Total elastic cross section

Elastic collision cross sections are important for track simulation and diiferential cross sections are needed to calculate angular deviation in the track trajectory. Pimblott et al. [9] have given an elaborate analysis for gaseous water and compared the results with the experiments of Katase et al. [12]. In brief, the total elastic cross section... 

To get accurate results from this approach, it is necessary that the collisional changes in the internal energy be small compared to the translational energy. Then one can accurately assume a common translation path for all coupled internal states. In the usual applications of this method, one does not include interference effects between different classical paths, so that translational quantum effects, including total elastic cross sections, are not predicted. If the perturbation approximation is also used, accuracy can be guaranteed only when the sum of the transition probabilities remains small throughout the collision. 

The calculated total elastic cross section for He(2 S) + Ar is given elsewhere.102 There are currently no data for comparison. Trujillo has also measured cross sections for He(23S ) + Ne,Kr.136 Using essentially the same apparatus Harper and Smith138 have extended the cross section measurements to He(23S,) + H2,CO,02,N2 and Ne + He,Ne,Ar,Kr,H2,C0,N2,02. 

The total elastic cross section [Pg.96]

The total elastic cross section and the forward (9 = 0) differential cross section are infinite. 

Fig. 6. Total elastic cross section for He(l 5) + He (2 F) as a function of incident energy. The meaning of C = 23.75 and C = 0 is the same as before.

It is interesting to find that a combination of elastic and reactive scattering results in additional information concerning the probability of reaction under certain conditions. In Chapter 2, where an expression was derived for the frequency per unit volume of binary collisions, we found that the total elastic cross section for scattering was given as db for... 

If the incident particle is a neutron, the total elastic cross section is finite and integrates to... 

The differential and total elastic cross sections are related to t k, 9) by... 

Hayashi s (1989) compilation highly overestimates the total inelastic cross section below 100 eV. These are inconsistent with measured W values. Although the total cross section is reasonably well determined, uncertainties in the elastic cross section might have led Hayashi to overestimate the inelastic cross section. Figure 4.5 shows these cross sections. It is seen, however, that one theoretical calculation is consistent with W value measurement (Pimblott et al., 1990). In any case, Hayashi s values for total inelastic cross section are much greater than all major calculations, and the discrepancy is directly traceable to overestimates of excitation cross sections. 

Figure 3 Inelastic and elastic cross sections for electron impact excitation of the water molecule the data are from the review by Mark et al. [19]. The total interaction cross section ctt was determined from the sum of cross sections for all elastic and inelastic processes. Inelastic channels include the vibrational modes Cvi (the bending mode with threshold 0.198 eV), cTv2 (the sum of two stretching modes with thresholds 0.453 and 0.466 eV), and CvS (a lump sum of other vibrational excitation modes including higher hormonics and combinational modes with an assigned threshold of 1 eV). The electronic excitations and <7 2 have threshold energies of 7.5 and 13.3 eV. Ionization cross sections are those of Djuric et al. (O), and Bolarizadah and Rudd ( ). (From Ref 19.)...

Figure 11 Total cross sections due to proton (left) and alpha particle (right) impact on water vapor. Total ionization cross sections were obtained by fitting polynomial functions to the experimental data [198-200]. The curve for excitation was assumed to be the same between protons and alpha particles. Elastic scattering was evaluated by the classical mechanics trajectory calculations [Eqs. (16) and (17)].

A quantitative evaluation of a measured energy dependence of the ratio has been made only for the system He(23S)-Ar for which V R) and T(fl) are known, so that the evaluation leads to a determination of parameters of V+(R). In classical model calculations,43 using a semiempirically determined potential V+(R)1] that only slightly deviates from the one determined from elastic scattering30 and r( ) = 4000 exp(-R/0.36) (au), which was determined by the requirements that the total ionization cross-section curve due to Pesnelle et al.43 be reproduced with the chosen K (R), for a Morse potential V+(R) the following parameter values were determined well depth 16 meV, equilibrium distance 5.67a0, and shape... 

The real part of the forward elastic scattering amplitude can be related to the total scattering cross section by means of the following dispersion relation ... 

Positron total scattering cross sections have been measured and calculated for a variety of atomic and molecular gases, and in this section we present a selection of results. In the light of the discussion given in section 2.4, particularly concerning small-angle elastic scattering, a critical evaluation... 

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