Statistical odd-even staggering in few fermions systems

The odd-even staggering (OES) in nuclear binding energies is a well-known fact. A rather similar effect can be found in other finite fermion systems. For instance, ultra small metallic grains and metal clusters. The staggering in nuclei and grains is attributed primarily to pairing correlations. In clusters, it is originated by the Jahn–Teller effect [Phys. Rev. Lett. 81, 3599 (1998)]. Here, we work with a simple, Lipkin-like, exactly solvable two-level fermion model. A statistical mechanics’ treatment of it shows that OES effects also emerge here, as revealed by theoretical tools connected with the so-called statistical complexity.