We investigate the ratio of spin precession frequency to orbital frequency for a spinning charged particle confined to circular orbit in the equatorial plane of a compact object, with a uniform magnetic field, as described by the Wald and the Ernst potentials. In order to see the difference in behaviours for particles with differentg values we consider the cases of electron and proton separately.

The variational conditions implied by the most probable equilibrium distribution for a dilute gas are set up exactly in terms of the digamma function without necessarily invoking a Stirling approximation. Through a sequence of lemmas it is proved that, at any given kinetic temperature, there are three classes of self-consistent solutions characterized by the parameterβ$$\beta \bar \gtrless 0$$ 0 and by non-Maxwellian tails. These ambiguities persist even for a free ideal gas.

Considering the importance ofE₆ as the grand unification group in superstring theories, several breakdown patterns ofE₆ through maximal subgroups are studied. The Higgs which break the low energy group and give masses to the fermions are determined in each case. At each scale we consider minimal Higgs and apply extended survival hypothesis to determine the limits on the mass scales. The combination of intermediate mass scales that give rise to acceptable electroweak mixing angle and unification mass is determined. Proton decay rate is found to be acceptable in all cases except one.

The Coulomb potential between two heavy ions at their interpretation condition has been represented in terms of two point charges with reduced effective charge, dependent on overlap volume. This representation enables visualization of the dynamic development of the deformations of the colliding nuclei as a function of the degree of overlap. The potential has been compared with well known potentials for heavy-ion collisions. This Coulomb potential gave good agreement in reproducing excitation functions for fusion for a large number of heavy-ion systems.

A layer of stratified combination composed of selected radiation shielding materials acquires better shielding property. Albedo is used in such measurements as an integral measure ofγ-ray scattering. The stratified slabs of alternating heterogeneous layers have been found to have a virtual homogeneous property with a definite effective atomic number. The angular distribution of back-scattered photons as well as the total number albedo values for iron, aluminium and concrete in stratified combination for 662 keV and 1250 keV photons are reported.

The total attenuation cross-sections in elements 6⩽Z⩽82 forK_α andK_β groups of lines of elements Zr, Sn and Ba andL_l,L_α,L_β andL_γ groups of lines of the elements Au, Pb, Th and U have been measured. The experimentally measured attenuation cross-sections have been found in good agreement with the theoretical estimates.

Detailed measurements of magnetization and ac susceptibility at low temperatures of 1% Zr-substituted Y₉Co₇ are presented. All results are indicative of itinerant weak ferromagnetism withT_c ∼ 9.5 K. The zero-field magnetizations followT² orT^4/3 behaviour as in the Ni-substituted system. The estimated critical exponents areβ=0.38±0.03,γ=1.16±0.05. It is argued that the main effect of the non-magnetic Zr-substitution in Y₉Co₇ is to stabilize the ferromagnetic ordering by suppressing the ‘hopping’ of Co atoms along thec-axis sites of the hexagonal structure.

We present exact solutions of Bean’s critical state model for some sample shapes having non-zero demagnetization factorN. Virgin and hysteresis magnetization curves are obtained for samples in the shape of (i) a sphere (ii) a spheroid (iii) a cylinder of circular cross-section with its axis perpendicular to the field and (iv) a cylinder of elliptical cross section with its axis perpendicular to the field. Some interesting features seen in these first solutions forN ≠ 0 are discussed.