  We propose a model for spectral diffusion of localized spins in
semiconductors due to the dipolar fluctuations of lattice nuclear spins. Each
nuclear spin flip-flop is assumed to be independent, the rate for this process
being calculated by a method of moments. Our calculated spin decoherence time
$T_{M}=0.64$ ms for donor electron spins in Si:P is a factor of two longer than
spin echo decay measurements. For $^{31}$P nuclear spins we show that spectral
diffusion is well into the motional narrowing regime. The calculation for GaAs
quantum dots gives $T_{M}=10-50$ $\mu$s depending on the quantum dot size. Our
theory indicates that nuclear induced spectral diffusion should not be a
serious problem in developing spin-based semiconductor quantum computer
architectures.
