A set of quantitative predictions for the D-N 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 D-N asymmetry for core crossing neutrinos is up to six times bigger than the D-N 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 D-N effect .
Furthermore , it is proposed that the D-N effect may limits the total flux of ^ { 8 } B neutrino produced in the Sun .
At last , the sensitivity of these predictions to the Earth model uncertainties is quantitatively discussed .