Non-resonant scattering

In the process of scattering and absorption, the electric component of the incident wave excites the vibrations of the oscillator. Under the effect of this component the electron performs forced vibrations. If the eigenfrequency ojq of the oscillator coincides with that of the light wave u>i, resonance absorption is observed. If these frequencies do not coincide, we have non-resonant scattering of light. 

Synchrotrons produce photons with energies in the range of nuclear Mossbauer transitions and can, in principle, be used to excite these transitions. However, synchrotron radiation can be monochromatized to only about 1 meV with new monochromators. Because the accessible nuclear levels are extremely narrow (between 10 and 10 eV), it is only about 10 of the incident photons that can excite the nuclear levels (excitation cross-section could be as much as 10 Fq). This is far weaker than radiation that is non-resonantly scattered by the electronic processes in the solid arising from the scattering of the entire 1 meV width of the incident radiation. 

Raman process the spin center transfer to another energy level via a virtual state involving two phonons and this is called non-resonance scattering process. 

Figure 4 Illustration of resonances in a one-dimensional square-well potential. The two lowest solid lines are bound-state wave functions, whereas the upper two solid lines illustrate resonance wave functions. The dashed curve represents a non-resonant scattering state . Shown is the modulus square of x the scaling is different for the different wave functions. In the numerical example in the text, Vi = 8 and V2 = 12.

In the e + M case, a very sensitive Indicator of shape resonance behavior Is the vibrational excitation channel. Vibrational excitation Is enhanced by shape resonances (3,17), and Is typically very weak for non-resonant scattering. Hence, a shape resonance, particularly at Intermediate energy (10-40 eV) (41,50), may be barely visible In the vlbratlonally and electronically elastic scattering cross section, and yet be displayed prominently In the vlbratlonally Inelastic, electronically elastic cross section. 

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. 

Non-resonant scattering inside the source can be reduced, either by careful choice of any other elements in the matrix, or, in the case of metal foils doped with a radioisotope which is the Mdssbauer precursor, by controlling the depth to which this generating impurity is diffused. 

The Raman effect arises from a non-resonant scattering interaction and is quite weak. Thus any resonant interaction, such as fluorescence, either from the sample of interest or from impurities contained in the sample, can completely mask the Raman spectrum. In addition, conventional Raman spectroscopy lacks the frequency-precision necessary for good spectral subtractions. Finally, high- resolution experiments are difficult with conventional grating instruments, since they become throughput-limited when the slit-width is reduced. These three problems are now completely solved, except for the presence of background signals, especially in relation to low frequency vibrations (less than 100 cm ). 

The combination of illuminating the sample with a strongly focused laser beam and observing the laser-induced fluorescence or the non-resonant scattered laser light with confocal microscopy allows the detection of single molecules and their diffusion through a liquid medium. Each molecule can emit N = T/2r photons (see Fig. 10.2) where T is the diffusion time through the laser beam and r the upper state lifetime. 

Fig. 6.48. A simple corpuscular picture of three cases where non-resonant scattering can be asymmetric, (a) Intrinsic spin-orbit coupling acts on an electron influenced by any attractive scattering centre, (b) Extrinsic spin-orbit coupling between the ionic spin S and the electron s temporary orbital angular momentum I. (c) An ion with a nonzero L can couple with I via an electrostatic mechanism (after Hurd 1975).

We will now give a more detailed description of the electron trapping phenomena and show that it is associated with the self-orthogonality phenomenon. It is known that the resonance of H2 which is responsible for the vibrational excitation in the low energy region, is an extremely short-lived resonance with a lifetime comparable with the duration of the non resonant scattering [17]. 

One other notable feature of the data shown in fig. 25 is that in the non-resonant scattering experiments no scattering was observed at the primary satellite position tm in the purely c-axis modulated phase that exists above 52 K, where the cross-section varies as sin 6 and is weak. This observation had to wait for resonant scattering techniques to be applied to the problem. 

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