  Cooper pairing between a conduction electron ($c$ electron) and an $f$
electron, referred to as the "$c$-$f$ pairing," is examined to explain s-wave
superconductivity in heavy-fermion systems. We first apply the Schrieffer-Wolff
transformation to the periodic Anderson model assuming deep $f$ level and
strong Coulomb repulsion. The resulting effective Hamiltonian contains direct
and spin-exchange interactions between $c$ and $f$ electrons, which are
responsible for the formation of the $c$-$f$ Cooper pairs. The mean-field
analysis shows that the fully gapped $c$-$f$ pairing phase with anisotropic
s-wave symmetry appears in a large region of the phase diagram. We also find
two different types of exotic $c$-$f$ pairing phases, the Fulde-Ferrell and
breached pairing phases. The formation of the $c$-$f$ Cooper pairs is
attributed to the fact that the strong Coulomb repulsion makes a quasiparticle
$f$ band near the center of the conduction band.
