Quantum theory of spectral collapse

The quasi-classical theory of spectral shape is justified for sufficiently high pressures, when the rotational structure is not resolved. For isotropic Raman spectra the corresponding criterion is given by inequality (3.2). At lower pressures the well-resolved rotational components are related to the quantum number j of quantized angular momentum. At very low pressure each of the components may be considered separately and its broadening is qualitatively the same as of any other isolated line in molecular or atomic spectroscopy. 

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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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). 

Quantum theory of spectral collapse 4.3 Non-Markovian binary theory... 

The whole shape of the spectrum (before and after collapse) is described by a more general formula of quantum theory which follows from Eq. (4.55) and Eq. (4.62) [185, 186]. For aj = inv the normalized spectral shape is... 

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