Scars of symmetries in complex atomic spectra

In transition arrays of complex atomic spectra, some well-defined subsets of lines bear the signatures, called scars, of their vanishing in one or several pure couplings. This is shown numerically, by means of line-by-line calculations, in the cases of the ${\mathit{d}}^{4\mathrm{-}}$ ${\mathit{d}}^3$p and ${\mathit{d}}^{8\mathrm{-}}$ ${\mathit{d}}^7$p transition arrays. It is also proved in a general way, using statistical distributions and the von Neumann–Wigner theorem.