Weak interactions. Generalized product functions

At the quantum-mechanical level, two systems A and B will be recognizably distinct if each is described by its own wavefunction thus 

Pauli principle but it may be symmetry-adapted by applying the antisymmetrizer (3.1.7). On adding a normalizing factor, and generalizing to the case of any number of interacting electron groups, we may write 

It will be recognized that a 1-determinant wavefunction may be regarded as a special case of (14.1.1) in which each group consists of a single electron in a corresponding spin-orbital. Thus 

Here the group function describes group R in state r, and k denotes a particular selection of group states, in exactly the same way that jc in (3.1.4) and (3.1.5) denoted a particular selection of spin-orbitals. 

It will normally be assumed that the group functions are individually antisymmetric, and in this case it is useful to write A in terms of partial antisymmetrizers Aa, Ab,. .., Ar,. .. for the separate groups. If we write (cf. (3.1.7)) Ar = Ar E epP, where P is a permutation of variables in only, it is well known from permutation theory that 

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The first theoretical handling of the weak R-T combined with the spin-orbit coupling was carried out by Pople [71]. It represents a generalization of the perturbative approaches by Renner and PL-H. The basis functions are assumed as products of (42) with the eigenfunctions of the spin operator conesponding to values E = 1/2. The spin-orbit contribution to the model Hamiltonian was taken in the phenomenological form (16). It was assumed that both interactions are small compared to the bending vibrational frequency and that both the... 

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