Resonance scattering factors

Fig. 9.34 Monitoring of inelastic excitations by nuclear resonant scattering. The sidebands of the excitation probability densities for phonon creation, S(E), and for annihilation, S —E), are related by the Boltzmann factor, i.e., S(—E) = S E) tTvp —Elk T). This imbalance, known as detailed balance, is an intrinsic feature of each NIS spectrum and allows the determination of the temperature T at which the spectrum was recorded...

Including resonance effects, the atomic scattering factor for a many-electron atom is written as... 

As is evident from Eqs. (1.36) and (1.37), and from the classical treatment as well, the effect of resonance on the intensity of X-ray scattering is pronounced when E E0, that is, in the vicinity of the absorption edges. Even for data collected at other wavelengths, it is necessary to correct the structure factors for anomalous scattering before the electron density can be calculated by the Fourier inversions of Eqs. (1.22) and (1.26), as further discussed in chapter 5. The anomalous scattering factors needed for this purpose are available in the literature (International Tables for X-ray Crystallography 1974, Kissel and Pratt 1990). 

When the atomic scattering factor is real (as it is when bonding effects on the charge density are neglected), and resonance scattering has been corrected for, the harmonic structure factor expression is equal to... 

Equation (B. 11) implies that /(H ) = /(H), that is, the rotational symmetry of the space group, is repeated in the diffraction pattern. In addition, if the atomic scattering factors / are real, which is the case when resonance effects are negligible, a center of symmetry is added to the diffraction pattern, that is, /(H) = F(H) F (H) = /( —H) even in the absence of an inversion center, which is Friedel s law. 

A remedy obviously should be available using polarization tricks. In conventional Raman spectroscopy, the isotropic and anisotropic components are deduced from linear combinations of the polarized and depolarized spectra, while a nonresonant part is not clearly recognized (41). In frequency-domain CARS it is known how to suppress the nonresonant contribution and solely measure resonant scattering (isotropic plus anisotropic part) (42). In time-domain CARS, polarization interference can do an even better job with three magic cases (derived in Refs. 35,39). These authors derived explicit expressions for the coupling factors F in Equations (2)-(4) ... 

Comparing the signal amplitudes of the data in Fig. 6a and b, the peak level of the nonresonant scattering is fully consistent with the prediction of Equation (8). The ratio of coupling constants of the resonant scattering is determined to y2/a2 = 0.8 0.2 equivalent to the depolarization factor p = 3j/2/(45a2 + 4y2) = 0.05 0.01. The number nicely agrees with the... 

The existing instruments for resonance scattering experiments may be classified according to the monochromator system. As synchrotron radiation is highly polarized in the plane of the orbit, the vertical reflection by the monochromator crystals is preferred. Under these conditions the polarization factor remains nearly constant. With reference to this design feature, the following arrangements exist or are under construction ... 

This is the dispersion of the geometrical structure factor in crystallography. The overall effect of resonant scattering is to cause the breakdown of Friedel s law so that the Bijvoet pairs of reflections S(h) and S(—h) are unequal (see e.g. ). The difference... 

The first term in equation 1.20 is the transmission of the non-resonant radiation and is independent of s. The first part of the second term is the resonant absorption in the absorber and the second part is the resonant absorption in the source. The factor accounts for non-resonant scattering in the absorber. 

This derivation, which ignores all coherent interference between potentiah and resonance scattering, is the simplest for keeping spin factors in order. We consider a reaction where an incident particle a reacts with an initial nucleus A to form a compound nucleus C, which then decays by one of a number of possible decay modes symbolized hy h- B into an outgoing nuclear subunit, or photon, h, plus a final nucleus B. The final nucleus B and the fragment h may be in their ground states with respect to internal degrees of freedom, or in one of various possible excited states. The assumptions are ... 

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