We develop a basis-free approach to time-reversal for the quantal angular momentum group,SU2, and apply these methods to the physical symmetrySU2_isospin,SU3_flavor,SU3_nuclear and the nuclear collective symmetry groupSL(3,R) of Gell-Mann and Tomonaga.

The Teitelboim-Plebañski method of average field is used to obtain the Lorentz-Dirac equation with gravitation.

The energy levels of a two-dimensional system are calculated for the rational potential,V(x, y; λ, g)=x²+y²+λ[x²/(1+gx²)+y²/(1+gy²)+a_xxx⁴+a_xyx²y²+a_yyy⁴] using the inner product technique over a wide range of values of the perturbation parameters (g, λ) and for various eigenstates.

The relaxational dynamics of a classical vector Heisenberg spin system is studied using the Fokker-Planck equation. To calculate the eigenvalues of the Fokker-Planck operator, a new approach is introduced. In this connection, a number space repesentation is introduced, which enables us to visualize the eigenvalue structure of the Fokker-Planck operator. The mean field approximation is derived and a systematic method to improve the mean field approximation is presented.

The role of filamentation instability of quark-gluon plasma, in explaining collective phenomena in relativistic heavy-ion collisions, has been analyzed. Using equations of SU(2) two fluid color hydrodynamics it is shown that this instability can significantly enhance nuclear stopping and might contribute to collective sideward flows.

We compare the effect of two body core on the charge form factor of³He by the hyperspherical harmonics expansion method using various 2BF potentials with the inclusion of three body force. We also include the meson exchange current contribution to the CFF for the same potentials in addition to the 3BF. The results indicate that the combined effect of 3BF and MEC (i) movesq_min² (the first diffraction minimum) appreciably to the left, amount of shift depends on the 2BF atr₁₂∼0.7 fm and (ii) enhancesF_max (the height of the secondary maximum of CFF) by an appreciable amount, the increment in general increases with the repulsive core of 2BF (r⩽0.1 fm).

Heavy ion fusion cross sections and compound nucleus average spin values obtained from distribution of fusion barriers are discussed. Various shapes of distribution functions are studied using a truncated Gaussian distribution function (TGD). It is shown that fusion cross section and average spin values are less sensitive to different parametrization of TGD function, whereas the second derivative of the product of energy and fusion cross sections (w.r.t. energy), obtained from the corresponding TGD functions are significantly different depending on the shape of the barrier distribution function. It is also shown byχ² analysis of fusion cross section data that some systems favour a narrow Gaussian distribution function whereas others, for which the vibrational and rotational collective states are less important, favour a flat barrier distribution. A physical interpretation of the dynamical process that gives rise to different barrier distribution is given in the framework of microscopic coupled channel calculations.

Experimental data on energy levels of the odd-odd deformed nucleus¹⁸⁰Re obtained from radioactive-decay and heavy-ion reaction studies are analysed to deduce spin-parity and configuration assignments for the six observed rotational bands based on the selection rules for fast beta transitions, criteria for the relative-energy ordering of the triplet and singlet bandheads, two-particle-plus-rotor model calculations including Coriolis mixing, rotational energy systematics involving staggering features, and considerations of gyromagnetic ratios, signature splittings and rotational band alignments.