Rydberg series unperturbed

Fig. 22.4 Observed decay rates of the 6snd D2 (O), 6snd 3D2 ( ), and 5d7d 1D2 (A) states. The lines indicate the expected vgs3 dependence for the unperturbed 6snd1D2 and 6snd 3 D2 Rydberg series. For points without error bars shown they are approximately the size of the...

The theory described in section 3.3 is called single channel QDT. It reduces an unperturbed Rydberg series to a small number of constants, which include /z. Were this the only achievement of QDT, it would not have assumed much importance in atomic physics, because most series in the spectra of many-electron atoms are in fact perturbed, so that a constant value of p is a rarity. 

The formula for autoionising resonances in terms of only three shape parameters B, C and D, which are constant for the whole series. 

In chapter 2, we saw how the quantum defect is defined from a slight modification of the Rydberg formula for H. It is found experimentally to be nearly constant for different series members, especially for unperturbed series in atoms with a compact core. The first task of QDT is to explain this fact, and to extract from this empirical observation an appropriate wavefunction, consistent with an effective one-electron Schrodinger equation, such that the quantum defect would turn out to be be nearly constant as the principal quantum number n is changed. 

The advantage of such plots is that all the members of a series (excepting, perhaps, the first few, for which /z in the unperturbed condition would not have settled down to a constant value anyway) can be included. The plot is a means of converting information which, at first sight, differs from one member to the next because the energy intervals are ever decreasing, into strictly comparable data in which the doubly-periodic (i.e. periodic in both i i and V2) nature of Rydberg states is properly displayed. 

The existence of one such point associated with each Rydberg member can be inferred by inspection of figs 8.13 and 8.14 all the curves pass through the common points, whatever the value of the coupling strength. They are thus universal points and lie on the profile of the interloper Eb, Tb, shown as a dashed curve in the figures. A series of similar points was previously found for the unperturbed Dubau-Seaton profiles ... 

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