The essential states mechanism

It is clearly a formidable task to evaluate eqn (8.33) for all the possible states. However, a considerable simplification occurs if we adopt the essential states mechanism, introduced by Mazumdar et al. (Dixit et al. 1991) following earlier work by Heflin et al. (1988) and Soos and Ramesesha (1989). The key idea behind this concept is that only a few states are strongly dipole connected, and that these states dominate the sum. In fact, as we saw in Section 8.3.4, the state with the largest dipole moment to the ground state is the lowest-lying exciton state, the n = 1 and j = 1, or the state. This, in turn, is most strongly 

In the weak-coupling (Mott-Wannier) limit m = 2 if particle-hole symmetry applies. Otherwise m 2. In the strong-coupling (Mott-Hubbard) limit m 2 always. The essentially states are shown schematically in Figs 6.7 and 6.9 for the weak-coupling and strong-coupling limits, respectively. 

Bearing in mind these caveats for the validity of the essential states mechanism, we shall now make the assumption that it is a reasonable approximation. This enables us to more readily interpret the third order nonlinear susceptibilities, and in particular, to relate experimental observations to the excited states of the polymer. We discuss this in the following sections. 

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Second, we invoke the essential-states mechanism, described in Chapter 8, which states that only a few states are strongly dipole connected. These are the groimd state and the lowest (pseudo)momentum eigenstate of each family of exciton states. For centro-symmetric polymers these states are ... 

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