This thesis presents a microscopic description of isoscalar giant resonance excitations in ??Ca and ??? Sn nuclei within the self-consistent Skyrme-Hartree-Fock-Random-Phase-Approximation (HF-RPA) theory. Such characteristic features of the Isoscalar Giant Resonance as strength function, transition density and cross-sections for ??Ca and ???Sn nuclei are obtained. In this analysis, the SL1 Skyrme interaction associated with 230 MeV for the value of nuclear matter incompressibility coefficient K is chosen. The selection of nuclei is based on the availability of recent experimental results from Texas A&M University. The coordinate space formulation of the RPA in terms of Green's function is employed to obtain isoscalar monopole and dipole transition strength distributions for ??Ca and ???Sn nuclei. Calculations are performed with the discretized single-particle continuum. Theoretical transition strength distributions are used to find quantities of interest such as energy positions of resonance states, sum rules and average resonance energies. The cross-section of 240 MeV ?-particle scattering on the above nuclei are analysed within the Distorted Wave Born Approximation (DWBA) using transition densities obtained from the HF-RPA calculations. From this analysis the cross-sections for ISGDR excitations are obtained and compared with the recent experimental data obtained at the Cyclotron Institute, Texas A&M University.
