Cross-section, absolute determination

Hydrocarbon molecules are abundant constituents of planetary atmospheres and major compounds in combustible gas mixtures and in fusion edge plasmas [7-11]. Methane is the simplest of these hydrocarbon molecules. Acetylene, C2H2, is the simplest hydrocarbon molecule that contains 2 carbon atoms. Thus absolute total and partial photon [24-27] and electron [15,28-34] ionization cross-sections and nascent fragment ion energy distributions [19,20,28,36-40] have been studied extensively for these molecules. For the deuterated methane molecule electron impact ionization and dissociative ionization cross-sections were determined for the CD (x=l—4) molecule and radicals applying a fast neutral beam technique [41]. Electron impact total ionization cross-sections have been determined also theoretically applying the BEB (Binary-Encounter-Bethe) model [42], the DM (Deutsch-Mark) method [43] and the JK (Jain-Khare) method [44], Partial electron impact ionization cross-sections were calculated for methane [45,46] as well as total electron impact cross-sections for various CH radicals [47]. The dissocia-... 

Experimental differential cross sections are put on an absolute scale by first normalising to the differential cross section for the first dipole transition (3p). The integrated cross section for this transition is determined by numerical integration using differential cross sections measured as close to 0 = 0 as possible, supplemented by shape extrapolation based on a calculation. Integrated cross sections are determined in ways that ultimately depend on measurements of the optical oscillator strength (5.84). They... 

Relative measurements are, in most cases, easier than absolute measurements. For this reason, investigators tend to perform the very minimum of absolute measurements and use their results in subsequent relative measurements. One of the most characteristic examples is the determination of the value of nuclear cross sections. Absolute measurements have been performed for very few cross sections. After certain cross sections have been measured, most of the others may be determined relative to the known ones. 

A method of computing activation cross sections by determination of the absolute disintegration rate of a foil irradiated in a known thermal flux is described. The method can also be used to determine an unknown thermal flux in which a foil has been irradiated, provided that an activation cross section for the foil material is assumed. The method used could be applied to many materials which become activated by thermal neutrons and whose resulting beta activity has a sufficiently long half-life so that counting of the sample is not a problem. The techniques involved in absolute beta counting are emphasized. 

It means that we may determine the cross section of the defect by measuring the variation of the inductance. It is an absolute measurement because the coefficient depends only of... 

At low energies the abstraction process dominates and at higher energies the exchange mechanism becomes more important. The cross-sections for the two processes crossing at 10 eV. The END calculations yield absolute cross-sections that show the same trend as the experimentally determined relative cross-sections for the two processes. The theory predicts that a substantial fraction of the abstraction product NHjD, which are excited above the dissociation threshold for an N—H bond actually dissociates to NH2D" + H or NH3 during the almost 50-ps travel from the collision chamber to the detector, and thus affects the measured relative cross-sections of the two processes. 

The absolute precision of ERS therefore depends on that of da/dfl (Ej, (t>). Unfortunately, some disagreement prevails among measurements of the recoil cross section. One recent determination is shown in Figure 4a for (t> = 30° and 25°. The convergence of these data with the Rutherford cross section near 1 MeV lends support to their validity. The solid lines are least squares fits to the polynomial form used by Tirira et al.. For (t> = 30°, the expression reads ... 

Susceptibility to radiation damage must be considered seriously if reference samples are to be calibrated for use in place of absolute systems. For the measurement of absolute C He, H) cross sections, films of polystyrene (CH) (which is relatively radiation hard) have been used successfiiUy, the RBS determination of carbon providing implied quantitation for the hydrogen present in the film. For a durable laboratory reference sample, however, there is much to recommend a known ion-implanted dose of H deep within Si or SiC, where the loss of hydrogen under room temperature irradiation will be neghgible. 

At various cross-sections along the flow direction, (i) the polymer velocity profile, (ii) polymer temperature profile, (iii) metal temperature profile, and (iv) pressure drop are all computed. Because the pressure at the exit is known, the absolute pressure profile along the flow direction can also be determined. 

In the capillary method, the time required for a liquid to flow through a capillary tube is determined. The melt under investigation flows with a constant rate through a tube with a small, definite cross-sectional area, such as a cylindrical capillary. The viscosity can be measured in an absolute way from the pressure drop. This method can yield the most reliable absolute data, the viscosity being given by a modified Hagen-Poiseuille equation ... 

The height of a given X-ray peak is a measure of the amount of the corresponding element in the sample. The X-ray production cross-sections are known with good accuracy, the beam current can be measured by, for example, a Faraday cup (Figure 4.1) and the parameters of the experimental set-up are easily determined so that the sample composition can be determined in absolute terms. 

The lab angular distributions shown in Fig. 12 contain information about the cross-section for each reaction. In practice, extraction of an absolute cross-section is difficult because of uncertainties in the number densities of the reactant beams and the ionization efficiencies of the products.130,135 However, in the determination of the product branching ratio, many of... 

Since the summation method allows absolute partial ionization cross sections to be determined, it is straightforward to extract the counting or ion production cross section from the data. Since this is the quantity which is given by many of the current... 

There are several other methods which have been used in the experimental determination of electron impact ionization cross sections. Nottingham and Bell76,77 developed a method specifically for the purpose of accurately determining the absolute electron impact ionization cross section of mercury. A semicircular electron velocity analyzer included in their design ensured that very high energy resolution was possible since only electrons of the required velocity emerged from the analyzer into the ionization chamber. Other aspects of the experiment are similar to the condenser plate method. 

Experimentally determined maximum absolute ionization cross sections for the inert gases and a range of small molecules are compared with the predictions of DM, BEB, and EM calculations in Table 1. Atomic orbital coefficients for the DM calculations were determined at the Hartree-Fock level and the EM cross sections are volume averaged for calculations carried out at the HF/6-31G level. Hie same data are plotted in Figure 5 with the calculated values on the ordinate and the experimental result on the abscissa. The heavy line represents a direct correspondence between experiment and theory. Although the ab initio EM method performs well for the calculation of qm and Em,T,17 the DM and BEB methods allow for the calculation of the cross section as a function of the electron energy, i.e. the ionization... 

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... 

H. Deutsch, K. Becker, S. Matt, and T. D. Mark. Theoretical Determination of Absolute Electron-Impact Ionization Cross Sections of Molecules. Int. J. Mass Spectrom., 197(2000) 37-69. 

With a similar experimental arrangement, Khaikin determined cross-sections for electron excitation and atom-atom collisions. Lilly and Holmes used this method to measure the relative transition probabilities of 12 visible neon lines originating from the 2s and 3s niveaus and normalized these probabilities by determing the absolute value for one line. 

Knowledge of the sample pressure is essential in all high-pressure experiments. It is vital for determinations of equations of state, for comparisons with other experimental studies and for comparisons with theoretical calculations. Unfortunately, one cannot determine the sample pressure directly from the applied force on the anvils and their cross-sectional area, as losses due to friction and elastic deformation cannot be accurately accounted for. While an absolute pressure scale can be obtained from the volume and compressibility, by integration of the bulk modulus [109], the most commonly-employed methods to determine pressures in crystallographic experiments are to use a luminescent pressure sensor, or the known equation of state of a calibrant placed into the sample chamber with the sample. W.B. Holzapfel has recently reviewed both fluorescence and calibrant data with the aim of realising a practical pressure scale to 300 GPa [138]. 

As for the absolute values of photoionization quantum yields ( ],), a situation of the dipole-simulation experiments in comparison with the real-photon experiments is much more serious and controversial because their absolute scales are determined by the assumption that the photoionization quantum yields should be unity around 20 eV photon energy in addition to the above-mentioned difficulty in obtaining absolute cross-section values in the dipole-simulation experiments. 

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