. Two-fluid theory with source term is used to describe the system. The system exhibits either subharmonic excitation of orders 1/2 and 1/3, or subharmonic excitation of orders 1/3, 1/4 and 1/5. The resonance frequency range and the amplitude of second harmonic for each case is calculated. A comparison with experimental data can be used to obtain the values of the parameters describing the source term.

    • Calculation of entropy of mixing of liquid metal alloys in a hard sphere system

      P Singh K N Khanna

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      A semi-empirical model, based on the hard sphere system, is used to determine the entropy of mixing of simple as well as compound-forming alloys. For the compound-forming liquid solutions, the method leads to fairly accurate results, showing thereby that the usual theory of hard spheres mixtures can be applied to compound forming alloys also. It has been shown that the compound formation is very sensitive to the temperature of the mixture. Numerical applications are attempted for NaHg and NaGa.

    • Evaluation of thesscf andpy approximations for quadrupolar fluids

      J Ram

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      Two approximations, the single super chainf-expansion (sscf), and Percus-Yevick (py) approximation, are evaluated for a molecular fluid in which the molecules interact with a pair potential, that is the sum of Lennard-Jones and quadrupole-quadrupole parts at two values of reduced quadrupole moment. These results are compared with Monte-Carlo results. Except for the harmonic coefficienth (222;r), thesscf approximation seems to be quite accurate for the lower value of quadrupole moment but at higher valuespy approximation produces much better results except forh(220;r).

    • Semiempirical molecular orbital calculations for four-, six- and eight-atom systems

      C P D Dwivedi

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      The geometry, bond order, binding energy, ionisation potential, dipole moment and net charges have been calculated for cis-N2O2, trans-N2O2, N2O4, BF3, CH3, NH3, BH3 and B2H6 systems using semiempirical molecular orbital methodsindo and the results compared with available experimental,ab initio andmindo/3 data.

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