Level spacings in complex atoms

We now turn to some experimental examples. The first attempt to study the statistics of levels in complex atoms is due to Rosenzweig and Porter [544, 543] who noticed that elements with incomplete 4/ subshells have a very rich line spectrum, and therefore tried to select groups of levels of the same J by binning , and then analysing them statistically. There are several problems with their approach. First, the levels originate from tables which contain data from different sources, which poses questions about spectral resolution, sensitivity, etc. Second, there is no physical parameter which could (even in principle) be turned off and which would provide an ordered spectrum for comparison. Third, there may even be doubts about the reliability of the binning procedure, which results in a rather small number of levels for each J. 

The accumulated density of states or spectral staircase is a convenient representation of the overall spectral density. It is defined mathematically as 

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Level spacings in complex atoms 10.11 Level spacings in complex atoms... 

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