On the fine structure photodetachment intensities using the irreducible tensorial expression of second quantization operators

Abstract. The fine-structure relative intensities of photodetachment in S at the vicinity of the threshold have been calculated recently [1] to analyze the microscope photodetachment images produced by the s-photoelectron. The branching ratios were obtained using the electric dipole approximation and the standard irreducible tensorial operator techniques. The same authors observed that these relative intensities were consistent with the Cox-Engelking-Lineberger formula [2] derived from the fractional parentage approach [3], in which the laser photon annihilates one of the p-electrons of the negative ion to promote it into the s-continuum. This agreement between the two formalisms was qualified as remarkable. With this paper, we show that this agreement is understood from a general interesting angular momentum expression relating a weighted sum of squared 9jsymbols and a weighted sum of products of squared 6j-symbols. We point out that the “standard” approach result is a special case of Pan and Starace’s parametrization [5] of the photodetachment cross sections in the term-independent approximation. The link with the Cox-Engelking-Lineberger result established in their work makes the agreement between the standard and the fractional parentage methods even more natural. The present work provides another 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. Indeed, the (SL)J-coupled form of the latter reproduces Pan and Starace’s cross section expression from which the standard result can be derived, while the 9j-coefficient characterizing the fractional parentage Cox-Engelking-Lineberger formula quickly emerges when using its (jj)J coupling form.