Total ionisation cross section hydrogen

The difficulties associated with making an atomic-hydrogen target have precluded direct measurements of total cross sections for hydrogen. Estimates may be made by adding the best available estimates for the integrated cross sections of particular channels and the total ionisation cross section. 

To estimate the total cross section for hydrogen we use the n=l and 2 estimates above. For n=3 we interpolate in the direct measurements of integrated cross sections by Mahan, Gallagher and Smith (1976). For higher discrete channels we use the roughly-valid rule that integrated cross sections for principal quantum number n are proportional to n. Very accurate measurements of the total ionisation cross section have been made by Shah et al. (1987). These total cross section estimates are shown in table 8.3 in comparison with the three calculations we are considering. 

The total ionisation cross section for hydrogen has been measured by Shah et al. (1987) in a crossed-beam experiment. Slow ions formed as collision products in the interaction region were extracted by a steady transverse electric field. H+ ions were distinguished by time of flight. Relative cross sections were normalised to previously-measured cross sections for hydrogen ionisation by protons of the same velocity. The proton cross sections were normalised to the Born approximation at 1500 keV. 

Fig. 10.14. Total ionisation cross section for hydrogen. Experimental data, Shah et al. (1987) full curve, convergent close coupling (Bray and Stelbovics, 1992fc) plus signs, coupled channels optical (Bray et al., 1991c), crosses, pseudostate method (Callaway and Oza, 1979) long-dashed curve, intermediate-energy R-matrix (Scholz et al., 1990) short-dashed curve, distorted-wave Born approximation.

The distorted-wave Born approximation for ionisation considerably overestimates the total ionisation cross section for hydrogen below about 150 eV. This is a good indication of its lower limit of validity. 

It has been measured for hydrogen (Fletcher et al, 1985 Crowe et al, 1990) and for lithium, sodium and potassium (Baum et ai, 1985) at incident energies from threshold to several hundred electron volts. The data were obtained by ionisation of polarised target atoms by polarised electrons. The relative total ionisation cross sections for parallel and antiparallel spins were determined by counting the ions, regardless of the kinematics of the final-state electrons. 

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. 

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