Level and line statistic in atomic spectra

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Abstract
The level distribution of an electronic configuration cannot be described in a simple and exact way according to the value of the total angular momentum J. Starting from the calculation of variances of the quantum numbers MJ and ML, and using a Gaussian model, approximate formulae are derived for the number of levels with a fixed J, for the total number of levels, for the number of Russell-Saunders terms of a given (S, L), for the total number of terms with a fixed S and for the number of levels of a jj term. From these results, closed formulae are derived for the total numbers of electric dipole lines in any transition array between two configurations, in intermediate coupling and in Russell-Saunders coupling, with an uncertainty of about 2%. Then, the statistics of the line strengths of an array is studied, and a simple distribution function is presented. When this simple model is used, for example, to calculate how many intense lines are expected to appear on top of an unresolved transition array, the agreement with exact calculations is good, except in very special cases where a sophisticated model is needed.