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The linear and the third-order nonlinear optical properties associated with intersubband transitions are studied for spherical Si nanodot embedded in an amorphous matrix. The effect of radiation intensity and the change in the size of the dot are investigated on the nonlinear photoabsorption coefficient, refractive index change, and the third-order nonlinear optical susceptibility for transitions from ground state (1s-1p) and excited states (1p-1d, 2s-2p). The oscillator strength is also calculated for these transitions along with the photoelectric cross sections from the initial 1s and 2s states of the dot. It is noted that a decrease in the size of the dot leads to blue shift in peak positions of photoabsorption coefficient, refractive index change, and third-order nonlinear susceptibility involving transitions from the ground and excited states.