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.