Model for pairing phase transition in atomic nuclei

A model is developed which allows the investigation and classification of the pairing phase transition in atomic nuclei. The regions of the parameter space are discussed for which a pairing phase transition can be observed. The model parameters include: number of particles, attenuation of pairing correlations with increasing seniority, single particle level spacing, and pairing gap parameter. It is argued that for nuclear models, the pairing phase transition has to be separated in temperature from the signal of the exhaustion of the finite model space.