In this talk I would like to give a brief review on the exact solutions of the nuclear pairing Hamiltonian. I will first introduce the early development of the seniority model and the nuclear BCS theory. The exact solution of a general pairing Hamiltonian can be obtained by diagonalizing the corresponding Hamiltonian matrix as defined in the seniority-zero model space. I will then compare the exact diagonalization approach and the Richardson approach. There is no dimension problem in the later case. But it is still challenging numerically to find the solutions of those nonlinear equations involved in the Richardson approach. At the end, I would like to compare the predictions given by above equations and those of the BCS theory on the ground state correlation energy. It may provide important information on the collectivity of the coherent wave function.   

Host: Prof. Yu-Min Zhao