  The mechanisms that determine spin relaxation times of localized electrons in
impurity bands of n-type semiconductors are considered theoretically and
compared with available experimental data. The relaxation time of the
non-equilibrium angular momentum is shown to be limited either by hyperfine
interaction, or by spin-orbit interaction in course of exchange-induced spin
diffusion. The energy relaxation time in the spin system is governed by
phonon-assisted hops within pairs of donors with an optimal distance of about 4
Bohr radii. The spin correlation time of the donor-bound electron is determined
either by exchange interaction with other localized electrons, or by spin-flip
scattering of free conduction-band electrons. A possibility of optical cooling
of the spin system of localized electrons is discussed.
