Compton scattering theory

The Compton scattering cannot be neglected, but it is independent of molecular structure. Then, fitting experimental data to formulas from gas phase theory, the concentration of excited molecules can be determined. Another problem is that the undulator X-ray spectrum is not strictly monochromatic, but has a slightly asymmetric lineshape extending toward lower energies. This problem may be handled in different ways, for example, by approximating its spectral distribution by its first spectral moment [12]. 

Experimental chemists are rarely concerned with quantum effects and it s not unusual to find them ignoring this fundamental theory altogether. Even when an effort is made to explore the topic more deeply traditional quantum phenomena like black-body radiation, Compton scattering and even the photoelectric effect may appear to be of somewhat limited importance. Experimentalists who rely on spectroscopic measurements get by with interpretations based on a few simple semi-classical rules, and without ever appreciating the deep significance of quantum theory. Maybe there is a problem with the rigorous mathematical formulation of quantum theory and too little emphasis on quantum effects routinely encountered in chemistry. 

Schrodinger s equation is widely known as a wave equation and the quantum formalism developed on the basis thereof is called wave mechanics. This terminology reflects historical developments in the theory of matter following various conjectures and experimental demonstration that matter and radiation alike, both exhibit wave-like and particle-like behaviour under appropriate conditions. The synthesis of quantum theory and a wave model was first achieved by De Broglie. By analogy with the dual character of light as revealed by the photoelectric effect and the incoherent Compton scattering... 

Work on the structure of crystals and fibers was not the only way in which Mark made use of x-rays. With several collaborators, he reported the results of a number of significant investigations of the physics of x-rays in 1926 and 1927. With Ehrenberg he reported studies of the index of refraction of x-rays, and with Leo Szilard studies verifying the linear polarization of x-rays scattered from electrons at 90. An investigation of the width of x-ray lines was carried out by Mark and Ehrenberg, and Mark and Kallmann reported work on the properties of Compton-scattered x-radiation and on the theory of the dispersion and scattering of x-rays. 

Abstract We present preliminary experimental results of inelastic X-ray scattering (IXS) on molecular vibrations of liquid H2O, DoO and the equimolar H>0 - D >0 mixture. The data analysis indicates the presence of an anomalous shortfall of scattering intensity from the O//-stretching vibrational modes. This effect has no explanation within the frame of conventional X-ray scattering theory. The possible connection of these observations with recent results of neutron and electron Compton scattering from protons in condensed matter is mentioned, as well as their interpretation in terms of attosecond entanglement. 

In the Compton scattering we have therefore a typical example of a process in which radiation behaves like a corpuscle of well-defined energy (and momentum) an explanation by the wave theory of the experimental results which we have described seems absolutely impossible. On the other hand, interference phenomena are quite irreconcilable with the corpuscular view of radiation. Until a few years ago, to explain this contradiction in the theory of light seemed to be beyond the bounds of possibility. 

Theoretical predictions of decoherence rates, based on known interactions between system and environment, are still only at a primitive level due to the complexity of most experimental situations. A simple example will be discussed in this chapter in relation to one of the experiments. The Compton scattering of neutrons also seems to allow measurements that have another connection to recent discussions on quantum information theory, namely, the energy needed to destroy information stored in quantum entanglement. At the end of this chapter, this possibility will be mentioned briefiy. 

This is shown in Fig. 22.8, which in addition contains two points from electron Compton scattering on hydrogen molecules. Those were obtained by Cooper et al. [16] and have been introduced at 37° (which corresponds to their -values) on the 0-scale. Their positions support the theory given above (which should be applicable also to electron Compton scattering), a 31 % anomaly for H2 and no anomaly for HD molecules (no quantum exchange effect). 

A broadening in Mark s intellect is shown clearly in his publications of this period. The topics in 1926 and 1927 alone ranged from atomic structure and quantum theory (1), and Compton radiation (2) to the scattering of x-rays by an ideal gas (3) and mineral structure (4). The shear diversity of his contacts and interests made him qualified for expanded responsibilities. 

Compton (1922) investigated the scattering of X-rays by a block of paraffin, and found that the radiation scattered at an angle of less than 90° possesses a greater wave-length than the primary radiation, so that the v of the scattered wave, contrary to the prediction of the classical theory, is smaller than the v of the... 

Fig. 19.8. Differences between the isotropic Compton profile computed from theory and various experiments. The theoretical data is from a multi-reference configuration interaction (MRCI) calculation in a (5s5p4d3f) basis set of Slater-type functions [104]. Experimental data (+), 25 keV electron impact at 12° [109] ( ), average of Ag Ka and Mo Ka X-ray scattering [108,105] ( ), 160 keV y-ray scattering [105] (O), 160 keV y ray scattering reanalyzed [105,106] (A), 60keV y-ray scattering [107]. The dotted lines enclose the band of uncertainty in the experimental data.

Einstein in the theory of the photoelectric effect, and Compton in the theory of die scattering of photons (Ch. 6), showed that photons have not only a discrete energy, but also a discrete momentum (cf. 4.2)... 

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