  Possible $N\Omega$-like dibaryons $N\Omega_{ccc}$ and $N\Omega_{bbb}$ with
quantum numbers $IJ^P=\frac{1}{2}2^+$ are investigated within the framework of
quark delocalization color screening model. We find both of these two states
are bound, and the binding energy increases as the quarks of the system become
heavier. The attraction between $N$ and $\Omega_{ccc}$ (or $\Omega_{bbb}$)
mainly comes from the kinetic energy term due to quark delocalization and color
screening. The effect of the channel-coupling provides more effective
attraction to $N\Omega_{ccc}$ and $N\Omega_{bbb}$ systems. Besides, the
scattering length, the effective range, and the binding energy, obtained from
the calculation of the low-energy scattering phase shifts, also supports the
existence of the $N\Omega_{ccc}$ and $N\Omega_{bbb}$ states. All these
properties can provide necessary information for experimental search for the
$N\Omega$-like dibaryons with heavy quarks. And the experimental progress can
also check the mechanism of the intermediate-range attraction of the
baryon-baryon interaction in quark models.
