Collective vector method for the simulation of large atomicE1transition arrays

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Abstract
We describe the application of the collective vector method to the evaluation of the moments of atomic transition arrays. We use these moments with the Lanczos algorithm to obtain a Stieltjes δ-function representation of the array. As an example the procedure is applied to a test array containing over 5000 lines in the exact spectrum and is seen to give a good representation of the array with only moderate computational requirements. In comparison the more familiar Gram-Charlier expansion leads to uninterpretable negative excursions making it unusable except for completely unresolved transition arrays.