The atomic cross sections

Atoms both scatter and absorb neutrons here we shall consider only the scattering cross sections and leave the practical consequences of absorption to be discussed latter ( 3.3.2). 

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Deutsch and Mark compared the classical expression with a theory developed by Bethe.37 Bethe s calculations showed that the ionization cross section for an atomic electron is approximately proportional to the mean square radius of the appropriate n,l electronic shell. Experiment had also shown a correlation between the maximum in the atomic cross section and the sum of the mean square radii of all outer electrons. This led to the replacement of the Bohr radius with the radius of the corresponding subshell the ionization cross section is now given by,... 

The expression for the atomic cross section a follows from mass absorption coefficient p/p of the element is given by p/p = Aa/M, where p is the density, and A and M are Avogadro s number and the atomic weight, respectively. This gives, analogously to Eq. (1.49),... 

The ionization cross section is a constitutive property and is the sum of the atomic cross sections. Knowing the elemental composition of a gas enables prediction of a response. Hydrogen is the carrier gas used. The detector is universal and capable of an MDL of 3x10 lg/see. It has the advantage of a wide linear dynamic range of 10 1. Some exception to the linear dynamic range and predictability of response has been made and certainly rests in the diversity of experimental conditions. 

Again the four dipole allowed channels In symmetry are shown. The dashed line Is two times the atomic nitrogen K-shell cross section. Note that the modulation about the atomic cross section, caused by the potential barrier extends to 100 eV above threshold before the molecular and atomic curves seem to coalesce. 

The reduced mass enters quadratically into expressions for the atomic cross sections. 

We now reintroduce the atomic index, /, and include the atomic cross section, a. Then, for the scattering intensity contribution to a given spectral band, that arising from the atom is. 

In a set of early experiments with synchrotron radiation the important role of the atomic cross section also in condensed systems was pointed out. In fact, large peaks of atomic origin have been observed at the absorption edges of condensed systems where the atomic cross section Jias strong resonances, e.g. for 3p—>sd and 2p— >sd transitions in transition elements and for 3d—>nf transitions in rare earths In fact the total absorption cross section can be factorized into an... 

A bound resonance at the threshold of a XANES spectrum can be determined by a resonance in the atomic cross section or by a molecular bound state, like the white line at threshold of the K-edge of tetrahedral clusters, shown in Fig. 14 and 15. Multiple... 

The effective atomic number is a convenient parameter for defining the X-rays attenuation properties of a complex medium as a biological tissue, and particularly for the calculation of dose in radiography. The concept of the effective atomic number is based on a proportional relation of the elemental cross-section per atom to Z where m depends on the process considered. For a specific interaction the atomic cross-section of an element is generally expressed as... 

This relationship allows determination of the relative percentage of a given element on a surface from the relative peak intensities. Values for the atomic cross sections have been calculated by Scofield [71]. Empirical equations for calculating the electron mean free path have been developed by Cadman et al. [72]. Wagner [73] has determined sensitivity factors for each element to relate peak intensities to atomic concentration. 

This unit for the atomic cross section is very convenient because the molar cross section becomes... 

Tables 3 and 4 list the resulting photoionization rates in the unattenuated interstellar radiation field of Draine (1978 cf. Eq. (3)) for a number of important atomic and molecular species. Although many of the atomic cross sections and rates are accurately known, the rates for most molecules are uncertain by at least a factor of two. An order of magnitude estimate of the photoionization rates of species not listed in Table 4 can be obtained by assuming a constant cross section of 10 cm above the (vertical) ionization threshold. Some prototypical calculations for different thresholds are included at the bottom of Table 4. Comparison with rates for species for which the cross sections are known shows that the assumption of rrion = 10 cm most likely results in an underestimate of the rate by a factor of a few. The variations of the photoionization rates with depth for the cases discussed in 5.3 are included as well. It is expected that virtually all of the molecular ionizations lead to the formation of a stable molecular ion.

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