Line interference in stochastic perturbation theory

Let us reconsider the four-level system shown in Fig. 4.1(6), which has two doublets in the spectrum split by 2A and 2e (Fig 4.4(a)). Since diagonal elements of G,kjm are the same in impact and Markovian theories we assume that F , = 0 without any restriction of generality. This is actually the case for any electric multipolar interaction and hence Ac0 = 0. The non-zero elements of the perturbation 

It corresponds to the long-range interaction (1/r2) [20]. The Fourier transform of Eq. (4.41) is 

Much simpler is the situation in the Markovian limit. The spectrum is governed by the co-independent operator 

As shown in Fig. 4.4a, splitting of the Q-branch doublet is usually so small that it can be neglected when calculating Consequently the additional condition 

With these simplifications the general formula (4.50) reduces to the well-known result of the Markovian (as well as impact) theory of spectral exchange in the doublet [9, 20] 

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