Based on simple physical and geometric assumptions , we have calculated the mean surface molecular density of spiral galaxies at the threshold between star formation induced by cloud-cloud collision and spontaneous gravitational collapse .
The calculated threshold is approximately \log \Sigma _ { \mathrm { crit } } \sim 2.5 , where \Sigma \mathrm { M _ { \solar } } \cdot \mathrm { pc } ^ { -2 } is the observed surface mass density of an assumed flat gas disk .
Above this limit , the rate of molecular cloud collisions dominates over spontaneous molecular cloud collapse .
This model may explain the apparent discontinuity in the Schmidt law found recently at 2 \lesssim \log \Sigma \lesssim 3 .