Compton X-ray 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. 

X-ray attenuation occurs via four basic modes of interaction, shown schematically in Figure 4. Coherent X-ray scatter (CXRS) is an energy preserving interaction between an X-ray photon and an entire atom or crystalline matrix. Incoherent or Compton scatter represents a direct interaction between an X-ray and an... 

Quantum mechanics had exploded between 1923 and 1927. A. H. Compton, in 1923, had discovered the change in frequency of X-rays scattered from the electrons (the Compton effect).25 Compton and, independently, Debye had underlined the importance of this discovery in support of the Einstein conception of light-quanta or photon propagation in space.26... 

The first convincing description of stationary quantum states was provided by the assumed wave nature of matter proposed by Louis de Broglie. The proposal had its roots in Einstein s explanation of the photoelectric effect and Compton s analysis of X-ray scattering. 

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. 

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.

Note that the incoherence of the Compton-modified x-ray scattering occurs by a mechanism that is very different from what is considered here. The Compton-modified scattering is incoherent because the phase coherence is lost in the inelastic scat-... 

Compton Scattering. It is difficult to eliminate the Compton-modified x-ray scattering reliably by experimental means, because the wavelength shift of the modified from the coherent scattering is rather small, especially at small scattering angles. The preferred practice is to include all the Compton-modified scattering in the measured intensity and then subsequently to subtract the Compton-modified intensity calculated theoretically from it. 

Compton scattering is an inelastic X-ray scattering process where momentum is lost to the scattering electron. This means that the energy of the scattered X-ray is shifted to lower energy, and will not be involved in constructive or destructive interference with other scattered X-rays of the original energy. This means that Compton scattered X-rays are incoherent, and must be treated differently than other coherent and elastically scattered X-rays. 

Such anion-anion overlap causes a broadening of the Compton profile, and it has been shown that quite good agreement between experiment and a free ion model may be obtained for other rock-salt compounds if the effect is included, although it is always smaller than in LiH. Thus for LiF and LiCl< > the anion-anion overlap is calculated to have a 10% effect on the Compton profile at low momentum values but only a 1 % effect on x-ray scattering factors. As expected, MgO shows larger overlap effects than the halides. In other, more covalent compounds, for example BeO< > and A1N< >, the expected large departures from ionic model behavior have been observed but have yet to lead to improved wavefunctions for the solids. 

Figure 2.7 Spectra of x-rays scattered by graphite at different angles showing modified lines wider than primary P and displaced to the theoretical position M. (After COmpton and Allison, Ref. 1.)...

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