On the fine structure photodetachment intensities using the irreducible   tensorial expression of second quantization operators
  The branching ratios of the fine-structure photodetachment intensities of S- have been calculated by Blondel et al. (J. Phys. B 39(2006)1409) using the standard irreducible tensorial operator techniques. They observed that the relative intensities were consistent with the well known Engelking-Lineberger formula (Phys. Rev. A19(1979)149) derived from the fractional parentage approach, and qualified this agreement as remarkable. In the present paper, we show that it can be understood from a general interesting angular momentum expression relating a weighted sum of squared 9j-symbols and a weighted sum of products of squared 6j-symbols. We also point out that the standard approach result is a special case of the photodetachment cross sections parametrization by Pan and Starace (Phys. Rev. A47(1993)295) who already established the link with the Engelking-Lineberger's result. The present work provides a new, elegant and deep link between the two formalisms, thanks to the irreducible tensorial expression of the second quantization form of the electric dipole transition operator. 
Oliver Scharf and Michel R. Godefroid