In superconductivity BCS theory it is a well known fact that due to electron-phonon interactions the electrons form states called Cooper-Pairs. As a result, the pair behaves like a bosonic particle, allowing a condensation state to occur. This is due to the anti-parallel spins of the electrons in this configuration. Theoretically, the same is true for even number of electrons. For example, four-sets of electrons with opposite spin states can gather together to form a boson-like particle. The question is, then, what is preferable about Cooper-Pairs in comparison to other boson-like configurations of even number of electrons?
Thanks in advance,