Strong, Weak and Merging Lines in Atomic Spectra

We present analytical estimates for the maximum line strength in a transition array, as well as for the numbers of strong and weak lines. For that purpose, two main assumptions are used as concerns the line strength distribution. The first one, due to Porter and Thomas, is more suitable for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>−</mo><msup><mi>J</mi><mo>′</mo></msup></mrow></semantics></math></inline-formula> sets, where <i>J</i> is the total atomic angular momentum, and the second one, based on a decreasing-exponential modeling of the line-amplitude distribution, is more relevant for an entire transition array. We also review the different approximations of overlapping and blanketing (band model), insisting on the computation and properties of the Elsasser function. We compare different approximations of the Ladenburg–Reiche function giving the equivalent width of an ensemble of lines in a frequency bin and discuss the possibility of using statistical indicators, such as the Chernoff bound or the Gini coefficient (initially introduced in economics for the measurement of income inequality), in the statistical characterization of transition arrays.