  Solar neutrino physics enters a stage of precision measurements. In this
connection we present a precise analytic description of the neutrino conversion
in the context of LMA MSW solution of the solar neutrino problem. Using the
adiabatic perturbation theory we derive an analytic formula for the $\nu_e$
survival probability which takes into account the non-adiabatic corrections and
the regeneration effect inside the Earth. The probability is averaged over the
neutrino production region. We find that the non-adiabatic corrections are of
the order $10^{-9}-10^{-7}$. Using the formula for the Earth regeneration
effect we discuss features of the zenith angle dependence of the $\nu_e$ flux.
In particular, we show that effects of small structures at the surface of the
Earth can be important.
