A comprehensive formalism for the description of neutrino oscillations
in the Earth in a general scheme with three massive neutrinos and the
mass hierarchy m(1) much less than m(2) much less than m(3) is presen
ted. Using this formalism, which is valid both in vacuum and in a medi
um, the matter effect on the oscillations of low-energy neutrinos is d
iscussed, pointing out the existence of very long oscillations which a
re independent of the neutrino masses and the neutrino energy, and are
very sensitive to the matter density along the neutrino trajectory. A
s an example of application of the formulation, a fit of the Kamiokand
e atmospheric neutrino data with the matter effect taken into account
for neutrinos propagating in the Earth is presented. The results of th
e fit indicate that 4 x 10(-3) eV(2) less than or similar to m(3)(2) l
ess than or similar to 4 x 10(-2) eV(2) and the oscillation amplitudes
in all channels (v(u) reversible arrow v(e), v(u) reversible arrow v(
tau), v(e) reversible arrow v(tau)) could be large. Hence, long-baseli
ne experiments with reactor (CHOOZ and Pale Verde) and accelerator (K2
K, MINOS and ICARUS) neutrinos could observe neutrino oscillations in
all channels with a relatively large statistics. (C) 1998 Elsevier Sci
ence B.V.