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3 Cross sections

The formulas used to obtain the cross sections may be found in earlier work ([Ganas 1998]). The computed cross sections are presented in Fig. 2. No experimental cross sections are available, so a direct comparison with experiment is not possible. However, an estimate of their accuracy can be obtained from the accuracy of the oscillator strengths for the allowed transitions. The Born cross sections are very sensitive to the values of the oscillator strengths ([Inokuti 1971]). In Table 2 we present a comparison between the oscillator strengths obtained from the present calculations and those obtained from experiment and other calculations. For the 3p - 4s transition, our calculated value is in good agreement with various experimental data, but is lower than the majority of theoretical data. For 3p - 5s, the present value is in good agreement with experimental and theoretical data, but for the 3p - 6s there is a factor of 2 difference between our value and experiment. However the oscillator strength for 3p - 6s is much smaller than it is for 3p - 5s or 3p - 4s.

For the 3p - 3d(3D1) transition, our calculated value is in good agreement with the experimental data of Smith et al. (1987), and with various theoretical data. For the 3p - 3d(3P1) transition, our value is higher than the experimental and theoretical data, by a factor of 2 in some cases. However, the oscillator strength for 3p - 3d(3P1) is much smaller than for 3p - 3d(3D1). For 3p - 4d, there is generally reasonable agreement between our results and those of experiment and other calculations. For the higher transitions 3p - 5d, 3p - 6d and 3p - 7d, there is no experimental information available.

If we limit our consideration to the three transitions with the largest oscillator strengths: 3p - 3d(3D1), 3p - 4s(3P1), and 3p - 4d(3D1), and if we compare these oscillator strengths with those of Smith et al. (1987), which are the most extensive experimental data available on Si I, we find that our results have an accuracy in the range 7% to 23%. We therefore estimate our high energy cross sections to have an accuracy somewhere in this range. Our low energy cross sections are likely to be inaccurate due to the breakdown of the Born approximation near the threshold of inelastic scattering.


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