Atomic cross section

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),... 

Fig. 5. Atomic cross-sections vs. photon energy in the ultraviolet range for different orbital states in various atoms (from Ref. 23) Eth threshold energy...

In electron microscopy, generally intense electron beams are used which can severely damage the surface (however, at high energies the electron-atom cross sections become smaller). Often, large magnetic fields are also present that could affect the surface structure. 

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. 

The Langmuir model also provides a convenient basis for estimating when Henry s law or saturation effects can be expected. If an individual attachment site has an area a 2 x 10 15 cm2, the order of atomic cross-sectional area (cf. Table 2.1), then Ns 5 x 1014 atoms/cm2 = 2 x 10 5cm3STP/cm2. Surface concentrations approaching this order of magnitude can be expected to exhibit saturation behavior. Conversely, much lower concentrations indicate 9 1 and lead to the expectation of Henry s law behavior. Possible adsorption effects important in noble gas geochemistry always involve much lower concentration than this illustrative value, which is one reason why Henry s law violation is not expected. 

VESUVIO measurements on Nhi) [Karlsson 1999] and polystyrene [Karls-son 2003 (b)], also show ratios of 77 to heavier atom cross sections which are independent of angle. In contrast measurements on Formvar [Chatzidimitriou-Dreismann 2003 (a)], shown in Fig. 6, give a marked fall off in the H to heavy atom cross section ratio as the scattering angle and hence q is increased. Measurements on NbH [Karlsson 1999] have an even stronger angular dependence. Thus no single 7 value can explain anomalies observed in different samples. 

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... 

---