Research On The Nuclear Shape Evolution And Phase Transition In Relativistic Mean Field Theory

In this thesis, the theoretical development on nuclear structure and several primary nuclear structure models are reviewed briefly. The framework of relativistic mean field (RMF) theory and its application to deformed nuclei are introduced. The systematic investigation on shape evolution is performed for Mo and Z～40 isotopes in RMF theory. Some main results are summarized as follows:i) Several primary models of nuclear structure like shell model, collective model and Interacting Boson Model (IBM) are introduced.ii) The theoretical framework of RMF is introduced. In RMF theory, nucleon is described as a Dirac particle with the interactions by exchangingδ,ω,ρand photon. The corresponding lagrangian is presented. The equations of motion are obtained from Euler-Lagrange equation, which gives Dirac equation, Klein-Gordon equation and electric-magnetic equation for nucleon, mesons and photons respectively. The applications of RMF theory to axially symmetric deformed nuclei are introduced,iii) The microscopic quadrupole constrained relativistic mean field model is applied to investigate the shape evolution for Mo isotopes with all the most used interactions, i.e., PK1, NL3, TM1 and NLSH. The calculated binding energies and deformationβ2 are shown to be consistent with the experimental data. The potential energy surfaces show a clear shape evolution between spherical U(5) and y-unstable O(6) for the even-even Mo isotopes with increasing neutron number, and 94Mo is suggested to be the y-unstable nucleus, which is favored by the experimental data. Similar conclusion is also drawn from the neutron single particle spectra. Finaly, the chain of 82Sr, 84,86Zr,88Mo,90Ru, 92,94Pd, 96,98Cd has been studied with PK1 and NL3 interactions, and a transition from oblate and prolate coexistence to oblate, to prolate, and finally to spherical is clearly exhibited.