Systematics of Effective Charge, Electric and Spin Vibrations.

A "multipole condition" is defined to determine the strength parameter in delta interaction. This then is used to study the isoscalar effective charge and various electric multipole resonances in TDA and RPA models. Various forms of the Skyrme interaction are used to study the various multipole modes. The lowest isoscalar Octopole mode appears collapsed for various N=Z nuclei in our "shell-model" RPA calculations. A fully self consistent RPA calculation leads to the conclusion that in general there is no collapse of the lowest 3('-) T=O state in nuclei. It is however found not to vary smoothly with mass number A. Recently a great deal of attention is being paid to "spin" vibrations in nuclei. We make a detailed study of magnetic dipole resonance in various N=Z nuclei. A spin dependent delta interaction is used to evaluate M1 energy weighted sum rule taking into account the ground state correlations. Tensor interaction is also used to evaluate the required sum rule. It is found that there is significant M1 strength at high energies. The effect of core polarization in nuclei can be considered within the context of a full Hartree-Fock calculation on these nuclei. So far Hartree-Fock calculations have been mostly done on even-even nuclei. We generalize this formalism to odd-even nuclei like ('17)O, ('41)Ca. Our calculations here show a close correspondence with the RPA results.