  We present a theory of the local field corrections to the spontaneous
emission rate for the array of silicon nanocrystals in silicon dioxide. An
analytical result for the Purcell factor is obtained. We demonstrate that the
local-field corrections are sensitive to the volume fill factor of the
nanocrystals in the sample and are suppressed for large values of the fill
factor. The local-field corrections and the photonic density of states are
shown to be described by two different effective permittivities: the harmonic
mean between the nanocrystal and the matrix permittivities and the
Maxwell-Garnett permittivity.
