Symmetrization of the Zeroth Order Basis

1 Symmetrization of the Zeroth Order Basis. By subjecting the elements of the direct product basis 

In the symmetrization process the primitive period isometric transformations Fp play an outstanding role. For all SRMs with r(3 (Fp) e SO(3) these operators are represented in the representation r NCI St by the unit matrix (cf. Sect. 2.3.3). 

This implies for such SRMs the important relation 

For all SRMs wither ( ) St ( ) the interrelation of the representations r(j) [St] and r(j) St may be investigated by means of the Frobenius theorem on induced representations40. If in addition St %) is a normal subgroup of St ( ), as it has actually been the case in most examples studied up to now, the irreducible 

In this section we first present a set of general transformation formulae for tensor operators associated with SRMs. These then serve as a mathematical tool for the formulation of Wigner-Eckart theorems and selection rules for irreducible tensor operators associated with multipole transitions of SRMs. The concept of isometric groups will allow a formulation of selection rules in strict analogy to the group theoretical treatment of quasirigid molecules first presented by Wigner5.  

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