t g g t r the photon vector potential. Following the effective mass approximation, the foregoing matrix element may be written as [140]

where O is the volume of the unit cell and ff(f) is the envelope function for the final (initial) state. For the case of the donor impurity we have, for Sfi = Sfi(R, A),

1/2 - r ro 2 Sfi = Í — ) N(R, A) I dr sin2 ikm r)

For an infinite GaAs quantum dot of radius r0 with one impurity inside, the transition probability per unit time for valence to donor transitions is given by w(M,R) = WqI-^T )S2Y(A)

where aB is the Bohr radius and F(A) is the step function. In this expression we have for A and

For a homogeneous distribution of impurities and assuming that the quantum dot radius is much larger than the lattice parameter one has for the total transition probability per unit of time

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