An alternative derivation of the projection method for constructing effective operators in the truncated shell model space is presented. The results of explicit numerical calculations in three different nuclear regions are discussed. Non-hermiticity of the effective Hamiltonian and various hermitisation procedures are investigated in detail.

The spectroscopic amplitudes, form factors, angular distributions and total cross-sections for two nucleon transfer reactions in Zr-region in the zero range distorted wave Born approximation are calculated using consistent set of shell model wave functions. A single normalisation factor gives a good fit to all the two neutron transfer reaction data whereas the corresponding fit for the two-proton transfer reaction data is less satisfactory.

Zero range DWBA analysis for two-particle (neutron and proton) transfer reactions is carried out, using simple shell model structure wave functions for⁵⁴Fe,⁵⁶Co and⁵⁸Ni, with⁵⁶Ni inert core. In this structure calculation, a microscopic set of two-body interaction matrix elements derived from the non-local separable potential of Tabakin are employed. These matrix elements include in the perturbation theory two corrections (i) the second-order Börn term and (ii) the appropriate core excitations. Unlike the situation in many two-particle transfer reactions, the fragmentation of the reaction strengths to the excited states with respect to the lowest states of same spin and parity in the above transfer processes is satisfactorily borne out from this analysis.

A mathematical procedure to calculate the contribution to the reaction cross-section from a shell of radiusr and thickness Δ around the scattering centre within the frame work of a nuclear optical model is presented. The method is illustrated by describing graphically the regionwise absorption in nucleon-nucleus and nucleus-nucleus optical scattering. It is demonstrated that unlike in nucleon-nucleus scattering, in the nucleus-nucleus scattering volume absorptive optical potential, in general, does not imply that absorption is taking place in the entire nuclear volume; it is confined to mostly the surface region.

The results of the relativistic mean field (RMF) calculations are presented for the ground-state properties of characteristic deformed nuclei covering the entire periodic table. The representative cases in the 2s − 1d, rare-earth and actinide regions are explicitly considered. The pairing correlations are considered in the constant gap approximation. It is observed that the set of parameters appearing in the Lagrangian chosen to reproduce the ground-state properties of nuclear matter and spherical doubly magic nuclei, also turns out to give a very satisfactory description of light- and heavy-deformed nuclei.

Valence nucleon effective mass, which is almost constant, is proposed within the relativistic mean field theories of finite nuclei (closed shell ± one nucleon). It acquires a slight spin-orbit splitting due to relativistic effects. The relativistic Dirac magnetic moment $$\vec \mu _{op} $$ is rewritten analytically in terms of angular momentum-Pauli spin coupled states and the effective mass. Introducing the nucleon effective charge, the iso-scalar and iso-vector corrections to the magnetic moment operator are extracted from the overall one parameter fit of the measured and the calculated values. The calculated values of magnetic moments are in overall fair agreement with the experiment as well as with the other detailed microscopic calculations.

The talk presents the current status and the perspectives of the relativistic mean field (RMF) description of various nuclear properties. Some remarkable successful applications of RMF to several different class of nuclear properties are first sketched in a short list. Three selective applications of RMF to the:

with different motivations, are discussed in detail. The talk ends with a partial list of possible future directions.