#### Bulg. J. Phys. vol.42 no.4 (2015), pp. 337-343

#### Recent Development of Large-Scale Shell-Model and Projected Shell Model

H.-K. Wang

go back^{1}, Y. Sun^{2}, F.-Q. Chen^{3}, Y.-Q. He^{4}, S.-F. Li^{1}^{1}*College of Physics and Telecommunication Engineering, Zhoukou Normal University, Henan 466000, People's Republic of China*^{2}*Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China*^{3}*Departamento de Fisica Teorica, Universidad Autdnoma de Madrid, E-28049 Madrid, Spain*^{4}*College of mathematics and statistics, Zhoukou Normal University, Henan 466000, People's Republic of China*Abstract.To describe excitations around a deformation equilibrium, especially for those nuclei without a well-defined shape, we have developed two kinds of shell models: large-scale shell model based on a spherical basis and projected shell model based on a deformed basis. As examples, we show level spectra of a near-spherical nucleus^{130}In calculated by the large-scale shell-model. The Hamiltonian adopts pairing-plus-multipole force with monopole corrections, and the model space is sufficiently large that includes six proton orbits and seven neutron orbits to allow both proton and neutron core-excitations. In another development to treat shape effects in heavy, deformed nuclei, improved shell-model wave functions are introduced to the projected shell model by superimposing angular-momentum and particle-number projected states constructed with different quadrupole-deformation and pairing-gap parameters as two-dimensional generator coordinates. Using these as trial wave functions, we solve the Hill-Wheeler Equation and analyze the obtained results for the transitional Gd isotopes.