Cross section calculation

The authors claim that apparent exceptions, where IOS is more accurate than CS are presumably due to a fortuitous cancellation of errors . The relative mistake in cross-section calculations was defined as... 

Why should calculations of evidently converge more slowly than those for b, and both more slowly than cross-section calculations It seems likely that this is a consequence of the very different interference structure of these three terms and their different phase dependence— particularly the slower convergence of the sin(ri — riy /) terms in the b expression (see Section III.C). When phase differences are small, as they will be for higher (. waves that are partly attenuated in the molecular core region by centrifugal barriers, the rapidly varying sine term will lend them a disproportionate influence on the final... 

The Incident Ion beam Intensity can be measured, and there are several tabulations of cross-section calculations. ( ) Also, the analyzer parameters, T, D, and d6 can be determined. The three aspects of this equation, which are not well understood nor easily determined. Include the number of atoms of a particular kind, the Ion survival probability, and the shadowing or geometric term. The first quantity Is quite often that which you would like to determine. The second two are often difficult to separate. Shadowing can be particularly Important when trying to observe second layer effect or when trying to determine the location of adsorbates.( ) However, shadowing for polycrystalline samples, though Important, Is very difficult to deal with quantitatively. 

Theoretical models of the electron impact ionization process have focused on the calculation of the ionization cross section and its energy dependence they are divided into quantum, semiclassical and semiempirical. Methods for the calculation of the ionization cross section and experimental techniques developed for the measurement of absolute ionization cross sections will be described in more detail below. Cross sections calculated using the semiempirical additivity method developed by Deutsch and Mark (DM) and their coworkers,12-14 the binary-encounter-Bethe (BEB) method of Kim and Rudd,15 16 and the electrostatic model (EM) developed by Vallance, Harland, and Maclagan17,18 are compared to each other and to experimental data. 

Figure 6. Comparison of electron impact ionization cross sections calculated by the...

The solvent enters the tower free of H2S and leaves containing 0.013 kmol of H2S/kmol of solvent. If the flow of inert gas is 0.015 kmol/s m2 of tower cross-section, calculate ... 

Figure 20. Experimental ionization cross section versus the cross sections calculated from Equation (20) with Zgff = 1.

Using 16.2 A2 as the N2 cross section, calculate Asp for the silica by the BET method. What value of o° is required to give the same BET area for the argon data ... 

At this point photoionization cross sections have been computed mostly for diatomic molecules, rr-electron systems, and other relatively small molecules [see Rabalais (242) for a summary of this work up to 1976]. Very few photoionization cross section calculations have been performed (108) on transition metal systems and the agreement with experimental intensities is rather poor. For the most part, therefore, one must rely on empirical trends when dealing with the photoionization of metal-containing molecules. A number of such trends have now emerged and are useful for spectral assignment. 

Cross-section calculations RFM and OFM full spectral calculations agree to better than 1 % near major absorption features. 

Cross section calculated from the molecular weight and density of liquid. The ratio of the partial pressure introduced (P) to the saturated vapor pressure (Pa). Adsorption amount on Cs2.2 divided by that on Cs2.5. J 1,3,5-Trimethylbenzene. e 1,3,5-Triisopropylbenzene. 

The open positronium formation channel in positron-alkali atom scattering was neglected in the coupled-state calculations of Ward et al. (1989) and McEachran, Horbatsch and Stauffer (1991), and only states of the target alkali atom were included in the expansion of their wave function. At low positron energies the elastic scattering cross sections calculated by... 

Fig. 3.13. Total (tot, upper solid line) and elastic (el, lower solid line) cross sections for positron-noble gas scattering near the positronium formation threshold from the R-matrix analysis of Moxom et al. (1994). Graphs (a)-(e) correspond to helium through to xenon. The data points shown are total cross section measurements from the literature (see Chapter 2 and Moxom et al., 1994, for details) except for the solid diamonds for helium, which are the

The most accurate values of the s-wave positronium formation cross section calculated by Humberston (1982) and Humberston et al. (1997) are shown in Figure 4.1. (The latter results are more accurate but there is no difference between the two sets of results on the scale of this figure.) This cross section is much smaller than the s-wave elastic scattering cross section and also, as we shall see, much smaller than other contributions to <7ps of low orbital angular momentum. It has recently been shown by Ward, Macek and Ovchinnikov (1998), using hidden crossing theory, that the small magnitude of the s-wave contribution to [Pg.156]

Campeanu (1982), using data of McEachran, Stauffer and Campbell (1980) — —, Campeanu (1982), using momentum transfer cross sections calculated by Schrader (1979). Xenon -------, Wright et al. (1985) — —, Campeanu... 

Figure 4.18 The near-threshold S-wave singlet (S = 0) and triplet (S = 1) absorption cross sections in e+ + H(1s) scattering, plotted versus reduced energy e = ( — th)/(r/2). The threshold energy th and the width T differ depending on the spin S. Full curves cross section 1,3(tabs °f Eq- (F5) from hyperspherical close-coupling calculations including the absorption potential —1(1,3 Vabs)- Dotted curves for e > 0 positronium formation cross section calculated without — / C Vabs). Broken curves for e < 0 absorption cross section 1,3a of Eq. (119) calculated without — Z(1,3Vabs) (first-order perturbation approximation). Circles Baz threshold formula fitted to the full curves. Figure from Ref. [16].

The Importance of Level Structure In Nuclear Reaction Cross-Section Calculations... 

Further comments on the size and extent of this bismuth cross-section calculational effort should be made. Table 5 summarizes the number of target states that we will need to consider (the 21 states include both ground and isomeric states), the number of separate reaction excitation functions that must be included, as well as estimates of the number of computer runs and the CDC 7600 CPU computer time that will be required. In our calculations, we typically use energy-bin sizes of 10 to 250 keV, depending on the reaction type and the energy ranges of concern. 

GAR84a] M. A. Gardner, "169Tm(n,3n)167Tm Cross-Section Calculations Near Threshold," Nuclear Chemistry Division FY 84 Annual Report, Lawrence Livermore National Laboratory, Livermore, CA, UCAR-10062-84/1 (1984). 

---