  The size-dependent decoherence of the exciton states resulting from the
spontaneous emission is investigated in a semiconductor spherical
microcrystallite under condition $a_{B}\ll R_{0}\leq\lambda$. In general, the
larger size of the microcrystallite corresponds to the shorter coherence time.
If the initial state is a superposition of two different excitonic coherent
states, the coherence time depends on both the overlap of two excitonic
coherent states and the size of the microcrystallite. When the system with
fixed size is initially in the even or odd coherent states, the larger average
number of the excitons corresponds to the faster decoherence. When the average
number of the excitons is given, the bigger size of the microcrystallite
corresponds to the faster decoherence. The decoherence of the exciton states
for the materials GaAs and CdS is numerically studied by our theoretical
analysis.
