The T = 1 pairing Hamiltonian in a two-level model

M. B. Barbaro, R. Cenni, Alfredo Molinari +1 more

M. B. Barbaro, R. Cenni, Silvia Chiacchiera +2 more

Shinji Iida, M. Yamamura

An exact solution of two-level pairing Hamiltonian is analytically given in the framework of the Hamiltonian form of classical mechanics. Following the shapes of the trajectories, whole phase space for pairing vibration can be divided into three sub-spaces. The solution, which is expressed in terms of the elliptic function, shows discontinuities at the boundaries of the three sub-spaces.

D. C. Zheng, Donald W. L. Sprung, H. Flocard

We study the pairing energy in the ground state of a system of N particles occupying a symmetric two-level model space with a level degeneracy \ensuremath{\Omega}. Assuming a pairing Hamiltonian, we calculate the energies of the projected BCS states, using the exact, the Kamlah, and the Lipkin-Nogami particle number projection methods. We find that conclusions regarding the quality of the BCS approximation as well as various approximate projection methods, drawn from studying the N=\ensuremath{\Omega} case alone, are not valid in the more general N\ensuremath{\ne}\ensuremath{\Omega} case when the pairing interaction is weak.

Daniel R. Bes, R.A. Broglia, R.P.J. Perazzo +1 more

S. Iida

It is investigated how classical pictures of the whole phase space are connected with the original quantal system by using the two-level pairing model.Discontinuous shape changes of classical trajectories are shown to be related with the sudden changes of patterns in the transition strength between energy eigenstates.By introducing the collective and intrinsic coordinates representing pairing rotations and vibrations, respectively, these discontinuities can be interpreted as the breakdown of the excited pairing •rotational band scheme.