Lying ≥4 eV above the ground state, Rydberg states are not populated thermally, except at very high temperatures. Accordingly, it is natural to assume that thermal effects are negligible in dealing with Rydberg atoms. However, Rydberg atoms are strongly affected by black body radiation, even at room temperature. The dramatic effect of thermal radiation is due to two facts. First, the energy spacings ΔW between Rydberg levels are small, so that ΔW < kT at 300 K. Second, the dipole matrix elements of transitions between Rydberg states are large, providing excellent coupling of the atoms to the thermal radiation. The result of the strong coupling between Rydberg atoms and the thermal radiation is that population initially put into one state, by laser excitation for example, rapidly diffuses to other energetically nearby states by black body radiation induced dipole transitions. Both the redistribution of population and the implicit increase in the radiative decay rates are readily observed. Although the above mentioned effects on level populations are the most obvious effects, the fact that a Rydberg atom is immersed in the thermal radiation field increases its energy by a small amount, 2 kHz at 300 K. While the radiation intensity is vastly different in the two cases, this effect is the same as the ponderomotive shift of the ionization limit in high intensity laser experiments.

QDT enables us to characterize series of autoionizing states in a consistent way and to describe how they are manifested in optical spectra. We shall first consider the simple case of a single channel of autoionizing states degenerate with a continuum. Of particular interest is the relation of the spectral density of the autoionizing states to how they are manifested in optical spectra from the ground state and from bound Rydberg states using isolated core excitation. We then consider the case in which there are two interacting series of autoionizing states, converging to two different limits, coupled to the same continuum.

First we consider the two channel problem shown in Fig. 21.1. Our present interest is in the region above limit 1, i.e. the autoionizing states of channel 2. Later we shall consider the similarity of the interactions above and below the limit. A typical quantum defect surface obtained from Eq. (20.12) or (20.40) for all energies below the second limit is shown in Fig. 21.2. The surface of Fig. 21.2 may be obtained with either of two sets of parameters, δ1 = 0.56, δ2 = 0.53, and R′l2 = 0.305, R′11 = R′22 = 0 or μ1 = 0.4, μ2 = 0.6, and U11 = U22 = cosθ and U12 = – U21 = sinθ, with θ = 0.6 rad. To conform to the usual convention, in Fig. 21.2 the vi axis is inverted.

In the first two chapters we have seen that the Na atom, for example, differs from the H atom because the valence electron orbits about a finite sized Na+ core, not the point charge of the proton. As a result of the finite size of the Na+ core the Rydberg electron can both penetrate and polarize it. The most obvious manifestation of these two phenomena occurs in the lowest ℓ states, which are substantially depressed in energy below the hydrogenic levels by core penetration. Core penetration is a short range phenomenon which is well described by quantum defect theory, as outlined in Chapter 2.

In the higher ℓ states the Rydberg electron is classically excluded from the core by the centrifugal potential ℓ(ℓ + 1)/2r2, and, as a result, core penetration does not occur in high ℓ states, but core polarization does. Since it is not a short range effect, it cannot be described in terms of a phase shift in the wave function due to a small r deviation from the coulomb potential. However, the polarization energies of each series of nℓ states exhibit an n–3 dependence, so the series can be assigned a quantum defect. Unlike the low ℓ states, in which the valence electron penetrates the core, measurements of the Δℓ intervals of a few high ℓ states enable us to describe all the quantum defects of the high ℓ states in terms of the polarizability of the ion core.

Perturbed Rydberg series

One of the most intensively studied manifestations of channel interaction in the bound states is the perturbation of the regularity of the Rydberg series, which is evident if one simply measures the energies of the atomic states. Although measurements of Rydberg energy levels by classical absorption spectroscopy show the perturbations in the series which are optically accessible from the ground state, the tunable laser has made it possible to study series which are not connected to the ground state by electric dipole transitions as well. One of the approaches which has been used widely is that used by Armstrong et al. As shown in Fig. 22.1, a heat pipe oven contains Ba vapor at a pressure of ∼1 Torr. Three pulsed tunable dye laser beams pass through the oven. Two are fixed in frequency, to excite the Ba atoms from the ground 6s21So state to the 3P1 state and then to the 6s7s 3S1 state. The third laser is scanned in frequency over the 6s7s 3S1 → 6snp transitions. The Ba atoms excited to the 6snp states are ionized either by collisional ionization or by the absorption of another photon. The ions produced migrate towards a negatively biased electrode inside the heat pipe. The electrode has a space charge cloud of electrons near it which limits the emission current.

The autoionizing two electron states we have considered so far are those which can be represented sensibly by an independent electron picture. For example, an autoionizing Ba 6pnd state is predominantly 6pnd with only small admixtures of other states, and the departures from the independent electron picture can usually be described using perturbation theory or with a small number of interacting channels. In all these cases one of the electrons spends most of its time far from the core, in a coulomb potential, and the deviation of the potential from a coulomb potential occurs only within a small zone around the origin.

In contrast, in highly correlated states the noncoulomb potential seen by the outer electron is not confined to a small region. In most of its orbit the electron does not experience a coulomb potential, and an independent electron description based on nℓn′ℓ′ states becomes nearly useless. There are two ways in which this situation can arise. The first, and most obvious, is that the inner electron's wavefunction becomes nearly as large as that of the outer electron. If we assign the two electrons the quantum numbers niℓi and noℓo, this requirement is met when ni approaches no, which leads to what might be called radial correlation. The sizes of the two electron's orbits are related. The second way the potential seen by the outer electron can have a long range noncoulomb part is if the presence of the outer electron polarizes the inner electron states.