  The self-consistent mean field approximation of two-flavor NJL model, which
introduces a free parameter $\alpha$ ($\alpha$ reflects the weight of different
interaction channels), is employed to investigate the contributions of the
vector-channel at finite isospin chemical potential $\mu_I$ and zero baryon
chemical potential $\mu_B$ and zero temperature $T$. The calculations show that
the consideration of the vector-channel contributions leads to lower value of
pion condensate in superfluid phase, compared with the standard Lagrangian of
NJL model ($\alpha=0$). In superfluid phase, we also obtain lower isospin
number density, and the discrepancy is getting larger with the increase of
isospin potential. Compared with the recent results from Lattice QCD, the
isospin density and energy density we obtained with $\alpha=0.5$ agree with the
data of lattice well. In the phase diagram in the $T-\mu_I$ plane for
$\mu_B=0$, we can see that the difference of the critical temperatures of phase
transition between the results with $\alpha=0$ and $\alpha=0.5$ is up to
$3\%-5\%$ for a fixed isospin potential. All of these indicate that the vector
channels play an important role in isospin medium.
