Abstract
The generalized Bose-Einstein condensation (GBEC) theory of superconductivity hinges on three distinct new ingredients: (a) treatment of Cooper pairs as real bosons, (b) inclusion of two-hole pairs on an equal footing with two-electron ones, and (c) insertion in the resulting ternary ideal boson-fermion gas of boson-fermion vertex interactions that drive formation/disintegration processes. Besides subsuming both BCS and BEC theories as well as the well-known crossover picture as special cases, GBEC leads to several-orders-of-magnitude enhancements in the critical superconducting temperature Tc. The crossover picture is applicable also to ultracold atomic clouds, both bosonic and fermionic. But known low-density expansions involving the interatomic scattering length a diverge term-by-term around the so-called unitary zone about the Feshbach resonance where a itself diverges. However, expanding a in powers of the attractive part of the interatomic potential renders smooth, divergence-free low-density expansions whose convergence can be accelerated with Pade approximants.
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