Coherent atomic cross section

In most cases, samples are a mixture of isotopes j with different scattering length bj and it is assumed that they are randomly distributed over the sample. Such random distribution of different isotopes produces incoherent cross-section. In analogy with isotope incoherence, spin incoherence is also observed. For nuclei with spin I l, the interaction depends on the orientation between neutron and nuclear spins scattering lengths and b for parallel and untiparallel spin, respectively, are different and the orientations of spins are randomly distributed in the nuclei even if they are the same kinds of nuclei. Then, incoherent and coherent atomic cross-sections are given by... 

Table 3.4. Coherent scattering cross-sections b (10"13 cm) scattering by atomic groups occurring in biological macromolecules, based on Table 3.1...

Lithium hydride, LiH, is a rather simple solid there are two atoms in the primitive cell and four electrons. It has the rock salt structure and its primitive cell contains one lithium and one hydrogen atom. Fig. 4.14. There are six dispersion curves of which three are acoustic and three optical. We can compare our calculations with the measured dispersion curves from LiD (rather than LiH because the deuterium coherent scattering cross section is required to measure the relative displacements of pairs of atoms ( 2.1). 

A further difference concerns the bound atom cross sections. The coherent cross section is not isotropic since the scattering processes involve... 

Here v and label the M different atom types, the are their number fractions, the <7 " are their coherent scattering cross sections, p is the density of scattering centers, and the average coherent scattering cross section is defined as... 

The total atomic cross-section <7totai can be expressed as the sum of the cross-sections of the different elementary processes - that is, the photoelectric effect (r), coherent (Rayleigh) scattering (cTooh). incoherent (Compton scattering) (Omooh). photonudear absorption Oph.n and pair production, which is to be distinguished in nudear-field pah-production (k- ) and dectron-field pair production (iCe) (see Equation 4.3). 

A careful study of neutron diffraction from a Ce02 crystal has provided the nuclear coherent scattering cross-section of cerium and the Debye-Waller factor of cerium and oxygen atoms. The anharmonic contribution to the Debye-Waller factor has been calculated (Valentine and Willis, 1965). 

If the displacements of the atoms are given in terms of the harmonic normal modes of vibration for the crystal, the coherent one-phonon inelastic neutron scattering cross section can be analytically expressed in terms of the eigenvectors and eigenvalues of the hannonic analysis, as described in Ref. 1. 

For non-interacting, incompressible polymer systems the dynamic structure factors of Eq. (3) may be significantly simplified. The sums, which in Eq. (3) have to be carried out over all atoms or in the small Q limit over all monomers and solvent molecules in the sample, may be restricted to only one average chain yielding so-called form factors. With the exception of semi-dilute solutions in the following, we will always use this restriction. Thus, S(Q, t) and Sinc(Q, t) will be understood as dynamic structure factors of single chains. Under these circumstances the normalized, so-called macroscopic coherent cross section (scattering per unit volume) follows as... 

Another remarkable way to use He scattering for the study of adsorbed layers is based on the large total cross-section for diffuse He scattering of isolated adsorbates (e.g. > 100 for a number of adsorbates like Xe, CO, NO and even for H, > 20 A ). This large cross-section is attributed to the long range attractive interaction between adatom and the incident He atom, which causes the He atoms to be scattered out of the coherent beams. The remarkable size of the cross-section allows the extraction of important... 

Level crossing has been used rather widely in the case of atoms and ions in order to determine lifetime, Lande factors, fine and hyperfine structure constants and relaxation cross-sections of coherence (cri,a2). For deeper acquaintance with these questions we recommend monographs and reviews [6, 96, 228, 296, 300, 301, 314] and the literature cited therein. 

Several investigations have been reported of excitation transfer from excited mercury atoms to ground-state atoms of silver, bismuth, cadmium, chromium, copper, indium, lead, and zinc. Most of these experiments which had been completed some time ago were surveyed by Seiwert [6,7]. Perhaps of particular interest is an investigation by Gough [105], who studied excitation transfer from mercury to cadmium and concluded that not only excitation energy but also coherence was transferred in the collisions. A similar conclusion was reached by Kraulinya, Sametis, and Bryukhovetskii [106] as the result of their study of the Hg-Tl system. Cross sections for Hg-Cd... 

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