ar X iv : n uc l - th / 0 60 20 70 v 1 2 7 Fe b 20 06 1 The multilevel pairing Hamiltonian versus the degenerate case

We study the pairing Hamiltonian in a set of non degenerate levels. First, we discuss the spontaneous breaking of the U (1) symmetry in the path integral framework in the degenerate situation. Next, in the multilevel case, we obtain approximate, but accurate, expressions for the ground state energy in terms of a few moments of the single particle levels distribution when the system is in a superconducting phase, namely when the coupling exceeds a critical value. Finally we show the proximity of the seniority and Gaudin excitations of the pairing Hamiltonian and propose a valid, analytic expression for their energy.