Theoretical Studies Of Nuclear Mass Formula And Nuclear Spontaneous Fisslon

The main topics of this thesis are:1) Based on the Weizsacker-Skyrme (WS) nuclear mass formula, a modified WS model labeled by WS+ BCS is carried out, which employed a microscopic BCS method combining a proce-dure similar to Strutinsky method to simultaneously evaluate shell and pairing corrections. The 2267 experimental nuclear data are extracted from the lat-est atomic mass evaluation of 2012 (AME2012) with N and Z larger than 7 and the one standard deviation uncertainty on the mass lower than or equal to 150keV, and then the fitted root-mean square (rms) deviation is pinned down to 0.493 MeV; 2) Considering the continuum state effect on the shell correc-tion in WS-like model, a new WS model named WS+CS are performed, and the final rms reduces to 0.46 MeV. Another work is that in the framework of Generalized Liquid Drop Model (GLDM) we make the quasimolecular shapes β-parameterized, which are employed to describe the nuclear deformation evo-lution, and thus implement the purpose of self-consistent calculations of Strutin-sky shell correction of each quasimolecular shape along the spontaneous fission pathway.Based on the WS+BCS model we mainly test the predictive power of this new formula from the aspects of nuclear bulk properties (such as binding ener-gies, deformations and so on) and the microscopic structure information (one-neutron separation energy, pairing gaps), and then compare it with other mass formulas or models, and finally employ it to predict the masses of still unknown or not well-known nuclei and calculate the a-decay energies of superheavy nu-clei. Rooted on WS+ CS model and compared with the original WS formula, besides the nuclear bulk properties (binding energies, deformations and so on) we concentrate on the improvement and superiority of them within considering continuum state effect in describing the microscopic structure information (for example, the shell gaps, α-decay energies). Therefore it proves the importance of considering continuum state in improving the descriptions of microscopic nuclear structure aspects.In framework of GLDM the specific implement of β-parameterized quasi-molecular shape need to be divided into two cases:For symmetric fission it is done analytically (taking the spherical harmonics Ylo as basis), whereas for asymmetric fission it is performed in a pure numerical way (least-squares method). We substitute the β-parameterized values of every quasimolecular shape into axial symmetry WSBETA code and calculate the corresponding shell correc-tions, so that the evaluations of the fission barrier are more self-consistently. Afterward, taking the asymmetric channels of U, Pu, Am, Cm, Cf, and Fm iso-topes and the symmetric channel 256 Fm as examples, we calculate their sponta-neous fission half-lives, and as a results the theoretical values agree well with the experimental data. In the future it may be used to analyze the contributions of the multipole freedom degrees on the potential energy surface and further-more the effect on the half-lives.