Electric field effect on fluorescence of molecules

22) previously given in Section 3.2. We will now analyze in greater detail the methods of solving this equation. As is known, the product E d has to be considered as a hermitian product of E and d [140]. It is just such a product which represents the amplitude with which the vector E is contained in the vector d. As a result we have for the matrix elements of the electric dipole transition 

For the matrix element M dg p) entering into the righthand part of Eq. (5.8) we obtain, applying the Wigner-Eckart theorem (D.7), 

Here the proportionality factor fp ( J d J ) 2/(2J +l) coincides with the dynamic part of the absorption probability introduced in Chapter 2. The sum in (5.10) presents the angular part of the absorption probability, whilst the factor (rmm + 0 %M ) 1 describes the effect upon /mm both on the part of perturbation by the external field, causing splitting of the magnetic sublevels j ujmm i and by spontaneous decay and collisions (anisotropic in the general case), together described by a set of relaxation rates Tmm Applying similar manipulations as for (5.7) to Eq. (5.6), we obtain an equation for fluorescence intensity  

In the calculation of circularly or elliptically polarized fluorescence it is necessary to keep in mind the fact that Eq. (5.11) yields the intensity of light with polarization (E ) [6, 192]. 

One of the most interesting effects that can be analyzed by applying the formulae obtained in the preceding section is the influence of an external 

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