Study of Isospin dependence of mean field and vibration in unstable nuclei

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We studied the paring correlations in unstable nuclei by Hartree-Fock(HF)-BCS mode and also HF-Bogolyubov model solving in the coordinate space. We studied also the response function of Electric quadrupole excitation and spin excitation taking into account the coupling to the continuum properly. We found that the response function is very sensitive to the separation energy of valence neutrons and shows a huge enhancement just above the threshold when the last neutrons have a very small separation energy less than 1MeV.We studied correlations among several nuclear matter properties in the Skyrme HF and relativistic mean field (RMF) models. Linear correlations are found between neutron skin thickness, the pressure of the neutron matter and also the symmetry energy coefficient using various Skyrme Hamiltonian and Lagrangians of mean field models. The correlations between the isovector nuclear matter properties and the isospin dependence of isoscalar giant monopole resonance s are also poi … More nted out. Charge exchange spin-dipole excitations of 90Zr and 208Pb are studied in order to extract the neutron skin thickness and to determine the neutron matter equation of states. The isospin dependence of the nuclear incompressibility is also studied in the HF+random phase approximation (RPA).The pairing correlations in weakly bound nuclei, so called Borromean nuclei, on the edge of neutron drip line, 6He and 11Li, is studied by using a three-body model in which two valence neutrons interact with each other by a density-dependent contact force. We pointed out the di-neutron type correlation play a dominant role in these nuclei. The behavior of the neutron pair at different densities is simulated by calculating the two neutron wave function at several distances between the core nucleus and the center of mass of the two neutrons. We found that the di-neutron wave function shows an analogy to the BCS and BEC phases of the Cooper pair wave functions found in the infinite nuclear matter. The Coulomb breakup cross sections will be also discussed to probe the theoretical conjectures. Less