  We present the analytical results at the mean-field level for the
asymmetrical fermion system with attractive contact interaction at the zero
temperature. The results can be expressed in terms of linear combinations of
the elliptic integrals of the first and second kinds. In the limit of small gap
parameter, we discuss how the asymmetry in fermion species affects the phases
of the ground state. In the limit of large gap parameter, we show that two
candidate phases are competing for the system's ground state. The Sarma phase
containing a pure Fermi fluid and a mixed condensate is favored at large degree
of asymmetry. The separated phase consisting of a pure Fermi fluid and a boson
condensate supports the system at smaller degree of asymmetry. The two phases
are degenerate in the limit of infinite pairing gap.
