4 larger than one, the predicted probability difference undergoes a relatively larger change with the increase in η . Neutrino factory.— Neutrino beams from a neutrino fac- tory [23] can also be employed in the neutrino oscillation to- mography. In our configuration, we choose an electron neu- trino beam with energy E$_{ν}$ = 7 GeV. Our calculation indi- cates that the difference in survival probabilities correspond- ing to the cases with and without the anomalous electron ac- cumulation is not obvious. Indeed, an observable difference of about 0.01% may be detected if the detector is 6000 km away from the source. However, such a length of baseline is much beyond the maximal distance in the crust layer and such a small difference may not be detected with the accuracy of FIG. 3: The dependence of the differences (in percent) in survival probabilities between cases without and with an anomalous accu- mulation of electrons on the η value for reactor antineutrinos whose width w = 20, 50, 80 and 100 km, respectively. TABLE I: The parameters of neutrino oscillation in matter for beams produced in a reactor and in a neutrino factory. For reactor electron antineutrinos E ν = 3.6 MeV and for neutrino factory electron neutri- nos E ν = 7 GeV. R$_{11}$ = exp ( i Δ m 2 M 2 E$_{ν}$ x ) + sin $^{2}$θ$_{M}$ [ 1 − exp ( i Δ m 2 M 2 E$_{ν}$ x )] , R$_{22}$ = exp i Δ m 2 M 2 E$_{ν}$ x + cos $^{2}$θ$_{M}$ 1 − exp i Δ m 2 M 2 E$_{ν}$ x , R$_{12}$ = R$_{21}$ = 1 2 sin $^{2}$2 θ$_{M}$ [ 1 − exp ( i Δ m 2 M 2 E$_{ν}$ x )] , (11) 2 E$_{ν}$V Δ m 2 ≈ 0 . 029 ≪ 1 , (12) φ m a → b = 1 2 E$_{ν}$ ∫ b a dx [ ( Δ cos 2 θ$_{0}$ ± √$_{2}$$_{E}$$_{ν}$$_{G}$$_{F}$ ρ ( x ) m$_{N}$ ) 2 + (Δ sin 2 θ$_{0}$ ) 2 ] 1 2 (13) ( ¯ ν III e ¯ ν III x ) = R $^{III}$R$^{II}$RI ( ¯ ν 0 e ¯ ν 0 x ) . (10) 0 2 4 6 8 Η 0 0.5 1 1.5 2 2.5 GLYPH<CapDelta> P GLYPH<LParen1> Ν GLYPH<OverBar> GLYPH<RArrow>Ν GLYPH<OverBar> GLYPH<RParen1>GLYPH<LParen1> % GLYPH<RParen1> width GLYPH<Equal> 80km 0 2 4 6 8 Η 0 0.1 0.2 0.3 0.4 GLYPH<CapDelta> P GLYPH<LParen1> Ν GLYPH<OverBar> GLYPH<Minus>GLYPH<Greater>Ν GLYPH<OverBar> GLYPH<RParen1>GLYPH<LParen1> % GLYPH<RParen1> w GLYPH<Equal> 100km 0 2 4 6 8 Η 0 0.1 0.2 0.3 0.4 GLYPH<CapDelta> P GLYPH<LParen1> Ν GLYPH<OverBar> GLYPH<RArrow>Ν GLYPH<OverBar> GLYPH<RParen1>GLYPH<LParen1> % GLYPH<RParen1> width GLYPH<Equal> 20km 0 2 4 6 8 Η 0 0.01 0.02 0.03 0.04 GLYPH<CapDelta> P GLYPH<LParen1> Ν GLYPH<OverBar> GLYPH<RArrow>Ν GLYPH<OverBar> GLYPH<RParen1>GLYPH<LParen1> % GLYPH<RParen1> width GLYPH<Equal> 50km picture very complicated and does not change our qualitative conclusion. In this configuration, there are three slabs, I, II and III. Ea ch of them is assumed to possess a uniform matter density and can be treated with an R -matrix [22]. The elements of the R -matrix are determined by the mass- squared difference Δ m 2 $_{M}$, neutrino energy E$_{ν}$ and antineu- trino path length in the slab. In a uniform slab, the elements of the R -matrices are where x is the antineutrino path length in the slab. we cal- culate the survival probabilities without and with the anoma- lous accumulation of electrons at the fault zone. In Fig. 2 we present the differences in survival probabilities of the re- actor electron antineutrino between cases without and with an anomalous accumulation of electrons for η =3 and differ- ent widths. For oscillations in medium with and without the anomalous electron accumulation, the maximal difference in P$_{¯}$ ν$_{e}$ → ¯ ν$_{e}$ is up to 2% when the width w = 100 km. Among all of the fault zone parameters, the width and the η value play important roles in antineutrino oscillations. For reactor electron antineutrinos, the dependence of the differ- ences of survival probabilities on η is plotted in Fig. 3 with antineutrino energy E$_{ν}$ = 3.6 MeV for different width values. Fig. 3 indicates that for η < 1 , the effect is tiny, and for η is for E$_{ν}$ = 3.6 MeV and η = 3. With the perturbation method, the exact adiabatic phase shift in matter is obtained as Result from perturbation method.— In a low matter den- sity medium, V ≪ Δ m $^{2}$/ 2 E$_{ν}$ , Ioannisian and Smirnov [24] developed a perturbation method where ϵ = 2 V E$_{ν}$/ Δ m 2 is taken as the expansion parameter for calculating the oscilla- tion probability. For the maximal matter density ηρ$_{0}$ in our case, one can determine the present neutrino facilities in our configuration. The re ason is obvious that the accelerator neutrinos have much larger en- ergy than the reactor antineutrinos, thus the oscillation length L M osc for neutrinos from a neutrino factory is much longer than that for the reactor ones as shown in Table I. Parameter Reactor Slab I II III L (km) 1418 w 200 ρ ( g/ cm $^{3}$) 2.8 2 . 8 × 3 2.8 Δ m 2 M (10 $^{$_{−}$5}$eV $^{2}$) 8 . 02 8 . 09 8 . 02 tan 2 θ M 2.42 2.30 2.42 L M osc (km) 111.18 110.36 111.18 Parameter Neutrino Factory Slab I II III L (km) 1418 w 200 ρ ( g/ cm $^{3}$) 2.8 2 . 8 × 3 2.8 Δ m 2 M (10 $^{$_{−}$3}$eV $^{2}$) 1 . 46 4 . 42 1 . 46 tan 2 θ M (10 $^{$_{−}$2}$) − 5 . 10 − 1 . 68 − 5 . 10 L M osc (10 $^{3}$km) 11 . 92 3 . 92 11 . 92