Second quantization and coefficients of fractional parentage

The coefficients of fractional parentage (CFP), treated by tradition as antisymmetrizing multipliers, do not exist as such in the second‐quantization representation, because, therein, by definition, there is nothing to antisymmetrize. This by no way means that the above‐mentioned representation is less relevant in theoretical atomic spectroscopy than is any other one. On the contrary, all the well‐known mathematical apparatus is still successfully applied, alongside with numerous new useful features. Moreover, the analysis presented here yields some results not so obvious from the point of view of the coordinate representation, namely, the consequent application of the second‐quantization representation led us to an expansion of many‐shell wave functions employing analogs of many‐shell CFP, which appeared to be considerably simpler than the traditional CFP expansion. Also, a generalization of Redmond's formula for the case of many‐shell CFP and a straightforward method of deriving summation rules for products of CFP are clear in the second‐quantization representation and are sketched here. © 1994 John Wiley & Sons, Inc.