  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.
