Lande’s interval rule

The Lande s interval rule underlies the definition of the spin-orbit operator Yvrhich first acts on atomic one-electron fimctions. Indeed, a single-electron spin-orbit interaction obeys this rule, which means that the Lande s average of a multiplet coincides with the non-split term [39]. For a given I symmetry, taking the non-split term as a reference, one defines a zero-diagonal operator in relation to the reference... 

Lande s interval rule specifies that the energy of two neighboring levels with quantum numbers J and T — 1 is proportional to / by the parameter X, as discussed below. 

Thus the energy depends only on S and the relative energies still satisfy the Land interval rule given in Eq. (6). 

Together with a (6sl8s So) = 0.67 (cf. Section 3.1.1) Eqs. (44) and (45) have been used to derive the solid circles shown in Figures 32 and 33 at n = 18. As can be seen from Eqs. (45) and (46), the hyperfine-induced isotope shifts are a direct measure of the Rydberg character of the So and Po states. The F = 7 component of the S level, however, experiences a total shift from the position predicted by the Lande interval rule caused by the interaction with both 7 = 0 states. Since the perturber Po lies below the S, state, both contributions are of opposite sign and fortuitously cancel. This is also evident from Figure 32b. 

This counting is based on the assumption (which is satisfied for many spectra) that in the first instance the motion of the model is determined by the principal and secondary quantum numbers of the single electrons, that then in the next instance the interaction of the vectors 1 with each other and the St with each other and only then in the third instance the interaction of I and s can be added as a small perturbation. This pictorial model even leads (adiabatic hypothesis) to a correct counting of the terms if the interaction ratio no longer represents reality, but the model in this case no longer yields the correct position of the terms, and the quantum numbers no longer represent the mechanical quantities of the model (which is apparent from the invalidity of the Lande interval rule for multiplets and the g-formula). 

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