Forster energy transfer from quantum dots to organics

5 Forster energy transfer from quantum dots to organics 

The electric field E(r) corresponding to this polarization can be found from the Poisson equation for the potential / (r)  

Hence we find that the rate of energy transfer (the reciprocal of the transfer time) is given by the expression 

In our spherical geometry the states of an electron-hole pair can be classified according to the values of the total angular momentum of the electron and hole. We shall assume that the electron-hole pair occupies the lowest excited state. In this state the total angular momentum is zero, and therefore the function (r, r) is spherically symmetric and P(r) = P(r). Orienting the 2-axis parallel to the vector dvc, we obtain for the charge density 

Here Yio( ) oc cos 9 is the spherical harmonic with l = 1 and m = 0 that is obtained when a spherically symmetric function is differentiated with respect to 2. Expanding the potential / (r) in the organic material, where there are no charges, in terms of multipoles, we see that only the dipole term, which is proportional to Yio( ), will be different from zero. Therefore the potential / (r) in the organic medium is formally identical to the potential of an effective point dipole with dipole moment peff  

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