  We consider the minimal two-band model for the Fe-based superconductors with
a phenomenological pairing interaction which mimics short-range
antiferromagnetic (AFM) fluctuations. Two superconducting (SC) gap solutions
are found to exist with the model: sign-changing s-wave gap ($\pm$s-wave) and
double d-wave gap states. Both solutions hold the approximate relation
$\Delta_{h} ^{max} N_h \approx \Delta_{e} ^{max} N_e$, a generic feature of two
band model with a dominant interband pairing interaction. We carried out the
calculations of the SC properties of the both SC states such as the density of
states, temperature dependencies of spin-lattice relaxation rate $1/T_1$,
Knight shift, and penetration depth, particularly taking into account of the
interband coherence factors. The results are discussed in comparison with the
currently available experimental data.
