Proton-Neutron Interacting Boson Model And Its Dynamical Symmetries

The Interacting Boson Model is a theoretical scheme to interpret the medium and heavy nuclei. In this paper,we discuss the analytical Waveiunetions of IBMI,usin the irreducible tensor me thod. In par(?)cular, we gave lor the (?)irst time, the analytical wavefunctions in SU(3) limit. At the same time, we also discuss the analytical wavefunetions of O(6),SI(3) limits.Another development oi IBM is tne proton-neutron interacting boson ,moael ,in whicn proton and neutron bosons are distinguished. Dynamical symmetries are vevy important in nuelear pnysics. We discuss various group. ehains in IBM2 and make this knowledge a more systematic one. We also uiscuss the SU(3),O(6) limits.We discuss the general from of IBM2 hamitltonian. We give the complete set of Casimir operators (?) IBM2. we give the transformation matrix between tne no(?)al orderea invariant product operators ana the Casimlr operators. This matrix is very useful to stuay aynamieal symmetries of certain hamil tonian. V/e analyse the symmetries of a (?) IBM2 hamil tonian. From the point of view of (?) (?) we propese another form of IBM2 (?)We nave cneckea tne commonly used NPBOS coue. We discover that there are mistakes in one coue and corrected them. Usingtne corrected NPBOS code, We e(?)ed tne spectra and E2transitions of ¹⁵⁰SM, ¹⁵²SM, Tne calculations agree witn the experiment well.Finally we give a aiucusion and conclusion.