Spectral exchange in impact theory

In quantum theory as well as in classical theory, linear absorption of light at frequency co is described by a spectral function 

The stochastic problem is to describe properly the time evolution of the Heisenberg operator d(t) averaged over all the realizations of collisional process in the interval (0,t). The averaging, performed in the impact theory, results in the phenomenological kinetic equation [170, 158] 

It is calculated in the S-matrix formalism and averaged over impact distances b and velocities v with Maxwellian distribution f(v) 

At the beginning we will use both to simplify the problem, as much as it was done in the pioneering works [158, 176]. 

One of the simplest examples of line interference is impact broadening of H atom La Stark structure, observed in plasmas [176] (Fig. 4.1.(a)). For a degenerate ground state the impact operator is linear in the S-matrix  

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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]... 

The quantum theory of spectral collapse presented in Chapter 4 aims at even lower gas densities where the Stark or Zeeman multiplets of atomic spectra as well as the rotational structure of all the branches of absorption or Raman spectra are well resolved. The evolution of basic ideas of line broadening and interference (spectral exchange) is reviewed. Adiabatic and non-adiabatic spectral broadening are described in the frame of binary non-Markovian theory and compared with the impact approximation. The conditions for spectral collapse and subsequent narrowing of the spectra are analysed for the simplest examples, which model typical situations in atomic and molecular spectroscopy. Special attention is paid to collapse of the isotropic Raman spectrum. Quantum theory, based on first principles, attempts to predict the. /-dependence of the widths of the rotational component as well as the envelope of the unresolved and then collapsed spectrum (Fig. 0.4). 

We will show below when and how the line interference and its special case, spectral exchange , appear in spectral doublets considered as an example of the simplest system. It will be done in the frame of conventional impact theory as well as in its modern non-Markovian generalization. Subsequently we will concentrate on the impact theory of rotational structure broadening and collapse with special attention to the shape of a narrowed Q-branch. 

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