and $\bar{\nu}_\tau$ by changing the sign of $V_e$ and $V_\tau$ in Eq. (20). The obtained resonance density is $$\rho_{res}(\nu_e \leftrightarrow \bar{\nu}_{\tau}) =
\frac{m_u \Delta m^2_{31} \cos2\theta_{13}}{2 \sqrt{2} G_F E_\nu}
\frac{1}{2Y_e-1} .$$ This equation shows that the resonance of the transition between $\nu_e$ and $\bar{\nu}_\tau$ exists in the case of normal mass hierarchy and $Y_e > 0.5$ \[see Fig. 2(f) and Fig. 5\] or in the case of inverted mass hierarchy and $Y_e < 0.5$ \[see Fig. 3(c) and Fig. 6\].

Conversion probabilities
------------------------

We show the conversion probabilities of SN neutrinos passing through the SN ejecta at 4 s after the core bounce. We set the neutrino energy of 20 MeV, the mixing angle $\sin^22\theta_{13} = 0.04$ corresponding to adiabatic MSW-H resonance, and $B_0 = 1 \times 10^{11}$ G. The shock effect at the RSF-H resonance is quite small at that time and with the neutrino energy. We assume that $Y_e = 0.49$ or 0.51 inside the mass coordinate of $M_r = 1.43 M_\odot$, of which the radius is $r = 1.6 \times 10^9$ cm at that time.

First, Fig. 4 shows the conversion probabilities from $\bar{\nu}_e$ \[4(a)\] and $\nu_{\mu,\tau}$ \[4(b)\]. The obtained result is similar to that in [@as03a; 