Perturbed Rydberg series

We now consider how many q reversals are expected in a Rydberg series and the conditions under which they occur. Experimental data (such as those in fig. 8.18) demonstrate that there can be more than just one q reversal in a Rydberg series perturbed by an intruder level. One might ask is this a sign of perturbations due to more than one interloper, or can one interpret the two reversals as having a common origin ... 

In this chapter we have implicitly assumed the Rydberg atom to be a one electron-atom. In the perturbed Rydberg series of, for example, alkaline earth atoms, Rydberg states can have mixed valence-Rydberg character. In such states the black body effects are reduced by a factor equal to the fractional Rydberg character.14... 

While the perturbation of the 6sni Rydberg series typically comes from the interaction with a single 5dn T state, core polarization comes from the interaction... 

Ba Rydberg energy levels (—) and continua (///) obtained by adding the second valence electron to these Ba+ levels. The horizontal arrows show the possible interactions between channels associated with different ion levels. Interactions with other bound states lead to series perturbations while interactions with continua lead to autoionization. 

Fig. 22.7 Schematic diagram of forced autoionization. Above the ionization limit the autoionizing state A, converging to a higher limit, is manifested as an autoionization resonance. Below the limit, in zero field the interaction of the perturber P with the Rydberg series results in the perturbation of the Rydberg series. Applying an electric field E depresses the ionization limit below P, and it appears as a forced autoionization resonance.

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. 

There may be such strong series perturbations that the simple rule for drawing the edges of the boxes no longer works, and overlaps or spaces between adjacent boxes then appear in the diagram. In this case, the geometrical construction should be used. This commonly arises when the lowest member of a Rydberg series is included in the plot. 

Since continuity across the threshold is so fundamental, it is worth testing the principle under conditions where / values can be measured to very high principal quantum numbers n, and where a strong intruding resonance located in the photoionisation continuum just above the threshold perturbs the course of intensities in the Rydberg series. An example of this kind occurs in the spectrum of Ba and is shown in fig. 4.3. The fact that, even in such a case, the df/dE curve joins completely smoothly shows that perturbations do not upset this principle, i.e. that it is of very general validity. 

Wigner s theory is most useful for studying cases of Rydberg series of interacting features in which an intruder appears. There are several distinct effects in the spectra of interacting resonances which result from perturbations, and are readily described by K-matrix theory. We first list them, and then discuss each one in turn. 

The strongest pieces of evidence complex atoms provide in favour of independent electron modes and simple Bohr-Sommerfeld quantisation are (i) the existence of Rydberg series and (ii) the regularity of the periodic table of the elements. As a corollary, we should look for quantum chaos (if it occurs) in atoms for which there is some breakdown in the quality of the shell structure, combined with prolific and heavily perturbed overlapping series of interacting levels. These conditions are most readily met, as will be shown below, in the spectra of the alkaline-earth elements, as a result of d-orbital collapse. 

Figure 3.10 Perturbations between the 6pw and llj>7r 1n Rydberg states of H2. Two Rydberg series converging to different vibrational levels of the X2E state interact via nonzero Av — 1 vibrational matrix elements of the d/dR operator.

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