Convergent close coupling

The convergent-close-coupling (CCC) method, which was originally developed for electron-hydrogen scattering, has also been applied to... 

Bray, I. and Stelbovics, A.T. (1993). Convergent close-coupling calculation of low-energy positron-atomic hydrogen scattering. Phys. Rev. A 48 4787-4789. 

I. Bray, Convergent close-coupling method for calculation of electron scattering on hydrogenlike targets, Phys. Rev. A 49 (1994) 1066. 

It is perhaps as interesting to compare the approximate calculations with the convergent-close-coupling calculation as with experiment. The one that takes all channels into account most completely is the coupled-channels-optical calculation (Bray, Konovalov and McCarthy, 1991c) in which P space consists of the n=l, 2 and 3 channels. It agrees closely, but not completely, with the convergent calculation and similarly with... 

Fig. 8.3. Differential cross section for electron scattering to the Is, 2s and 2p states of hydrogen at 54.4 eV. Experimental data for Is are interpolated (Williams, 1975), for 2s and 2p they are taken from Williams (1981). Calculations are solid curve, convergent close coupling (Bray and Stelbovics, 1992h) long-dashed curve, coupled channels optical (Bray et al, 1991c) short-dashed curve, distorted-wave second Born (Madison et al, 1991) chain curve, intermediate-energy R matrix (Scholz et al, 1991) dotted curve, pseudostate method (van Wyngaarden and Walters, 1986).

The comparison of theory and experiment in table 8.3 is somewhat unsatisfactory. The coupled-channels-optical and pseudostate calculations agree with each other and with the convergent-close-coupling calculation within a few percent, yet there are noticeable discrepancies with the experimental estimates. The convergent-close-coupling method calculates total ionisation cross sections in complete agreement with the measurements... 

Fig. 10.14 shows that the convergent-close-coupling method describes the total ionisation cross section within experimental error for the whole energy range above total energy = 4 eV. Just above threshold it underestimates the cross section by up to 30%. 

The experimental data for hydrogen are compared with calculations in fig. 10.16. Both the convergent-close-coupling and coupled-channels-optical methods come close to complete agreement with experiment. The total ionisation cross section is a more severe test of theory, since it is an absolute quantity, whereas the asymmetry is a ratio. However, the correct prediction of the asymmetry reinforces the conclusion, reached by comparison with all other available experimental observables, that these methods are valid. 

Fig. 10.16. Total ionisation asymmetry for hydrogen. Open circles, Fletcher et al. (1985) squares, Crowe et al. (1990) full curve, convergent close coupling (Bray and Stelbovics, 1992b) crosses, coupled channels optical (Bray et al, 1991c).

In the past decade, much progress has been made in the quantum mechanical theory of molecular reactive scattering, It has become possible, at least for very simple, collinearly dominated atom-diatom systems not having too many electrons, for one to carry out calculations of detailed state-to-state reactive cross sections. To date, converged close coupling (CC) results are available only for the simplest system, H + H2, but studies of isotopic variations... 

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