Abstract
It is shown that for spherically symmetric flows with nonmonotonic velocity fields, the solution of the two-level-atom transfer equation in the observer's frame remains a viable method, even at high flow speeds, on computers with vector-processing capabilities. This result is of importance because for such cases comoving-frame methods are, at best, extremely difficult (no successful calculation having been published to date), and Sobolev-theory methods become both cumbersome to use and inaccurate in many situations of interest. The basic algorithm is described and is illustrated by computations for spherically symmetric decelerating expansions.
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