Escape factors for upper and lower limits to the source function appropriate for spherical geometry have been evaluated using a set of Stark-broadened line profiles, computed with different approximations, for the Ly-∝ line of Ar xviii. The method used to compute the escape factors, which is based on a general formalism, can be applied to any kind of line profile and is suitable for any geometry. The escape factor is expressed as an integral over the frequency of a functional of the line profile; hence our treatment highlights its dependence on the line profile. Comparisons are made with previous calculations that used Holtsmarkian line profiles and significant differences are noted. This work has been submitted for publication to J. Phys. B (London). This work was supported by the U.S. DOE Grant No. DEA508-833PP-40177.
The split-step Fourier algorithm for solving the acoustic parabolic equation involves two Fourier transforms, one forward and the other inverse. These may, of course, be replaced by a convolution. For the standard parabolic equation, the particular form of one of the convolved factors allows the convolution integral to be solved using a single Fourier transform. Application of this technique results in a limitation on the allowed range step. When applicable, however, the convolution algorithm reduces computer run times to about 60% of those required by the standard split-step Fourier algorithm. Examples are presented and limitations are discussed.
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