New Algorithm For The Proton-Neutron Interacting Boson Model And Its Application

The interacting boson models including the IBM-1,which does not distinguish protons from neutrons,and the IBM-2,which distinguishes protons from neutrons,are very important theoretical tools for study of nuclear structures and they have been widely used to describe almost all aspects of nuclear structures.In the thesis,a new algorithm,of which the computing program is built through the mathematica software,to solve the interacting boson models has been developed based on the SU(3)basis.To examine the accuracy and computing efficiency of the new algorithm and the associated program,the numerical results in the 0(6)limit of both the IBM-1 and IBM-2 that are solved through adopting the new algorithm have been taken to compare with the analytical results expressed with the O(6)group representation-s.It is shown that the spectral structures predicted from the analytical formula exactly coincide with the numerical results obtained by using the new algorithm,which justifies the new algo-rithm and the associated program.In addition,the consistent-Q Hamiltonian in the IBM-2 are solved by using the new algorithm and the results are further applied to describe the low-lying structure of the typical X(5)nucleus,152 Sm.The results indicate that this simple Hamiltoni-an with given parameters can well produce the dynamical structure of the X(5)critical point symmetry and meanwhile provide a reasonable explanation of the spectral structure of 152 Sm including the ground-state band,?-band and ?-band,which has embodied the values of this simple consistent-Q Hamiltonian in application as well as the efficiency of the new algorithm in calculations.