between the RSF-L and the RSF-X, these two resonances appear separately. The densities and corresponding squared masses strongly depend on mass hierarchy as well as $Y_e$.

In order to find flavor transition at the RSF-H resonance, it is useful to consider the two-flavor approximation. First, we consider the transition between $\bar{\nu}_e$ and $\nu_{\tau}$. The flavor change by the RSF-H is solved using the following equation: $$i \frac{d}{dr}
\left( \begin{array}{c}
\bar{\nu}_e \\ \nu_{\tau}
\end{array} \right)
= \left( \begin{array}{cc}
\frac{\Delta m^2_{31}}{2 E_\nu}s_{13} -V_e & \mu_{e\tau}B_\bot \\ 
\mu_{e\tau}B_\bot & \frac{\Delta m^2_{31}}{2 E_\nu}c_{13} +V_\tau 
\end{array} \right)
\left( \begin{array}{c}
\bar{\nu}_e \\ \nu_{\tau}
\end{array} \right) .$$ After calculating the eigenvalues of this equation, we derive the resonance density of the transition between $\bar{\nu}_e$ and $\nu_{\tau}$ as $$\rho_{res}(\bar{\nu}_e \leftrightarrow \nu_{\tau}) =
\frac{m_u \Delta m^2_{31} \cos2\theta_{13}}
{2 \sqrt{2} G_F E_\nu}
\frac{1}{1-2Y_e} .$$ The resonance of the transition between $\bar{\nu}_e$ and $\nu_\tau$ exists when the resonance density is larger than zero. This condition holds in the case of normal mass hierarchy and $Y_e < 0.5$ \[see Fig. 2(c) and Fig. 4\] or the case of inverted mass hierarchy and $Y_e > 0.5$ \[see Fig. 3(f) and Fig. 7\].

We can also discuss the condition of the transition between $\nu_e$ 