Incoherent absorption

Finally, if one has a condition with incoherent radiation of a small band width Av exciting a broad absorption band with a(v + A ) one finds ... 

The Goeppert-Mayer two- (or multi-) photon absorption, mechanism (ii), may look similar, but it involves intennediate levels far from resonance with one-photon absorption. A third, quasi-resonant stepwise mechanism (iii), proceeds via smgle- photon excitation steps involvmg near-resonant intennediate levels. Finally, in mechanism (iv), there is the stepwise multiphoton absorption of incoherent radiation from themial light sources or broad-band statistical multimode lasers. In principle, all of these processes and their combinations play a role in the multiphoton excitation of atoms and molecules, but one can broadly... 

Experiments on the sky. Two experiments have been carried out at the sky, using two laser installations built for the American and French programmes for Uranium isotope separation, respectively AVLIS at the Lawrence Livermore Nat l Lab (California) in 1996 and SILVA at CEA/Pierrelatte (Southern France) in 1999. The average power was high pa 2 x 175 W, with a pulse repetition rate of 12.9 and 4.3 kHz, a pulse width of 40 ns and a spectral width of 1 and 3 GHz. Polarization was linear. The return flux was < 5 10 photons/m /s (Foy et al., 2000). Thus incoherent two-photon resonant absorption works, with a behavior consistent with models. But we do need lower powers at observatories ... 

Figure 5 X-ray mass attenuation coefficients for aluminum as a function of photon energy. At low energies, photoelectric absorption predominates. At higher energy, incoherent (Compton) scatter becomes almost the exclusive contributing mode. Eventually, pair production dominates at very high energies (above 10 MeV).

A primary hydration number of 6 for Fe + in aqueous (or D2O) solution has been indicated by neutron diffraction with isotopic substitution (NDIS), XRD, 16,1017 EXAFS, and for Fe " " by NDIS and EXAFS. Fe—O bond distances in aqueous solution have been determined, since 1984, for Fe(H20)/+ by EXAFS and neutron diffraction, for ternary Fe " "-aqua-anion species by XRD (in sulfate and in chloride media, and in bromide media ), for Fe(H20)g by neutron diffraction, and for ternary Fe -aqua-anion species. The NDIS studies hint at the second solvation shell in D2O solution high energy-resolution incoherent quasi-elastic neutron scattering (IQENS) can give some idea of the half-lives of water-protons in the secondary hydration shell of ions such as Fe aq. This is believed to be less than 5 X I0 s, whereas t>5x10 s for the binding time of protons in the primary hydration shell. X-Ray absorption spectroscopy (XAS—EXAFS and XANES) has been used... 

After subtracting the sample-independent background and correcting for absorption, multiple scattering, and incoherent scattering we obtain the structure function, S(Q), which is normalized to unity at Q cx). In terms of the atomic position and Q, S(Q) is given by ... 

This breakdown of the linear relationship between the absorption coefficient a and the product of densities, Q1Q2, indicates that the observed absorption is not a binary process. Specifically, for the case at hand, one can no longer assume that the measured absorption consists of an incoherent superposition of the pair contributions. Rather, the correlations of the dipoles that are induced in subsequent binary collisions lead to a partially destructive interference, an absorption defect that occurs if the product of the time T12 between Ne-Xe collisions, and microwave frequency, /, approaches unity [404], We note that for the spectra shown above, Figs. 3.1 and 3.2, the product fx 2 is substantially greater than unity at all frequencies where experimental data are shown and, consequently, incoherent superpositions of the waves arising from different induced dipoles occur. The intercollisional absorption defect is limited to low frequencies (Lewis 1980). 

A further factor which affects the shape of a resonance line is the transport of resonance radiation through the. parent gas. Milne s early theory of self-absorption by the imprisonment of resonance radiation has been revised by Holstein (3) and Bichermau (4), taking into account the incoherent scattering of resonance photons. Furthermore, Walsh (" ) has extended the imprisonment lifetime calculation for cases where Doppler and collision broadening of the resonance line are simultaneously present, and in addition this author has examined the complications caused by the, hfs. The line shape, linewidth, and other properties of self-absorbed lines hare been discussed recently bv Tako (6), who summarizes the various effects of self-absorption as follows ... 

The isolated intrachain scattering is used to determine the persistent local conformation by comparison between the scattering from single chains and the experimental data. The experimental data needs to be corrected for absorption, polarisation, multiple and incoherent scattering and in addition the intensities normalised to electron units, before quantitative intensity comparisons are possible. The s-weighted reduced intensity function si(s) is a better choice for such comparisons where ... 

Flynn and Stoneham [1970] were the first to suggest that diffusion of the light impurity atom is enhanced by symmetrically coupled vibrations. To incorporate this effect, which is called fluctuational barrier preparation, the authors have proposed to take into account the dependence of the tunneling matrix element on displacements of the heavy nuclei. This approach goes beyond the familiar Condon approximation. In this version of phonon-assisted tunneling, the phonon-dressed incoherent transitions are also induced by a suitable reduction in the barrier height via emission or absorption of phonons. 

The absorption spectrum, branching ratios, and final state distributions depend uniquely — at least in principle — on the initial quantum state of the parent molecule before it absorbs the photon. Recent experimental advances have made it possible to prepare with a first laser (wavelength Ai) the parent molecule in a particular state before a second laser (wavelength A2) dissociates it (Hausler, Andresen, and Schinke 1987 Vander Wal, Scott, and Crim 1991). This allows the study of molecular dynamics on a truly state-specific level. Incoherent averaging caused by the simultaneous dissociation of several initial states is thus avoided. The... 

Figure 2. Cotton s experimental apparatus for measuring absorption coefficients for left-and right-circularly polarized light. p1 incoherent source Lj, L2, focusing lenses Nj, N2, Nicol polarizing prisms M2, limiting apertures Fj, F2, quarter-wave Fresnel rhombs S, sample cell p2, location for light detection (visual). From ref. [2].

Figure 11.3 Incoherent interference control (IIC) scheme and potential energy curves fori, Na2 - Na + Na(3d), Na(4s), Na(3p). In this scheme an (on + a), photon excitation to the continuum interferes with an co2 photon from an initially unpopulated state. Two-photons absorption proceeds from an initial state, 0) (in Na2 it is taken to be the v = 5, 7 = 37 state), via the ]is1) (u = 35, 7 = 36,38) intermediate resonance belonging to the interacting, S /3n electronic states. The oj2 photon couples the continuum to the (initially unpopusf lated) E2) (v = 93, J — 36 or u = 93, 7 = 38) level of the lSll/3ril, electronic state j (Taken from Fig. 1, Ref. [201].). feg...

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