From the very beginning of our involvement in the investigation of light induced polarization of angular momenta of molecules we were fascinated by the variety of information about the properties of molecules which they bear. At the same time the description and interpretation of these phenomena appeared to us to be extremely complicated and unclear. In fact, at times it seemed as if our computers understood the problem better than we did.

This book is an attempt to clarify the processes during the course of which polarized (ordered) angular momenta distribution is created in an ensemble of molecules in the gas phase by the effect of light. We discuss the effect of static external magnetic and electric fields on the angular momenta distribution. In particular, we wish to emphasize the ‘geometric’ meaning and interpretation of the phenomena. This may, we believe, be a further step in attempts to simplify the theoretical description, thus making it more accessible to a wide range of users, both physicists and chemists.

The fundamental basis for optical polarization (alignment, orientation) of angular momenta is the law of conservation of angular momenta in photon–molecule interaction. In this book we examine a variety of macroscopic manifestations of spatial anisotropy of angular momenta, such as angular distribution and polarization of emitted light, including changes under non-linear absorption, and the influence of collisions and external fields. Quantum angular momentum theory, in particular that which is based on irreducible tensorial set representation, presents a well-developed approach that is widely used in subatomic, atomic and molecular physics.

The advancement of knowledge of electron–atom collisions depends on an iterative interaction of experiment and theory. Experimentalists need an understanding of theory at the level that will enable them to design experiments that contribute to the overall understanding of the subject. They must also be able to distinguish critically between approximations. Theorists need to know what is likely to be experimentally possible and how to assess the accuracy of experimental techniques and the assumptions behind them. We have aimed to give this understanding to students who have completed a program of undergraduate laboratory, mechanics, electromagnetic theory and quantum mechanics courses.

Furthermore we have attempted to give experimentalists sufficient detail to enable them to set up a significant experiment. With the development of position-sensitive detectors, high-resolution analysers and monochromators, fast-pulse techniques, tuneable high-resolution lasers, and sources of polarised electrons and atoms, experimental techniques have made enormous advances in recent years. They have become sophisticated and flexible allowing complete measurements to be made. Therefore particular emphasis is given to experiments in which the kinematics is completely determined. When more than one particle is emitted in the collision process, such measurements involve coincidence techniques. These are discussed in detail for electron–electron and electron–photon detection in the final state. The production of polarised beams of electrons and atoms is also discussed, since such beams are needed for studying spin-dependent scattering parameters. Overall our aim is to give a sufficient understanding of these techniques to enable the motivated reader to design and set up suitable experiments.

The detailed study of the motion of electrons in the field of a nucleus has been made possible by quite recent developments in experimental and calculational techniques. Historically it is one of the newest of sciences. Yet conceptually and logically it is very close to the earliest beginnings of physics. Its fascination lies in the fact that it is possible to probe deeper into the dynamics of this system than of any other because there are no serious difficulties in the observation of sufficiently-resolved quantum states or in the understanding of the elementary two-body interaction.

The utility of the study is twofold. First the understanding of the collisions of electrons with single-nucleus electronic systems is essential to the understanding of many astrophysical and terrestrial systems, among the latter being the upper atmosphere, lasers and plasmas. Perhaps more important is its use for developing and sharpening experimental and calculational techniques which do not require much further development for the study of the electronic properties of multinucleus systems in the fields of molecular chemistry and biology and of condensed-matter physics.

For many years after Galileo's discovery of the basic kinematic law of conservation of momentum, and his understanding of the interconversion of kinetic and potential energy in some simple terrestrial systems, there was only one system in which the dynamical details were understood. This was the gravitational two-body system, whose understanding depended on Newton's discovery of the 1/r law governing the potential energy. By understanding the dynamics we mean keeping track of all the relevant energy and momentum changes in the system and being able to predict them accurately.

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.