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

The limiting nuclear polarization in a quantum dot under optical  electron-spin orientation and applicability of the box-model of the  electron-nuclear dynamics