Absence of BCS Condensation of Atoms in a Repulsive Fermi Gas of Atoms

Possible Bose-Einstein condensation of molecules and Bardeen-Cooper-Schrieffer (BCS) condensation of Cooper pairs of atoms in an ultracold Fermi gas of atoms with a repulsive two-body interaction are studied by using the path integral representation of the grand partition function. From the self-consistent equations obtained in the present work for the order parameters, we have found that BCS condensation of atoms can't occur in such a Fermi gas of atoms and that the condensate observed experimentally is composed of condensed molecules or possibly of preformed Cooper pairs. To substantiate our conclusions from the self-consistent equations for the order parameters, the effective atom-atom interaction mediated through molecules has also been computed with the Foldy-Wouthuysen transformation and has been found to be repulsive, which implies a net repulsive two-body interaction between atoms and hence the absence of BCS condensation of atoms.