Scattering cross section for

Figure Bl.24.13. A thin film of LaCaMn03 on an LaA103 substrate is characterized for oxygen content with 3.05 MeV helium ions. The sharp peak in the backscattering signal at chaimel 160 is due to the resonance in the scattering cross section for oxygen. The solid line is a simulation that includes the resonance scattering cross section and was obtained with RUMP [3]. Data from E B Nyeanchi, National Accelerator Centre, Fame, South Africa.

The classical scattering cross section for a given process is simply... 

Beryllium has a high x-ray permeabiUty approximately seventeen times greater than that of aluminum. Natural beryUium contains 100% of the Be isotope. The principal isotopes and respective half-life are Be, 0.4 s Be, 53 d Be, 10 5 Be, stable Be, 2.5 x 10 yr. Beryllium can serve as a neutron source through either the (Oi,n) or (n,2n) reactions. Beryllium has alow (9 x 10 ° m°) absorption cross-section and a high (6 x 10 ° m°) scatter cross-section for thermal neutrons making it useful as a moderator and reflector in nuclear reactors (qv). Such appHcation has been limited, however, because of gas-producing reactions and the reactivity of beryUium toward high temperature water. 

Table 4.1-1 Comparison of the neutron scattering cross-sections for Li and Li with all the other atoms present in a binary mixture of LiSCN with AICI3.

Two factors determine the intensity of the scattered beam the scattering cross section for the incident ion-target atom combination and the neutralization probability of the ion in its interaction with the solid. It is the latter quantity that makes LEIS surface sensitive 1 keV He ions have a neutralization probability of about 99 % on passing through one layer of substrate atoms. Hence, the majority of ions that reach the detector must have scattered off the outermost layer. At present, there is no simple theory to adequately describe the scattering cross section and the neutralization probability. However, satisfactory calibration procedures by use of reference samples exist. The fact that LEIS provides quantitative information on the... 

Since the nuclear and electronic scattering cross sections for alpha particles are well known, the relative concentrations of the elements and their depth profiles can be easily obtained. The relative element concentrations are determined by the relative scattering intensities. The depth profile is obtained from the energy spread of the scattered particles, which lose energy before and after the nuclear collision, by inelastic scattering with electrons. The knowledge of the elements areal density and of the film thickness allows the determination of film density. 

In the first Bom approximation [12], the scattering cross section for a beam of neutrons incident on a magnetic material, assuming form (3) for the interaction, is given by the square of the scattering amplitude, F(kf, ki), where... 

In substitutional metallic solid solutions and in liquid alloys the experimental data have been described by Epstein and Paskin (1967) in terms of a predominant frictional force which leads to the accumulation of one species towards the anode. The relative movement of metallic ion cores in an alloy phase is related to the scattering cross-section for the conduction electrons, which in turn can be correlated with the relative resistance of the pure metals. Thus iron, which has a higher specific resistance than copper, will accumulate towards the anode in a Cu-Fe alloy. Similarly in a germanium-lithium alloy, the solute lithium atoms accumulate towards the cathode. In liquid alloys the same qualitative effect is observed, thus magnesium accumulates near the cathode in solution in bismuth, while uranium, which is in a higher Group of the Periodic Table than bismuth, accumulated near the anode in the same solvent. 

Figure 3 Elastic and inelastic scattering cross sections for scattering into an annular detector of inner collection angle 0i, for lOOkV electrons.

In principle, Eq. (8.1) can be applied only for small scattering centers with small scattering cross sections. For extended centers (e.g., a cell, a glass ball) with high scattering cross section, Eq. (8.1) has to be replaced by... 

Applications that would benefit from the described achievements are commonly bottlenecked by a lack of general procedures to interpret intensity data. Recently, it was suggested to interpret STEM data by extraction of single atom scattering cross sections For HRTEM, Figure 8 highlights a suitable method for intensity quantification from reconstructed electron exit waves. 

High-resolution Raman spectroscopy of gases with different He-Ne and Ar laser lines was also performed by Weber etal. The authors determined relative scattering cross-sections for the pure rotational Raman spectrum of Oj. 

FIGURE 2.13 (a) X-ray scattering factors for hydrogen, carbon, chloride and ferrous ions (b) the neutron scattering cross sections for several elements, as a function of sinOA. 

Figure 8.2 The elastic scattering cross section for collisions of O2 molecules in the lowest energy Zeeman state Mg = = —1) as a function of the magnetic field. The collision energy is 10 ...

Quantum theory of scattering. The differential scattering cross section for isotropic potentials is given by the scattering phase shifts r e as... 

Electrons of 150 eV and neutrons of 0.1 eV possess a DeBroglie wavelength of about 1 A, which matches the elementary lattice dimensions in crystals. The appreciable scattering cross sections for electrons causes them to be strongly absorbed and thus... 

The most important experiment of this type is thermal neutron scattering A complete determination of the differential scattering cross section for the scattering of neutrons from liquids completely determines the Van Hove scattering function.18 This function is related through a space-time Fourier transform to the autocorrelation function of the number density at two... 

Gs°(r, t) and Gsc(r, t) determine the incoherent differential scattering cross section for slow neutrons from CO through a weighted sum of their space-time Fourier transforms. Each of these functions is normalized to unity when integrated over all space. 

The elastic scattering cross section for a perturber in state (i incident on a Rydberg atom in state a with momentum K is obtained from the optical theorem. Explicitly3... 

In contrast to the case of X-ray scattering, cross sections for low-energy electrons from atoms are large (on the order of 10 A2/atom). 

The shape resonances have been described by Feshbach in elastic scattering cross-section for the processes of neutron capture and nuclear fission [7] in the cloudy crystal ball model of nuclear reactions. These scattering theory is dealing with configuration interaction in multi-channel processes involving states with different spatial locations. Therefore these resonances can be called also Feshbach shape resonances. These resonances are a clear well established manifestation of the non locality of quantum mechanics and appear in many fields of physics and chemistry [8,192] such as the molecular association and dissociation processes. 

As the positron energy is raised above the positronium formation threshold, EPs, the total cross section undergoes a conspicuous increase. Subsequent experimentation (see Chapter 4) has confirmed that much of this increase can be attributed to positronium formation via the reaction (1.12). Significant contributions also arise from target excitation and, more importantly, ionization above the respective thresholds (see Chapter 5). In marked contrast to the structure in aT(e+) associated with the opening of inelastic channels, the electron total cross section has a much smoother energy dependence, which can be attributed to the dominance of the elastic scattering cross section for this projectile. 

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