Adiabatic approximation, collapse

Figure 4.4. Decay of the surface specular reflection vs thermal disorder, static disorder, and surface annihilation caused by photodimerization. The surface reflection intensity of structure I is plotted vs broadening by temperature (full circles) and by photodimerization (hollow diamonds) which causes static disorder and annihilation of surface anthracene molecules. The solid line is deduced from theoretical calculations (2.126) in the adiabatic approximation. The cloud of hollow diamonds suggest that the density a of unperturbed surface molecules has been reduced below the critical value, with the consequent collapse of the specular reflection cf. (4.20). The inset shows the perfect surface structure (1), the temperature-broadened surface structure (2), and the structure of a photodimerized surface (3), which allowed us to plot the experimental curves.

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). 

Let us assume that the lifetime of the delocalized state is limited by proton transfer between one of the base pairs such that as soon as one proton coordinate cross the XT/CT intersection, the delocalized state collapses to from a localized state. Assuming the usual Condon separation between the nuclear and electronic dynamics, we can write this within the non-adiabatic Marcus approximation... 

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