Photoelectric cross section

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. 

A schematic cross-section of one type of photomultiplier tube is shown in Figure 26. The photomultiplier is a vacuum tube with a glass envelope containing a photocathode and a series of electrodes called dynodes. Light from a scintillation phosphor liberates electrons from the photocathode by the photoelectric effect. These electrons are not of sufficient number or energy to be detected reliably by conventional electronics. However, in the photomultiplier tube, they are attracted by a voltage drop of about 50 volts to the nearest dynode. 

The essence of the XSW technique now lies in the effect these modulations have on the photoelectric cross-section of a target atom a distance c above the mure surface. The incident X-rays can eject a core electron from the atom so generating a vacancy and resulting in the emission of a fluorescent X-ray photon The probability of an incident photon ejecting the core electron, the photoelectric cross-section, is directly proportional to the electric field experienced by the atom Hcncc. the fluorescence yield, T(0.for an atom or ion distribution A (z) a distance above the mirror surface can be written... 

For lOOkeV photons, the photoelectric cross section is proportional to where Zis the atomic number of the atom. For 3 MeV photons, the photoelectric cross section is proportional to The Compton photon cross... 

In order to analyze the intensity of the various photoelectron peaks, it is necessary to know their associated transition probabilities, or photoelectric cross-sections. 

The photoelectric cross-section o is defined as the one-electron transition probability per unit-time, with a unit incident photon flux per area and time unit from the state to the state T en of Eq. (2). If the direction of electron emission relative to the direction of photon propagation and polarization are specified, then the differential cross-section do/dQ can be defined, given the emission probability within a solid angle element dQ into which the electron emission occurs. Emission is dependent on the angular properties of T in and Wfin therefore, in photoelectron spectrometers for which an experimental set-up exists by which the angular distribution of emission can be scanned (ARPES, see Fig. 2), important information may be collected on the angular properties of the two states. In this case, recorded emission spectra show intensities which are determined by the differential cross-section do/dQ. The total cross-section a (which is important when most of the emission in all direction is collected), is... 

Fig. 2-2, Room-temperature absorption coefficients and cross sections of NO by photoelectric detection A = 590-960 A absorption coefficients to base e for 1 atm of gas at 273°K (from Metzger and Cook309 with permission).

Figure 17.14 Summary of the relative importance of the three mechanisms by which photons interact with matter. The curves indicate the locations in the atomic number-photon energy plane at which the cross section for Compton scattering is equal to that for photoelectric absorption, left side, or is equal to that for pair production, right side.

Chemical Modifications of Surface Functional Groups with Elements Having High Photoelectric Cross Sections... 

The surface composition of the fly ash samples was obtained using a Varian I.E.F. spectrometer operating at around 1x10 torr. The powder samples were mounted on the probe using two sided tape. The relative compositions were calculated using Weingle s photoelectric cross sections as a measure of relative intensities (3). 

Wide scans (0 to 1000 eV) were performed for surface elemental analyses. The wide scans were carefully inspected for trace element contamination. Detailed 20 eV scans of the C-ls (275 to 295 eV), 0-ls (520 -540 eV) and Al-2s (105 to 125 eV) regions for the pyrolytic carbon and of the C-ls and 0-ls for the polystyrene were run to determine both elemental stoichiometry and chemical shifts. Standards were available to give accurate chemical shift data for various carbon-oxygen functional groups. These included poly(ethylene terephthalate), poly(ethylene oxide) and anthraquinone (17 ). The latter was run at -50°C in order to minimize volatility under our high vacuum conditions. Table I sunmarizes these results. All spectra were charge - referenced to a C-ls line for an alkyl-like carbon at 284.0 eV. The Scofield theoretical XPS photoelectric cross sections ( ) were used for elemental quantitation. 

Corrected peak area using photoelectric cross-sections relative to C Is. 

The Compton effect is essentially an elastic collision between a photon and an electron during this interaction, the photon gives a fraction of its energy to the electrons, and its frequency v is therefore decreased. The cross section for this effect decreases with increasing energy, but the decrease is less rapid than for the photoelectric effect. 

ASTM E 84 Steiner Tunnel Test. This test, which uses very large samples (20 ft x 20 1/4 in.) is referenced in all model building codes for evaluating flame spread and smoke emission of foam plastic insulation. The test apparatus consists of a chamber or tunnel 25 ft. long and 17 3/4 X 17 5/8 in. in cross section, one end of which contains two gas burners. The test specimen is exposed to the gas flame for ten minutes, while the maximum extent of the flame spread and the temperature down the tunnel are observed through windows. Smoke evolution can also be measured by use of a photoelectric cell. The flame spread and smoke evolution are reported in an arbitrary scale for which asbestos and red oak have values of 0 and 100, respectively. More highly fire-retardant materials have ratings of 0-25 by this method. 

FIGURE 3. Absorption cross sections for CO by photoelectric detection with an instrumental band pass of 0.025 nm. Absorption cross section is to the base e 1 Mb = 10 8c(n2 (from Myer and Samson with permission). 

In traversing through matter. X-rays are attenuated by coherent (Rayleigh) and incoherent (Compton)scattering and are absorbed by the photoelectric process (6, 7). X-rays of energy below 100 keV are mainly absorbed by the photoelectric process with a cross section (i.e., the probability for absorption) proportional to (6), where E is the X-ray energy and Z... 

Frequency-Dependent Photoelectric Cross Sections and 4f-Photoemission from... 

Fig. 3. Calculated photoelectric cross sections (plotted from data of Ref. 15).

Calculation of the photoelectric cross sections by /. H. Scofield (15) subsequently allowed comparisons to be made between experimental and calculated intensities. In Fig. 3 we have plotted the results of his calculations for hv = 1.5 keV. 

Significance in Practical Problems. Close to the source, the Compton scattering of the primary gamma rays is the main process. In cobalt, for instance, the total Compton cross section is 0.054 cm.2/gram and the photoelectric cross section is 0.00028 cm.2/gram at 1.25 Mev. This... 

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