Oscillations of the $^{7}Be$ solar neutrinos inside the Earth

We explore in detail oscillations of solar $^{7}Be$ neutrinos passing through the Earth. The depth of oscillations is at the (0.1-0.2)% level, and the length is approximately 30 km. The change of the oscillatory modulations with energy is comparable to the width of the $^{7}Be$ line, which is determined by the temperature in the center of the Sun. This means that, depending on the length of the trajectory (nadir angle), one obtains different degrees of cancellations when averaging the oscillations over the $^{7}Be$ neutrino energy. Thus, by exploring these oscillations in detail, it is possible to determine the width of the $^{7}Be$ line and therefore the temperature of the Sun and to fix $\Delta m^2_{21}$ precisely. Furthermore, it allows us to perform tomography of the Earth, in particular to measure the deviation from a spherical mass distribution and detect small inhomogeneities. Studies of the Be neutrinos open up a possibility to test quantum mechanics of neutrino oscillations and search for sterile neutrinos. We also estimate the accuracy of these measurements with future scintillator (or scintillator uploaded) detectors of $\sim 100 kton$ mass