  We have combined Halpha and recent high resolution CO(J=1-0) data to consider
the quantitative relation between gas mass and star formation rate, or the
so-called Schmidt law in nearby spiral galaxies at regions of high molecular
density. The relation between gas quantity and star formation rate has not been
previously studied for high density regions, but using high resolution CO data
obtained at the NMA(Nobeyama Millimeter Array), we have found that the
  Schmidt law is valid at densities as high as $10^3 \mathrm{M_\odot}
\mathrm{pc}^{-2}$ for the sample spiral galaxies, which is an order of
magnitude denser than what has been known to be the maximum density at which
the empirical law holds for non-starburst galaxies. Furthermore, we obtain a
Schmidt law index of $N=1.33\pm0.09$ and roughly constant star formation
efficiency over the entire disk, even within the several hundred parsecs of the
nucleus. These results imply that the physics of star formation does not change
in the central regions of spiral galaxies. Comparisons with starburst galaxies
are also given. We find a possible discontinuity in the
  Schmidt law between normal and starburst galaxies.
