of the electron fraction, $Y_e$ = 0.49 and 0.51. We also consider the simple time variation model for $Y_e$ in this discussion. The electron fraction of the outer ejecta is assumed to be the same as that of the progenitor model because the electron fraction does not change by the neutrino irradiation there.

We note that the electron fraction inside the proto-neutron star should be very small due to neutronization. However, the density in the region is much larger than the resonance density of the RSF-H conversion, so that virtually no conversion is expected there. Thus, we neglect the change of the electron fraction in this region.

The magnetic field profile of the SN is quite uncertain. In this study, we assume that the SN magnetic field transverse to the neutrino propagation changes as $\propto r^{-3}$ according to [@as03a; @as03b; @as03c]. The magnetic field $B_\bot$ is described as $$B_\bot = B_0 \left( \frac{r_0}{r} \right)^3,$$ where $r_0 = 10^8$ cm and $B_0$ is the magnetic field at $r_0$. The value of $B_0$ is used as a parameter. Typical strength is set to be $B_0 = 10^{11}$ G. We discuss the magnetic field in massive stars and SNe in Sec. IV.

Supernova 