  A set of quantitative predictions for the day-night asymmetry in the Super -
Kamiokande detector is presented. For these predictions, neutrino events are
collected in ``samples'' defined by the trajectories in the Earth of the
corresponding solar neutrinos. The more important samples considered here are:
the full sample of neutrinos detected at night, the sample of night neutrinos
which cross the Earth core and the sample of night neutrinos which does not
cross the Earth core. For energy integrated event rates, the day-night
asymmetry for core crossing neutrinos is up to six times bigger than the
day-night asymmetry for the full sample of night neutrinos. When the reduction
in statistics is considered, an effective enhancement up to a factor $\approx
2.3$ is obtained. The selection of core crossing neutrinos may be relevant for
the recoil - $e^-$ spectra too. From these results it is reasonable to expect
the Super Kamiokande detector be able to constrain the small mixing angle
solution of the solar neutrino problem ($\sin^2 2 \theta_v \leq 0.01$) through
the day-night effect. Furthermore, it is proposed that the day-night effect may
limits the total flux of 8B neutrino produced in the Sun. At last, the
sensitivity of these predictions to the Earth model uncertainties is
quantitatively discussed.
