Spherical Mean-field Plus Pairing Model For ^12-28O And ^34-58Ca

In this thesis,the algebraic approach to the exact solution of the spherical mean-field plus standard pairing model and the spherical mean-field plus extended monopole-pairing model are introduced in depth.A comparison of them and related analysis are made.A new polynomial approach for solving the spherical mean-field plus standard pairing model is pro-posed based on the Heine-Stieltjes polynomial and to solve two coupled matrix equations.Thus,we reach the same calculation of the Richardson-Gaudin theory.In comparison to the tradition-al BCS method,the advantage of this new way lies in the fact that it offers exact numerical solutions with less CPU time.the spherical mean-field plus extended monopole-pairing model is import this term that nuclei can hop from this orbits to another orbits based on the standard pairing model.Within this extension,the model still can be solved strictly,and only can be got by solving one unknown number,the calculation will also become more easily.The odd-even mass differences and the first pairing excitation energies of^18-25O are fitted by using these two models within the ds valence shell.The calculation results show that these two models,with reasonable deviation from the experimental data,can be used to describe the ground-state prop-erties of^18-25O rather well.It is stated that the spherical mean-field plus extended monopole pairing model is more advantageous in saving CPU time,so that relatively large-scale open-shell calculation within the model becomes feasible.Finally,the spherical mean-field plus extended monopole-pairing model is used to fit the first pairing excitation energies,the odd-even mass differences,the odd-even difference of two-neutron separation energies,the odd-even differ-ence of?decay energies,and the odd-even difference of double?decay energies of^12-28O and^34-58Ca with open-shell calculations including the first eleven spherical orbits.The results show that the fitting of the first pairing excitation energies and the odd-even mass differences are close to the corresponding experimental data,but not so good in the calculation of another three odd-even difference in particular some nuclide of calcium.