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The approach which is best suited for our purposes is the opacity sampling technique (cf. Peytremann 1974; Sneden et al. 1976). This method allows us to account for the line shift in the wind, since a rearrangement of opacities, as required for opacity distribution functions (cf. Hubeny XXX1997), does not take place. In this way, the correct influence of line blocking on bound-bound transitions (cf. item (iii)), which has to conserve the frequential position, can be treated.
For the opacity sampling, a set of frequency points is distributed in a logarithmic scale over the relevant spectral range (160Å-1200Å for O stars) and the transfer equation is solved for each point. Note that for the ionization calculations it is important to extend the line-blocking calculations to the range shortward of the HeII edge (cf. Pauldrach et al. 1994a).
In this way the exact solution is reached by increasing the number of frequency points. By investigating the accuracy of typical photoionization integrals we found that convergence can be achieved with approximately 1000 to 2000 frequency points in the relevant range (cf. Sellmaier 1996; Pauldrach et al. 1997). The advantages of the opacity sampling method are obvious: we can investigate the effects of line blocking on selected bound-bound transitions if we spread additional points around the transition frequency of interest; furthermore, we can apply the Doppler shift to the line absorption and emission coefficients.