  Here we investigate mixing of the low-lying three- and five-quark $\Omega$
states with spin-parity quantum numbers $\frac{1}{2}^{-}$ and
$\frac{3}{2}^{-}$, employing the quark-antiquark creation triggered by
Nambu-Jona-Lasinio (NJL) interaction. Wave functions of the three- and
five-quark configurations are constructed using the extended constituent quark
model, within which the hyperfine interaction between quarks is also taken to
be the NJL interaction induced one. Numerical results show that the NJL-induced
pair creation results in vanishing mixing between three- and five-quark
$\Omega$ configurations with spin-parity $1/2^{-}$, but mixing between three-
and five-quark $3/2^{-}$ $\Omega$ states should be very strong. And the mixing
decreases energy of the lowest $3/2^{-}$ $\Omega$ state to be $1785\pm25$~MeV,
which is lower than energy of the lowest $1/2^{-}$ state in this model. This is
consistent with our previous predictions within the instanton-induced
quark-antiquark creation model.
