Cross section for X-ray absorption

In bulk samples, X-ray yields need to be adjusted by the so-called "ZAF" correction. Z stands for the element number (heavier elements reduce the electron beam intensity more than lighter elements, because they are more efficient back-scatterers), A for absorption (different elements have different cross sections for X-ray absorption), and F for secondary fluorescence (the effect described above). Corrections are much less important when the sample is a film with a thickness of 1 pm or less, because secondary effects are largely reduced. The detection limit is set by the accuracy with which a signal can be distinguished from the bremsstrahlung background. In practice, this corresponds to about 100 ppm for elements heavier than Mg. 

The number of photons (the intensity) is reduced but their energy is generally unchanged. The term p is called the mass attenuation coefficient and has the dimension cm g . The product pi = pp is called the linear absorption coefficient and is expressed in cm . p(E) is sometimes also called the total cross section for X-ray absorption at energy E. 

The absorption cross section for x-rays in the range 100-20000 eV is determined by photoexcitation of electrons from atomic core levels. In this energy range pair production is forbidden and the weakness of electromagnetic field is such that only first order processes are important. 

The calibration of a PIXE system, i.e., the determination of sensitivity factors, which assign absolute concentration data to numbers of counts in X-ray peaks, can be performed in two different ways. First, sensitivity factors can be deduced theoretically or in a semiempirical way from calculated cross sections for X-ray excitation and from X-ray absorption data for the absorbents present between the points of emission and detection, in the actual experimental setup. Second, sensitivity factors can be deduced from measurements performed on standard samples consisting of pure elements or pure chemical compounds. The detection solid angle and the energy-dependent detector efficiency should also be determined. 

X-rays are electromagnetic in nature and atoms have moderate absorption cross sections for X ray radiation resulting in moderate energy exchange with the... 

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. 

In thin sections natural graphite is translucent, strongly pleochroic, and uniaxial. It has a negative sign of birefringence and two extinctions per revolution under crossed Nicol prisms. The atomic number of carbon accounts for its low absorption coefficient for x-rays and electrons. 

The X-ray spectrum observed in PIXE depends on the occurrence of several processes in the specimen. An ion is slowed by small inelastic scatterings with the electrons of the material, and it s energy is continuously reduced as a frmction of depth (see also the articles on RBS and ERS, where this part of the process is identical). The probability of ionizii an atomic shell of an element at a given depth of the material is proportional to the product of the cross section for subshell ionization by the ion at the reduced energy, the fluorescence yield, and the concentration of the element at the depth. The probability for X-ray emission from the ionized subshell is given by the fluorescence yield. The escape of X rays from the specimen and their detection by the spectrometer are controlled by the photoelectric absorption processes in the material and the energy-dependent efficiency of the spectrometer. 

In the present study we have extracted the EXAFS from the experimentally recorded X-ray absorption spectra following the method described in detail in Ref. (l , 20). In this procedure, a value for the energy threshold of the absorption edge is chosen to convert the energy scale into k-space. Then a smooth background described by a set of cubic splines is subtracted from the EXAFS in order to separate the non-osciHatory part in ln(l /i) and, finally, the EXAFS is multiplied by a factor k and divided by a function characteristic of the atomic absorption cross section (20). 

Figure 1. Schematic illustration of the energy levels associated with X-ray absorption spectroscopy. Abscissa is energy, increasing to right. Ordinate for lower trace is absorption cross-section.

Regardless of the choice of the sample thickness, the total amount of sample particles in the x-ray probe beam under optimized conditions is directly proportional to the x-ray spot size and inversely proportional to the x-ray absorption cross section, whose photoinduced (small) changes we want to measure [12]. Typical x-ray foci at synchrotrons are in the 0.1 - 0.3 mm range. For the examples treated below, this means that we have between 1014 and 1016 molecules in the probed volume. In order to achieve a reasonable photoinduced signal we should excite as many solute molecules as possible. Neglecting the optical absorption cross sections for photoexcitation for the moment, this requires on the order of 1015 laser photons per pulse, or ca. 0.25 mJ of pulse energy (e.g., at 800 nm). In other words, one should aim to... 

---