Born approximation, zeroth-order

In Chapters 4 and 5 we made use of the theory of radiationless transitions developed by Robinson and Frosch." In this theory the transition is considered to be due to a time-dependent intramolecular perturbation on non-stationary Born-Oppenheimer states. Henry and Kasha > and Jortner and co-workers< > have pointed out that the Born-Oppenheimer (BO) approximation is only valid if the energy difference between the BO states is large relative to the vibronic matrix element connecting these states. When there are near-degenerate or degenerate zeroth-order vibronic states belonging to different configurations the BO approximation fails. 

The evaluation of P requires knowledge about the photoelectron amplitude. It should, of course, be calculated as a continuum amplitude from the Dyson equation, but for a general molecule that is still a tough problem, and one proceeds by making more or less ad hoc choices. The perhaps simplest description of the photoelectron is v kf,r) — (27t) 5 ex.p ikf r). This choice of a plane wave is often referred to as the sudden approximation, or the zeroth-order Born approximation. If a primitive atomic orbital basis aj(r — Pa) is used. 

Before discussing this new method it is useful to recall briefly the methods which we have already discussed. Note, first of all that calculations of the dielectric tensor must be based, as is known, upon a microscopic theory Such a theory for ionic crystals was first developed by Born and Ewald (2) for the infrared spectral region. The application of this approach for the region of exciton resonances has also been demonstrated in (3). In an approach identical to that of Born and Ewald (2) the mechanical excitons (see Section 2.2) are taken as states of zeroth-approximation. In the calculation of these states the Coulomb interaction between charges has to be taken into consideration without the contribution of the long-range macroscopic part of the longitudinal electric field. If this procedure can be carried out, then the Maxwell total macroscopic fields E and H can be taken as perturbations. In the first order of perturbation theory, we find... 

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