  We demonstrate that the high pressure of the hot intracluster medium (ICM)
can trigger the collapse of molecular clouds in a spiral galaxy, leading to a
burst of star formation in the clouds. Our hydrodynamical simulations show that
the high gaseous (ram pressure and static thermal) pressure of the ICM strongly
compresses a self-gravitating gas cloud within a short time scale ($\sim$
$10^{7}$ yr), dramatically increasing the central gas density, and consequently
causing efficient star formation within the cloud. The stars developed in the
cloud form a compact, gravitationally bound, star cluster. The star formation
efficiency within such a cloud is found to depend on the temperature and the
density of the ICM and the relative velocity of the galaxy with respect to it.
Based on these results, we discuss the origin of starburst/poststarburst
populations observed in distant clusters, the enhancement of star formation for
galaxies in merging clusters, and the isolated compact HII regions recently
discovered in the Virgo cluster.
