  We study the low-temperature dynamics of a shallow donor, e.g., $^{31}$P,
impurity electron spin in silicon, interacting with the bath of nuclear spins
of the $^{29}$Si isotope. For small applied magnetic fields, the electron spin
relaxation is controlled by the steady state distribution of the nuclear spins.
We calculate the relaxation times $T_1$ and $T_2$ as functions of the external
magnetic field, and conclude that nuclear spins play an important role in the
donor electron spin decoherence in Si:P at low magnetic fields.
