Cross section single-atom

One of the most successful applications of the laser to chemistry and physics lies in the area of diagnostics. Thanks to its intensity, monochromaticity and its continually expanding tunability, the internal states of chemical species can be probed readily to the concentration level of —10 -10 particles/cm. For several metal atoms which have large optical cross-sections, single-atom detection with the laser was achieved a few years ago. ... 

A critical comparison between experiment and theory is hindered by the range of experimental values reported in the literature for each molecule. This reflects the difficulty in the measurement of absolute ionization cross sections and justifies attempts to develop reliable semiempirical methods, such as the polarizability equation, for estimating the molecular ionization cross sections which have not been measured or for which only single values have been reported. The polarizability model predicts a linear relationship between the ionization cross section and the square root of the ratio of the volume polarizability to the ionization potential. Plots of this function against experimental values for ionization cross sections for atoms are shown in Figure 7 and for molecules in Figure 8. The equations determined... 

Fig. 10. Theoretical absorption coefficient for a cluster formed by the central Mn and six oxygens. Going from top to bottom the total cross section, the atomic contribution (dotted-dashed line), the single scattering contribution, n = 2, (EXAFS) and the contributions of successive orders of multiple scattering pathways of orders n = 3,4 and 5 are shown...

Due to the high atomic density of solids, it is hard to reach single-collision conditions for processes, such as outer-shell ionization that have cross sections of atomic dimensions. As, furthermore, it would be difficult to detect outer-shell ionization events in a solid, such measurements have until now not been performed. However, for inner-shell ionization, thin foils have the obvious advantage of localization... 

Another usefiil quantity related to extinction coefficient is the cross section, a, defined for a single atom or molecule. It may be thought of as the effective area blocking the beam at a given wavelength, and the value... 

In addition to qualitative analysis of nearly all the elements of the periodic table, EEL spectra also enable determination of the concentration of a single element which is part of the transmitted volume and hence gives rise to a corresponding ionization edge. As in all comparable spectroscopic techniques, for quantification the net edge signal, which is related to the number N of excited atoms, must be extracted from the raw data measured. The net intensity 4 of the feth ionization shell of an individual element is directly connected to this number, N, multiplied by the partial cross-section of ionization ) and the intensity Iq of the incident electron beam, i.e. ... 

Fig. 31. Approximation of van der Waals cross-sections of inclusion channels in 1 alcohol clathrates21 (dimensions are in A hatched regions represent O atoms of the host matrix continous solid lines indicate surfaces of apolar attribute) (a) 1 MeOH (1 2) (approximately parallel to the 0(I -Cul vectors, cf. Fig. 17a) (b) 1 2-PrOH (1 2) (orientation as before) (c) 1 2-BuOH (1 1) (through a center of symmetry at 1,1/2,1/2, cf. Fig. 30c non-zero electron density contours) (d) 1 ethylene glycol (1 1) (in the plane of the C—C single bonds of a guest molecule, indicated by projected stick models non-zero electron density contours)...

This formalism was originally devised for single ionization of ground-state atoms, but has now been successfully applied to the calculation of electron impact ionization cross sections for a range of molecules, radicals, clusters, and excited state atoms. Like many of the semiempirical and semiclassical methods used to describe the electron impact process, the theory has its roots in work carried out by J.J. Thomson, who used classical mechanics to derive an expression for the atomic electron impact ionization cross section,2... 

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... 

More details of the emission of ultralow- and low-energy electrons from fast heavy ion-atom collisions may be seen in the doubly differential cross sections as functions of the longitudinal electron velocity for increasing transverse electron velocity. Examples considered in this chapter include singly ionizing... 

Normally these conditions are satisfied in fast highly charged ion-atom collisions. From Eq. (66) we can derive the equations for the singly differential cross sections with respect to the components of the longitudinal momentum distributions for the electron, recoil-ion, and projectile. The longitudinal electron momentum distribution da/dpe for a particular value of p, may be derived by integrating over the doubly differential cross section with respect to the electron energy Ek ... 

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