Band mixing calculations have been done for²⁴Ne including the two degenerate prolate and oblate Hartree-Fock states and also some particle-hole excited states in the projection formalism using an interaction obtained by Preedom and Wildenthal. The energy spectrum agrees very well with the experimental results as well as the exact shell model calculations. Thus the band mixing calculations provide a good approximation to the lengthy exact shell-model calcuations. In addition they offer a physical insight into the collective nature of the nucleus as nuclear states are described in terms of only a few ‘intrinsic’ states.

Deformed Hartree-Fock calculations are performed for some light nuclei in a large configuration space consisting of first four major shells. The interaction employed is the modified Skyrme interaction in which the deformed density is replaced by the band averaged scalar density that makes the Hamiltonian rotationally invariant rendering the spectroscopic calculations feasible. It is shown that the introduction of density dependence spreads out the energy spectra and that the Skyrme variant SIV which has a weak density dependence gives best overall agreement for energy spectra and the available data for the electromagnetic properties of the nuclei studied. It is found that the maximum contribution to the energy of any state in the low lying spectrum comes from thes-state attractive ands-state repulsive parts of the Skyrme interaction. It is also shown that when two-body density dependent version of Skyrme interaction is used, the Koopmans theorem no longer holds.

A current confinement model for glue-balls is proposed to maintain complete similarity with relativistic harmonic oscillator model (rhm) with Lorentz scalar and vector potentials for quarks. The spurious motion of the centre of confinement is accounted for in these models in exactly the same manner. We shall review some of the successes of therhm in hardronic masses, magnetic moments of baryons, nucleonic sizes and polarisability and proton-antiproton annihilation, as well as the recent results on glue-balls.

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.

Confinement model for gluons using a ‘colour super current’ is formulated. An attempt has been made to derive a suitable dielectric function corresponding to the current confinement. A simple inhomogeneous dielectric confinement model for gluons is studied for comparison. The model Hamiltonians are second quantized and the glueball states are constructed. The spurious motion of the centre of confinement is accounted for. The results of the current confinement scheme is found in good agreement with experimental candidates.

Confined-gluon-exchange among relativistically confined quark clusters is used to obtain singlet S and P wave N-N scattering phase-shifts. A good agreement is obtained with the experimental results.

On the basis of a successful phenomenological current confinement model for gluons we have obtained a closed analytical expression for the confined gluon propagator (CGP) for the specific small frequencies in the co-ordinate space using a translationally invariant ansatz. We have also derived compact expression for generalm-dimensional harmonic oscillator ‘propagator’ for specific energies. Using the CGP the complete expression for the one gluon exchange potential (COGEP) between the quarks has been derived using the Fermi-Breit formalism which will be useful in the study of hadron spectroscopy and hadron-hadron interactions. TheN - Δ splitting is calculated using the spin-spin part of the COGEP.

Confined gluons-exchange among relativistically confined quarks is used to calculate the ground state masses and the radially excited states of pseudo scalar and vector mesons. A good agreement is obtained with the experimental masses. The limitation of the perturbative treatment of estimating theN−Δ andπ−ρ splitting using one-gluon-exchange potential is pointed out.

Polarization observables for the nucleon-nucleon (NN) scattering are investigated in the frame work of relativistic harmonic model belowE_lab=250 MeV, with the inclusion of theσ andπ meson exchange. The results can be interpreted as the ‘Cheshire cat principle’ of NN interaction.