  For the model Hamiltonian describing the electron-nuclear dynamics of a
quantum dot, we obtained an exact expression for the limiting nuclear
polarization as a function of the number of groups of equivalent nuclei. It is
shown that the refinement of the model Hamiltonian by increasing the number of
the groups results in a slow growth of the limiting nuclear polarization. This
allowed us to put forward arguments in favor of applicability of the box-model
(with all the nuclei being equivalent) for description of the electron-nuclear
spin dynamics within the time intervals of around hundreds of periods of the
optical orientation.
