t = 3 sec  1000  100000  1e+07  1e+09  1e+11 sin $^{2}$2 $_{13}$=10 -3  100  1000  100000  1e+07  1e+09  1e+11  0.01  0.1 sin $^{2}$2 $_{13}$=10 -5  1000  100000  1e+07  1e+09  1e+11 sin $^{2}$2 $_{13}$=10 -4  1000  100000  1e+07  1e+09  1e+11 sin $^{2}$2 $_{13}$=10 -2  1000  100000  1e+07  1e+09  1e+11 sin $^{2}$2 $_{13}$=10 -2 t = 0 sec  1000  100000  1e+07  1e+09  1e+11 sin $^{2}$2 $_{13}$=10 -3  1000  100000  1e+07  1e+09  1e+11 sin $^{2}$2 $_{13}$=10 -4  100  1000  100000  1e+07  1e+09  1e+11  0.01  0.1 r / Ro [solar radius] sin $^{2}$2 $_{13}$=10 -5 r / Ro [solar radius] FIG. 3: The oscillation length, L$_{osc}$ = 2 E Δ ˜ m 2 sin 2 ˜ $_{θ}$, and the level crossing length, δr = sin 2 θ cos 2 θ | 1 n$_{e}$ dn$_{e}$ dr | − $^{1}$, of neutrinos for 5 MeV in the case of inverted mass hierarchy as a function of a radius r in units of solar radius R ⊙ = 6 . 96 × 10 cm. The left panels are at t = 0 sec, and the right panels are at t = 3 sec, respectively. We calculate by the value of sin $^{2}$2 θ$_{13}$ = 10 − $^{2}$, 10 − $^{3}$, 10 − 4 and 10 − 5 from top to bottom. Red and green lines are the oscillation length for 13 mass eigenstate for neutrinos and anti-neutrinos, and blue line are the level crossing length. 29