Some Statistical Properties of Level and Line Distributions in Atomic Spectra

Steven A. Moszkowski

ResearchPublished 1960

An investigation, from the statistical viewpoint, of the properties of level and line spectra due to mutual interactions among electrons. It is shown that the first and second moments of the spectra (weighed by the appropriate statistical weight factors) vary in a regular way with the number of particles in the shell, the second moment reaching a maximum in the middle when the shell is about half full. The detailed shape of the distribution, called the "strength function," is also examined using a number of simplified models. If only close together single particle orbits are mixed by the interactions (which is the situation usually assumed in shell model-type calculations), then the strength function for levels is essentially exponential and that of lines somewhat like a Gaussian.

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Moszkowski, Steven A., Some Statistical Properties of Level and Line Distributions in Atomic Spectra. Santa Monica, CA: RAND Corporation, 1960. https://www.rand.org/pubs/research_memoranda/RM2610.html.
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