The density functional theory is based on the existence and uniqueness of a uni- versal functional E[ρ]. In nuclear physics, the density functional is a useful model to study the properties of nuclear matter and ground states of finite nuclei. Re- cent astronomical observations, nuclear reaction experiments, and microscopic cal- culations have placed new constraints on the nuclear equation of state (EoS) and revealed that most nuclear-structure models fail to satisfy those constraints upon extrapolation to infinite matter.
A newly developed density functional is inspired by an effective field theory of a dilute Fermi system and Brueckner model. In the framework of a generalized energy density functional (EDF) called KIDS, the nuclear EoS is expressed as an expansion in powers of the Fermi momentum or the cubic root of the density. Parameters of the KIDS EDF are determined from well-defined saturation properties of nuclear matter or theoretically predicted nuclear EoS like Monte Carlo simula- tion with phenomenological potential models or microscopic calculations such as the work of Akmal-Pandharipande-Ravenhall (APR).
The major purpose of the present thesis is to study nuclear matter and nuclear structure with KIDS EDF. First we apply our EDF model to spherical nuclei using the Skyrme-type potential. Skyrme-type parameters are obtained from the nuclear matter EDF. Additional two parameters that cannot be fixed by KIDS EDF are de- termined by fitting to 6 data: the binding energies and charge radii of 40Ca, 48Ca and 208Pb. Second, we investigate the effect of effective mass on nuclear structure. Additional two parameters are determined by the given isosclar and isovector effec- tive masses. The third aim is to validate the minimal and optimal number of EoS parameters required for the description of homogeneous nuclear matter over a wide range of densities relevant for astrophysical applications and to examine the validity of the adopted expansion scheme for an accurate description of finite nuclei.
KIDS EDF is found to give consistent agreement to experimental data and be- havior of the most updated theories. We present results for single and double magic nuclei : 16O, 28O, 40Ca, 48Ca, 60Ca, 90Zr, 132Sn and 208Pb. And bulk and static nu- clear properties are found practically independent of the assumed effective mass value. It is a unique result in bridging EDF of finite and homogeneous systems in general. We also find that the 7 parameters are efficient to describe a nuclear matter when the EoS is expanded in the power series of the Fermi momentum. Higher- order EoS parameters do not produce any improvement to describe nuclear ground- state energies and charge radii. It means that they cannot be constrained by bulk properties of nuclei.
Thesis Advisor: Prof. Yongseok Oh