  In this paper we investigate the one-loop radiative corrections to the
neutrino indices of refraction from supersymmetric models. We consider the
Next-to Minimal Supersymmetric extension of the Standard Model (NMSSM) which
happens to be a better supersymmetric candidate than the MSSM for both
theoretical and experimental reasons. We scan the relevant SUSY parameters and
identify regions in the parameter space which yield interesting values for
V_{mu tau}. If R-parity is broken there are significant differences between
MSSM and NMSSM contributions contrary to the R-parity conserved case. Finally,
for a non-zero CP-violating phase, we show analytically that the presence of
V_{mu tau} will explicitly imply CP-violation effects on the supernova electron
(anti-) neutrino fluxes.
