Overlapping radiation fields

I note, however, the caveat above Our work to date has ignored the possibility of overlapping levels due to the high density of molecular states coupled with the background radiation field. We expect to examine these cases shortly. 

Since the state E, n", N", t) contains the effect of the full Hamiltonian at time fq then the photodissociation amplitude A(E, n, N, t i, A)) into the final state will energy E, internal quantum numbers n and radiation field described by N, starting in the initial state ] , initial state and the incoming fully interacting state. That is,... 

A possible absorption spectrum for a molecule near its unimolecular dissociation threshold is shown in figure 8.1. Below the absorption lines for the molecular eigenstates are very narrow and are only broadened by interaction of the excited molecule with the radiation field. However, above the excited states leak toward product space, which gives rise to characteristic widths for the resonances in the spectrum. Since the line widths do not overlap, the resonances are isolated. Each... 

Since the radiation field inside the active resonator or inside the mode-matched passive cavity is concentrated within the region of the Gaussian beam (Sect.5.11), the laser-excited fluorescence can be effectively imaged onto the entrance slit of a spectrometer with a larger efficiency than in the commonly used multipass cells. The use of a spectrometer is necessary not only in fluorescence or Raman spectroscopy but also in absorption spectroscopy, if minute concentrations of an absorbing component have to be selectively detected in the presence of other constituents with overlapping absorption lines but different fluorescence spectra. 

An important feature of the use of soft radiation is that both the extinction distance and the absorption distance are small, and therefore the X-rays penetrate only a veiy small distance into the crystal. We therefore examine only a small slice of the crystal close to the surface. The strain fields of dislocations deeper into the crystal do not contribute significantly to the image and, in a transmission experiment, overlapping of the images leads to an upper limit of about 10" cm on the dislocation density for individual defect imaging. With the Berg-Barrett technique this can be pushed to about 10 cm ... 

FIGURE 9.12 (a) Calculated FE-CARS radiation profile when a HGOl excitation field overlaps with a lateral interface between a resonant and a nonresonant material. Note that the intensity along the optical axis is no longer zero due to partial lifting of the phase step by the interface. The inset shows the excitation field relative to the orientation of the interface, (b) Comparison of the calculated spectral dependence of CARS in a bulk material with a weak resonance and FE-CARS measured at an interface similar to the one considered in (a). Note the Raman-like spectral dependence of the FE-CARS signal. 

Up to now we have been discussing in this Chapter many-particle effects in bimolecular reactions between non-interacting particles. However, it is well known that point defects in solids interact with each other even if they are not charged with respect to the crystalline lattice, as it was discussed in Section 3.1. It should be reminded here that this elastic interaction arises due to overlap of displacement fields of the two close defects and falls off with a distance r between them as U(r) = — Ar 6 for two symmetric (isotropic) defects in an isotropic crystal or as U(r) = -Afaqjr-3, if the crystal is weakly anisotropic [50, 51] ([0 4] is an angular dependent cubic harmonic with l = 4). In the latter case, due to the presence of the cubic harmonic 0 4 an interaction is attractive in some directions but turns out to be repulsive in other directions. Finally, if one or both defects are anisotropic, the angular dependence of U(f) cannot be presented in an analytic form [52]. The role of the elastic interaction within pairs of the complementary radiation the Frenkel defects in metals (vacancy-interstitial atom) was studied in [53-55] it was shown to have considerable impact on the kinetics of their recombination, A + B -> 0. 

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