Convention Fano-Racah

This basis may be converted to the Fano-Racah convention [11] by multiplying all kets in the right-hand side of Eq. 10 by the same phase factor i. Adding spin results in a shell consisting of six possible states. These states may be created by operators... 

This relationship expresses the adjoint character of the annihilation operators. The effect of the time reversal operator on these tensors in the Fano-Racah phase convention is given by ... 

The phase choice (sign) is referred to the Condon-Shortley convention the factor —1 occurs only for positive odd values of m. Another phase choice, according to the Fano-Racah convention, can be met in literature and hence... 

Fano and Racah (1959) employ a different convention, which results in... 

An important note concerning the phase choice follows. One of the conventions, the standard phase system introduced by Fano and Racah, states that on hermitean conjugation the following property holds true... 

However, for many purposes it is desirable to extend the theory of irreducible tensorial sets to the real irreducible representations that are carried by sets of real spherical harmonics. In the present paper this has been put into effect by using the properties of the invariant irreducible products considered by Fano and Racah. In particular, the phase conventions proposed in that work have been preserved so that invariants (reduced matrices, W- and -coefficients) are identical in the two representations. 

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