Mean field description of finite nuclei under extreme conditions of isospin and temperature

Nowadays, investigation of nuclei far from the stability line has become a central topic in the nuclear physics community. With the advances in the experimental facilities, scientist are able to study the different parts of the nuclear landscape with larger proton-neutron asymmetry which is quite important to understand the underlying dynamics of atomic nuclei. In the theoretical framework, the self-consistent mean field models are the appropriate tools in order to probe the static and dynamic properties of atomic nuclei. In recent years, the formation of the low-energy modes below the Giant Resonance region become a popular topic in nuclear physics, both experimentally and theoretically. Especially, the low-energy part of the dipole resonances attracted scientist due its relation with neutron skin thickness, nuclear symmetry and also with the astrophysical processes like r-process nucleosynthesis. However, the nature and behavior of low-energy modes are not clear yet. In the First part of this thesis, the high-energy and low-energy dipole and monopole modes are investigated within the mean field framework using Skyrme HF+RPA at zero temperature. In particular, we focus on the behavior of the low-energy part of the monopole and dipole spectrum by analyzing the transition densities and collectivity of an excited state. The calculations reveal that the behavior of the low-energy modes are rather different from the high-energy part of the spectrum. They show a complex isoscalar and isovector behavior. In addition, low-energy monopole excitations exhibit a pure single-particle excitation. These pure single-particle excitations allow to analyze the splitting of the corresponding spin-orbit partners. Recently, exciting results are obtained far from the stability line with the change of the nuclear magic numbers. The magicity of 54Ca nuclei with N=34 magic number has been confirmed with the experimental results which took place at RIKEN. The effect of the tensor force on the evolution of the single-particle energies of nuclei are also investigated within the framework of this thesis. We employ both HFB and HF-BCS methods using Skyrme-type energy density functionals. An increase is obtained in the neutron spinorbit splittings of p and f states due to the effect of the tensor force which also makes 54Ca a magic nucleus candidate. In addition, QRPA calculations on top of HF+BCS are performed to investigate the first J = 2+ states of the calcium isotopic chain in order to explore the magicity of the 52Ca and 54Ca nuclei. We confirm that the tensor part of the interaction is quite essential in explaining the neutron subshell closure in 52Ca and 54Ca nuclei. Investigation of the properties and dynamics of nuclei under effect of temperature provide even more detailed information about the structure and properties of nuclei. In the second part of this thesis, the effect of the temperature on the ground state and excited state properties of nuclei are investigated within finite temperature mean field models. Firstly, the temperature dependent the HF-BCS approximation has been used in the calculation of the ground state properties of nuclei. Pairing phase transitions from superfluid to the normal state are studied with respect to the temperature. The temperature dependence of the nuclear radii and neutron skin are also analyzed. An increase of proton and neutron radii is obtained in neutron rich nuclei especially above the critical temperature. Using different Skyrme energy functionals, it is found that the correlation between the effective mass in symmetric nuclear matter and the critical temperature depends on the pairing prescription. The temperature dependence of the nucleon effective mass is also investigated, showing that proton and neutron effective masses display different behavior below and above the critical temperature, due to the small temperature dependence of the density. Secondly, the effect of the temperature on the multipole response of nuclei is investigated within the fully self-consistent finite temperature RPA. It is shown that the low-energy part of the dipole and monopole spectrum is rather sensitive to the temperature. In particular, formation of the new low-energy modes are observed under temperature effects. Lastly, the effect of the temperature on the multipole response of open-shell nuclei is investigated within the FT-QRPA for the first time.