Emissive zones of complex atomic configurations in highly ionized atoms

The radiative properties of very complex atomic configurations in highly ionized species can be determined easily by means of statistical moments, computed ab initio from relativistic radial orbitals. A case of current interest, the spectrum of Gdxii, is studied as an example. The locations and the widths of the zones of the upper configurations responsible for the bulk of the spontaneous emission are determined formally and numerically. The fact that these zones may sometimes lie well above the center of gravity of the configuration can be interpreted by considering the relevant $G^1(nl,n^{\prime }l-1)$ Slater integral and its angular coefficients. Moreover, it is shown that two transition arrays involving the same upper configuration may actually originate from disconnected zones of the latter. A linear relationship is established formally between the coefficients of $G^1(nl,n^{\prime }l-1)$ and the $J$-file sums of Condon and Shortley. This gives us the opportunity to evaluate the sum of the line strengths of all the transitions originating from a given upper level and, therefore, a method for checking oscillator-strength angular calculations.