Resonant energy transfer collisions, those in which one atom or molecule transfers only internal energy, as oppposed to translational energy, to its collision partner require a precise match of the energy intervals in the two collision partners. Because of this energy specificity, resonant collisional energy transfer plays an important role in many laser applications, the He–Ne and CO2 lasers being perhaps the best known examples. It is interesting to imagine an experiment in which we can tune the energy of the excited state of atom B through the energy of the excited state of atom A, as shown in Fig. 14.1. At resonance we would expect the cross section for collisionally transferring the energy from an excited A atom to a ground state B atom to increase sharply as shown in Fig. 14.1. In general, atomic and molecular energy levels are fixed, and the situation of Fig. 14.1 is impossible to realize. Nonetheless systematic studies of resonant energy transfer have been carried out by altering the collision partner, showing the importance of resonance in collisional energy transfer.

The use of atomic Rydberg states, which have series of closely spaced levels, presents a natural opportunity for the study of resonant collisional energy transfer. One of the earliest experiments was the observation of resonant rotational to electronic energy transfer from NH3 to Xe Rydberg atoms by Smith et al.

My intent in writing this book is to present a unified description of the many properties of Rydberg atoms. It is intended for graduate students and research workers interested in the properties of Rydberg states of atoms or molecules. In many ways it is similar to the excellent volume Rydberg States of Atoms and Molecules edited by R. F. Stebbings and F. B. Dunning just over a decade ago. It differs, however, in covering more topics and in being written by one author. I have attempted to focus on the essential physical ideas. Consequently the theoretical developments are not particularly formal, nor is there much emphasis on the experimental details.

The constraints imposed by the size of the book and my energy have forced me to limit the topics covered in this book to those of general interest and those about which I already knew something. Consequently, several important topics which might well have been included by another author are not included in the present volume. Two examples are molecular Rydberg states and cavity quantum electro-dynamics.

Finally, it is a great pleasure to acknowledge the fact that this book would never have been written without the efforts of many people. First I would like to acknowledge the help of my colleagues in the Molecular Physics Laboratory of SRI International (originally Stanford Research Institute).

The large size and low binding energies, scaling as n4 and n−2, of Rydberg atoms make them nearly irresistible subjects for collision experiments. While one might expect collision cross sections to be enormous, by and large they are not. In fact, Rydberg atoms are quite transparent to most collision partners.

Collisions involving Rydberg atoms can be broken into two general categories, collisions in which the collision partner, or perturber, interacts with the Rydberg atom as a whole, and those in which the perturber interacts separately with the ionic core and the Rydberg electron. The difference between these two categories is in essence a question of the range of the interaction between the perturber and the Rydberg atom relative to the size of the Rydberg atom. A few examples serve to clarify this point. A Rydberg atom interacting with a charged particle is a charge–dipole interaction with a 1/R2 interaction potential, and the resonant dipole–dipole interaction between two Rydberg atoms has a 1/R3 interaction potential. Here R is the internuclear separation of the Rydberg atom and the perturber. In both of these interactions the perturber interacts with the Rydberg atom as a whole. On the other hand when a Rydberg atom interacts with a N2 molecule the longest range atom–molecule interaction is a dipole–induced dipole interaction with a potential varying as 1/R6.

A radiative collision is a resonant energy transfer collision in which two atoms absorb or emit photons during the collision. Alternatively, a radiative collision is the emission or absorption of a photon from a transient molecule, and, as shown by Gallagher and Holstein, radiative collisions can also be described in terms of line broadening. In a line broadening experiment there are typically many atoms and weak radiation fields, and in a radiative collision experiment there are few atoms and intense radiation fields. The only real difference is whether there are many atoms or many photons. Due to the short collision times, ∼10−12 s, simply observing radiative collisions between low lying states requires high optical powers, and entering the regime where the optical field is no longer a minor perturbation seems unlikely. Due to their long collision times and large dipole moments, Rydberg atoms provide the ideal system in which to study radiative collisions in a quantitative fashion. As we shall see, it is straightforward to enter the strong field regime in which the radiation field, a microwave or rf field to be precise, is no longer a minor perturbation. Ironically, while the experiments are radiative collision experiments, with few atoms and many photons, the description of the strong field regime is given in terms of dressed molecular states, which is more similar to a line broadening description.

Because it can be efficient and selective, field ionization of Rydberg atoms has become a widely used tool. Often the field is applied as a pulse, with rise times of nanoseconds to microseconds, and to realize the potential of field ionization we need to understand what happens to the atoms as the pulsed field rises from zero to the ionizing field. In the previous chapter we discussed the ionization rates of Stark states in static fields. In this chapter we consider how atoms evolve from zero field states to the high field Stark states during the pulse. Since the evolution depends on the risetime of the pulse, it is impossible to describe all possible outcomes. Instead, we describe a few practically important limiting cases.

Although we are not concerned here with the details of how to produce the pulses, it is worth noting that several different types of pulse, having the time dependences shown in Fig. 7.1, have been used. Fig. 7.1(a) depicts a pulse which rises rapidly to a plateau. Atoms in a fast beam experience this sort of pulse when passing into a region of high homogenous field. Fig. 7.1(b) shows a rapidly rising pulse which decays rapidly after reaching its peak. While not elegant, such pulses are easily produced. For pulse shapes such as those of Figs. 7.1 (a) and (b) the ability to discriminate between different states comes mostly from adjustment of the amplitude of the pulse.

Hydrogenic spectra

A good starting point is photoexcitation from the ground state of H. The problem naturally divides itself into two regimes: below the energy of classical ionization limit, where the states are for all practical purposes stable against ionization, and above it where the spectrum is continuous.

As an example, we consider first the excitation of the n = 15 Stark states from the ground state in a field too low to cause significant ionization of n = 15 states. From Chapter 6 we know the energies of the Stark states, and we now wish to calculate the relative intensities of the transitions to these levels. One approach is to calculate them in parabolic coordinates. This approach is an efficient way to proceed for the excitation of H; however, it is not easily generalized to other atoms. Another, which we adopt here, is to express the n = 15 nn1n2m Stark states in terms of their nℓm components using Eqs. (6.18) or (6.19) and express the transition dipole moments in terms of the more familiar spherical nℓm states.

In the excitation of the Stark states of principal quantum number n from the ground state only p state components are accessible via dipole transitions, so the relative intensities for light polarized parallel and perpendicular to the static field, π and σ polarizations, are proportional to the squared transformation coefficients |〈nn1n2m|nℓm〉|2 from the nn1n2m parabolic states to the nℓm states for ℓ = 1 and m = 0 and 1. In Fig. 8.1 we show the relative intensities by means of the squared transformation coefficients |〈15n1n2m|15pm〉|2 for m = 0 and 1.

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.