  Recent observations indicate that some class 0 sources have orders of
magnitude higher accretion rates than those of class I. We investigated the
conditions for the high accretion rates of some class 0 sources by numerical
calculations, modelling an external trigger. For no external trigger, we find
that the maximum value of the accretion rate is determined by the ratio
$\alpha$ of the gravitational energy to the thermal one within a flat inner
region of the cloud core. The accretion rate reaches $\sim 10^{-4} M_{\sun}
yr^{-1}$ if the cloud core has $ \alpha > 2$. For an external trigger we find
that the maximum value of the accretion rate is proportional to the momentum
given to the cloud core. The accretion rate reaches $ > 10^{-4} M_{\sun}
yr^{-1}$ with a momentum of $\sim 0.1 M_{\sun} km s^{-1}$ when the initial
central density of the cloud core is $\sim 10^{-18} g cm^{-3}$. A comparison
between recent observational results for prestellar cores and our no triggered
collapse model indicates that the flat inner regions of typical prestellar
cores are not large enough to cause accretion rates of $\sim 10^{-4} M_{\sun}
yr^{-1}$. Our results show that the triggered collapse of the cloud core is
more preferable for the origin of the high accretion rates of class 0 sources
than no triggered collapse.
