Solving for the particle-number-projected HFB wavefunction

Recently we proposed a particle-number-conserving theory for nuclear pairing (Jia, 2013) [19] through the generalized density matrix formalism. The relevant equations were solved for the case when each single-particle level has a distinct set of quantum numbers and could only pair with its time-reversed partner (BCS-type Hamiltonian). In this work we consider the more general situation when several single-particle levels could have the same set of quantum numbers and pairing among these levels is allowed (HFB-type Hamiltonian). The pair condensate wavefunction (the HFB wavefunction projected onto good particle number) is determined by the equations of motion for density matrix operators instead of the variation principle. The theory is tested in the simple two-level model with factorizable pairing interactions, and semi-realistic models with the zero-range delta interaction and the realistic Bonn-CD interaction