Lande interval rule level

Hi) The separation between adjacent J levels is XJf where Jj is the larger J quantum number. This is called the Lande interval rule. 

The biquadratic exchange coupling constants adopt rather small values the experimental data show that exchange coupling constants obey j/J 0.05. The separation of the energy levels, however, alters significantly as the deviation from the Lande interval rule is dramatic for higher spin values [19]... 

Upon performing the summation we find that the reduced matrix element vanishes and there is no splitting by spin-orbit coupling within the term itself. This may seem to contradict the Lande interval rule which predicts a splitting into three levels with energies given by... 

An exact estimate of the error is difficult to obtain because we cannot use the simplifications that a Lande interval rule would give. Notice, for example, that the ordering of the levels in Po comes in the order J — 2,0,1 instead of the order 2,1,0 given by the Lande rule. In this chapter we will in partieular be interested in the SOC for Pb. We can here expect the error in the computed stabihzation to be of the same order as the error in the computed SO splitting, about 0.10 eV. 

Lande interval rule A rule in atomic spectra stating that it the spin-orbit coupling is weak in a given multiplet, the energy differences between two successive /levels (where /is the total resultant angular momentum of the coupled electrons) are proportional to the larger of the two values of/. The rule was stated bythe German-born US physicist Alfred Lande (1888-1975) in 1923. 

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. 

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. 

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