The SU(3) Algorithm and Simple Application of the Proton-neutron Interacting Boson Model

With the robust shell-model foundation, the proton-neutron interacting boson model(IBM-2) is considered to be one of the standard models for the descriptions of heavy and intermediate-heavy nuclei. In this work, we demonstrate a new algorithm that is used to solve the IBM-2 Hamiltonian in the weak-coupling SU(3) basis in contrast to the original NPBOS algorithm in terms of the weak-coupling U(5) basis. Specifically, the SU(3) matrix element of a typical interactional term is given as an example to illustrate how to solve the IBM-2 Hamiltonian using the SU(3) group-algebra technique. With this algorithm, the consistent-Q Hamiltonian has been solved and applied to fit the low-lying experimental data for ^{152, 154}Sm, which therefore provides an example for using the IBM-2 to describe the transitional nuclei and testing the validity of the SU(3) algorithm.