Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2006-02-27
AnnalsPhys.322:2665-2681,2007
Physics
Nuclear Physics
Nuclear Theory
20 pages, 4 figures
Scientific paper
10.1016/j.aop.2007.01.005
We study the pairing Hamiltonian in a set of non degenerate levels. First, we review in the path integral framework the spontaneous breaking of the U(1) symmetry occurring in such a system for the degenerate situation. Then the behaviors with the coupling constant of the ground state energy in the multilevel and in the degenerate case are compared. Next we discuss, in the multilevel case, an exact strong coupling expansion for the ground state energy which introduces the moments of the single particle level distribution. The domain of validity of the expansion, which is known in the macroscopic limit, is explored for finite systems and its implications for the energy of the latter is discussed. Finally the seniority and Gaudin excitations of the pairing Hamiltonian are addressed and shown to display the same gap in leading order.
Barbaro Maria B.
Cenni Rinaldo
Chiacchiera Silvia
Molinari Anna
Palumbo Fabrizio
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