Partitioning of the g Factors

In order to fit vibration-rotation spectra of several isotopologues of diatomic molecules to the effective Hamiltonian, Eq. (6.90), one normally partitions the corrections to the reduced masses, i.e. the g factor radial functions gj R) and gv R), into two isotopically independent terms that are associated with one or the other nucleus 

The second terms are the electronic contributions to the rotational and vibrational g factors, whereas the last three terms are static response functions involving the total 

Recalling that according to Eq. (4.25) the 2 -component of the electric dipole moment Pz Rom, R) for the internuclear distance R and with the origin of the coordinate system at the centre of mass, is given as 

Choosing the coordinate system such that Ra,z — Rcm,z = R p/Ma, which implies for a molecule of polarity +AB that p,z 0, we can finally write 

On the other hand, simply averaging the two isotopically invariant g factors gives another partitioning of the g factors 

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Partitioning of the g Factors 151 The analogous derivations for nucleus A would then give... 

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