  The coherent elastic neutrino-nucleus scattering (CEvNS) plays a crucial role
at the final evolution of stars. The detection of it would be of importance in
astroparticle physics. Among all available neutrino sources, galactic
supernovae give the highest neutrino flux in the MeV range. Among all liquid
xenon dark matter experiments, XMASS has the largest sensitive volume and light
yield. The possibility to detect galactic supernova via the CEvNS-process on
xenon nuclei in the current XMASS detector was investigated. The total number
of events integrated in about 18 seconds after the explosion of a supernova
10~kpc away from the Earth was expected to be from 3.5 to 21.1, depending on
the supernova model used to predict the neutrino flux, while the number of
background events in the same time window was measured to be negligible. All
lead to very high possibility to detect CEvNS experimentally for the first time
utilizing the combination of galactic supernovae and the XMASS detector. In
case of a supernova explosion as close as Betelgeuse, the total observable
events can be more than ten thousand, making it possible to distinguish
different supernova models by examining the evolution of neutrino event rate in
XMASS.
