From the Copson and Linet solution for the electrostatic field due to a point charge near a Schwarzschild black hole, we have deduced the field due to two equal charges placed symmetrically (diametrically opposite) about the hole. It turns out that the motion of a test-charged particle is completely solvable only in the equatorial plane, because theϑ-equation does not yield the first integral forϑ ≠π/2. We have however considered circular orbits about the axis forϑ=constant ≠π/2 by requiring bothϑ andr to remain fixed all through the motion. Forϑ ≠π/2 orbits, in contrast to the similar classical situation, there occur forbiddenϑ-ranges. This seems to be a relativistic effect.

Some interesting features of a class of two-dimensional Hamiltonians with indefinite kinetic energy are considered. It is shown that such Hamiltonians cannot be reduced, in general, to an equivalent dynamical Hamiltonian with positive definite kinetic energy quadratic in velocities. Complex nonlinear evolution equations like the K-dV, the MK-dV and the sine-Gordon equations possess such Hamiltonians. The case of complex K-dV equation has been considered in detail to demonstrate the generic features. The two-dimensional real systems obtained by analytic continuation to complex plane of one-dimensional dynamical systems are also discussed. The evolution equations for nonlinear, amplitude-modulated Langmuir waves as well as circularly polarized electromagnetic waves in plasmas, are considered as illustrative examples.

The low energy effective scalar potential arising from the supergravity model proposed by Nilles, Srednicki and Wyler is minimized exactly. Bounds are derived for the parameters of the theory from the requirement that SU(2) × U(1) be broken at the tree level. These results support earlier approximate results.

We have conducted a search for globally supersymmetric preon models with gauged colour-flavour symmetries. Theories with both two- and three-preon composites, and colour-flavour groups from E₆ down to the standard model, are examined under the following conditions: asymptotically-free metacolour, anomaly-free gauged symmetries, and Pauli principle obeyed. It is found that there are no models with three or more supersymmetric families. If supersymmetry is broken, one model with four families emerges. The purely fermionic preon theories can also be considered as the light sector of a chiral supersymmetric theory, with supersymmetry breaking at the preon level.

We consider here a variational method for describing composite particles. We use equal time anticommutators/commutators, and regard the field operators as arbitrary except for the constraint from the above. The expectation value of the Hamiltonian is extremized both with respect to the field operators and with respect to the wave functions, the former extremization being the new feature here. Comparison with other calculations has been made, and correspondence with them has also been established. We further show here how an “effective mass” can arise from a potential.

Residual interaction calculations have been made for predicting the sign and the magnitude of the odd-even shifts observed in the rotational levels of theK=0 bands in the doubly-odd rare earth nuclei. It is shown that, contrary to the conclusions reached in earlier studies, the same zero-range spin-dependent residual interaction can reproduce the odd-even shifts as well as the GM splitting energies. This has been made possible with the inclusion of the phase factors for the total intrinsic spin and the total parity of the two-quasi-particle states in the Newby matrix elements. Predictions are made for the odd-even shifts for otherK=0 bands arising from several configurations not confirmed or observed so far.

Low temperature plasma parameters in a toroidal magnetic field are measured. The effect of an externally applied perpendicular electric field on the plasma parameters is studied. The lifetime of the plasma is measured in the presence and absence of the RF electric field. Decrease in the plasma lifetime in the presence of RF field is attributed to detrapping of the primary electrons to a larger volume. Plasma lifetime increases when a small vertical magnetic field is added to the toroidal magnetic field.

Van der Waals’ attractive interaction between a neutral atom and a metal surface (semi-infinite jellium) is studied via dielectric response approach in the non-retarded limit. It is shown that the interaction energy can be written in terms of the same form factorF(k, ω), which appears in the formula for dynamic image potential and which depends on the density-density response function of only the metal. The interaction energy written as the change in the zero-point energy of the electromagnetic fluctuations is expressed in terms of a secular determinant whose elements consist of the response function of the metal and the dynamic polarizability of the atom. The usual classical result is obtained when the coupling between the atom and metal is small. In the present analysis, it is shown that for short atom-metal separations, this coupling is important and yields substantial modification over the classical result. Numerical results for such situations are presented for the non-dispersive description of metal and a few inert gas atoms.

The electrical ionic conductivity of unirradiated and irradiated CaF₂: Nd crystals in the range of 60 to 800°C has been measured. The conductivity plot is basically divided into four parts, i.e., intrinsic and extrinsic unassociated, extrinsic associated, and extrinsic segregated regions. Activation energy (for unirradiated samples) in the extrinsic unassociated region is in the range of 0.69 to 1.20 eV depending on the doping concentration while for the intrinsic region, it is of the order of 1.89 eV. The conductivity in the extrinsic unassociated region increases with increase of Nd content in the sample. Also, the conductivity in the extrinsic region forγ-irradiated sample is higher than that for unirradiated one. In the intrinsic region, however, the conductivity is independent of dopant concentration orγ-irradiation. From these results it is surmised thatF⁻ interstitials are the charge carriers in this region for CaF₂: Nd³⁺ system.

The Pattison-Williams method of using Fourier-transformed Compton profiles for obtaining Fermi momenta in simple metals, is extended to set up a scheme for inferringd orf band occupancies in transition metals, rare earths etc. CP measurements are reported for Ni,α-Mn andβ-Mn and then the new scheme is applied to obtain 3d occupancies in these systems. Some comments on the use of this method for other systems are also made.

In this paper a new approach to the problem of electron propagation in one-dimensional arrays is developed. The approach is based on the concept of reflectance defined in the paper and propagation or non-propagation is determined by the single question of the reflectances being unity or not. This notion throws fresh insight into the localized state in one-dimensional systems and here the notion that all electrons in one-dimensional systems are localized is discussed.