Coupled-channels-optical method equivalent local

The equivalent-local coupled-channels-optical method... 

Fig. 8.8 shows that the coupled-channels-optical method with the equivalent-local polarisation potential (McCarthy and Shang, 1992) gives a good semiquantitative description of the experimental data of Williams (1976 ) for elastic differential cross sections below the n—2 threshold. At energies just below the n=3 threshold the resonances affect the n=2 excitations. Fig. 8.9 shows the energy dependence of the integrated cross sections for the 2s and 2p channels. Since a resonance is a property of the compound system, not the channel, the resonances observed in... 

Since helium occurs naturally as an atomic gas it has been used for many years as a target for electron-collision experiments. However detailed calculations involving approximations for the complete set of target states have been performed only by the equivalent-local coupled-channels-optical method, described in section 7.6.2. 

The equivalent-local form of the coupled-channels-optical method does not give a satisfactory description of the excitation of triplet states (Brun-ger et al, 1990). Here only the exchange part of the polarisation potential contributes. The equivalent-local approximation to this is not sufficiently accurate. It is necessary to check the overall validity of the treatment of the complete target space by comparing calculated total cross sections with experiment. This is done in table 8.8. The experiments of Nickel et al. (1985) were done by a beam-transmission technique (section 2.1.3). The calculation overestimates total cross sections by about 20%, due to an overestimate of the total ionisation cross section. However, an error of this magnitude in the (second-order) polarisation potential does not invalidate the coupled-channels-optical calculation for low-lying discrete channels. 

Fig. 8.9. Integrated cross section for electron scattering to the 2s (above) and 2p (below) states of hydrogen below the n=3 threshold. The positions and quantum numbers of resonances are shown on the upper scale. Experiment, Williams (1988) solid curve, coupled channels optical (equivalent local) (McCarthy and Shang, 1992) long-dashed curve, pseudostate method (Callaway, 1982) short-dashed curve, 9-state coupled channels.

Table 8.8. Total cross sections for electron-helium scattering. CCO, coupled-channels-optical (equivalent local) method (McCarthy et al.,1991) experiment. Nickel et al. (1985). Units are KT cmi ...

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