  We investigate to what extent the oscillation or conversion of neutrinos
enhances the expected event rate of the supernova relic neutrino background
(SRN) at the Super-Kamiokande detector (SK). The SRN \bar\nu_e's can be almost
completely exchanged with \nu_\mu-like neutrinos by the MSW oscillation under
the inverse mass hierarchy with \Delta m^2 ~ 10^{-8}--10^5 [eV^2], or by the
magnetic moment of Majorana neutrinos with \mu_\nu >~ 10^{-12} \mu_B and \Delta
m^2 ~ 10^{-4}--10^0 [eV^2]. In the standard calculation of the SRN flux, the
event rate of the SRN \bar\nu_e's at the SK in the observable energy range of
15--40 MeV can be enhanced from 1.2 yr^{-1} to 2.4 yr^{-1} if all \bar\nu_e's
are exchanged with \nu_\mu-like neutrinos. The enhancement is prominent
especially in the high energy range (\gtilde 25 MeV). In the astrophysically
optimistic calculation, the event rate becomes as high as 9.4 yr^{-1}. Because
the theoretical upper bound of the SRN events without oscillation is about 5
yr^{-1} taking account of the various astrophysical uncertainties, we might
have to resort to the neutrino oscillation if more than 5 events in a year, as
well as a significantly harder spectrum, were observed in the SK.

High Energy Physics - Phenomenology;Astrophysics