Fluctuation of high energy muons and induced Cherenkov photons in water

The range fluctuation on high energy muon is exactly treated in the sense of computer numerical experiment. The survival probabilities obtained by our simple time sequential method are compared with those obtained by the tra- ditional method (vcut procedure method). The agreement between them is well. We examine the typical behaviors of individual muons, with the shortest range, with average like range and with the longest range and clarify their character- istics. Further more, we notice that the agreement between them is well as far as the muons' behaviors are concerned, but we expect that the behavior of the Cherenkov light yields become different between them.