Electron–atom collisions that ionise the target provide a very interesting diversity of phenomena. The reason for this is that a three-body final state allows a wide range of kinematic regions to be investigated. Different kinematic regions depend sensitively on different aspects of the description of the collision.

Up to now there has been no calculation of differential cross sections by a method that is generally valid. We use a formulation due to Konovalov (1993). Understanding of ionisation has advanced by an iterative process involving experiments and calculations that emphasise different aspects of the reaction. Kinematic regions have been found that are completely understood in the sense that absolute differential cross sections in detailed agreement with experiment can be calculated. These form the basis of a structure probe, electron momentum spectroscopy, that is extremely sensitive to one-electron and electron-correlation properties of the target ground state and observed states of the residual ion. It forms a test of unprecedented scope and sensitivity for structure calculations that is described in chapter 11.

Other kinematic regions require a complete description of the collision, which may be facilitated by including the boundary condition for the three charged particles in the final state. This is nontrivial because there is no separation distance at which the Coulomb forces in the three-body system are strictly negligible. The pioneering experiments of Ehrhardt et al. (1969) are of this type.

An accurate description of ionisation channels is essential in a theory of scattering, even to low-lying discrete states at low incident energy. The first test of such a description is provided by the total ionisation cross section and asymmetry.

The material presented so far was based on the creation of anisotropic distribution of molecular angular momenta under the direct effect of light absorption. We are now going to discuss briefly some ideas and examples of experimental realization of other methods leading to the production of polarized molecules, including those which are not directly connected with light effects, such as polarization caused by collisions and external electric or magnetic fields.

Photodissociation and photoionization

It was assumed in the preceding chapters that optical transitions between bonded states of molecules take place with no change in their chemical composition. Photodissociation and photoionization form a general class of photofragmentation processes in collisions between a molecule and a photon which lead to simple chemical reactions of disintegration into atomic or molecular fragments, or into ions and electrons.

The photodissociation process

The photodissociation process takes place most frequently at excitation of the molecule to a non-bonded state, with subsequent dissociation into products. Since the angular part of the transition probability, according to Chapter 2, is still dependent on the mutual orientation of the Ê-vector of the initiating light beam and on the transition dipole moment d, one may expect spatial anisotropy of angular momenta distribution both in the dissociation products and in the set of molecules which remains undestroyed.

Let us start with the second effect which is most close to the ideas discussed in Chapter 3 in connection with optical polarization by ‘de-population’. Indeed, if the photodissociation process proceeds via one fixed (upper) electronic state, then, firstly, the expressions for angular transition coefficients G(θ,ϕ), as considered in Chapter 2 (see formula (2.8)), remain valid.

In the last chapter we discussed how our understanding of electron impact excitation of atoms has substantially improved in recent years. Sophisticated experimental techniques are available for revealing sensitive details of the collision process, in addition to providing accurate and reliable differential and total cross section data. These details include the shape and inherent angular momentum of the excited atoms after the scattering process, measured as a function of the scattering angle and incident energy. These studies have provided stringent tests of current scattering theories, particularly at intermediate energies and backward angles.

In conventional collision experiments the strong Coulomb interaction generally masks the much weaker relativistic spin-dependent interactions. The role of the spin-dependent interactions, such as the exchange and spin–orbit interactions, has also been clarified by sophisticated measurements with spin-polarised electrons and/or spin-polarised targets, sometimes employing spin analysis after the collision process (Kessler, 1985, 1991; Hanne, 1983).

Such measurements were first applied with considerable success to elastic scattering. Indeed one was able to discuss experiments which would determine all the theoretically calculable amplitudes (Bederson, 1970). For inelastic processes, such measurements necessitate the simultaneous application of spin selection techniques and the alignment and orientation measurements discussed in the previous chapter. The experiments have become feasible with the advancement of experimental techniques. The first successful differential electron impact excitation study with spin-polarised electrons and alignment and orientation measurements was performed by Goeke et al. (1983) for the e–Hg case.

To understand an electron–atom collision means to be able to calculate correctly the T-matrix elements for excitations from a completely-specified entrance channel to a completely-specified exit channel. Quantities that can be observed experimentally depend on bilinear combinations of T-matrix elements. For example the differential cross section (6.55) is given by the absolute squares of T-matrix elements summed and averaged over magnetic quantum numbers that are not observed in the final and initial states respectively. This chapter is concerned with differential and total cross sections and with quantities related to selected magnetic substates of the atom.

In the study of electron–atom collisions there has been a constant emphasis on increasing the state selectivity of the particles in both the initial and final states. Thus while total cross section measurements define the initial kinetic energies, measurements of differential cross sections as a function of angle give additional information on the final momentum states of the separating particles. Added state selectivity is obtained through the use of spin-polarised electrons, or spin-polarised atoms, and with spin analysis of scattered particles (see e.g. Kessler (1985)). The great progress that has been made with the use of spin-selected particles will be discussed in the next chapter. Much of the progress that has been made has been for the case of elastic scattering.

Collisional alignment and orientation

The status for inelastic collisions is a little less satisfactory than for elastic collisions. Collisional excitation of atoms involves excited states with several magnetic substates.

The background for the details of multichannel scattering calculations has now been established. We consider methods based on the integral-equation formulation of chapter 6. These momentum-space methods have proved accurate at all energies in a sufficient variety of situations to justify the belief that they can be generally applied. In some situations sufficient accuracy is achieved without resorting to the full power of the integral-equation solution. The methods used in these situations are distorted-wave methods. Their relationship to the full solutions will be examined in a simplified illustrative case. A brief outline will be given of alternative methods based on a coordinate-space formulation of the multichannel problem.

There are two characteristic difficulties of multichannel many-fermion problems. The first is that computational methods can of course directly address only a finite number of channels whereas the physical problem has an infinite number of discrete channels and the ionisation continuum. The second is that the electrons are identical so that the formulation in terms of one-electron states must be explicitly antisymmetric in the position (or momentum) and spin coordinates.

We first show how to set up the problem within the framework of formal scattering theory using antisymmetric products of one-electron states. The problem is then formulated in terms of the calculation of reduced T-matrix elements relating the absolute values of initial and final momenta in different angular-momentum states. This depends on a knowledge of the corresponding potential matrix elements, whose calculation we treat in detail. We then show how the target continuum is accounted for in the scattering formalism.

We have considered the measurement of observables in electron–atom collisions and the description of the structure of the target and residual atomic states. We are now in a position to develop the formal theory of the reaction mechanism. Our understanding of potential scattering serves as a useful example of the concepts involved.

Reactions are understood in terms of channels. A channel is a quantum state of the projectile–target system when the projectile and target are so far apart that they do not interact. It is specified by the incident energy and spin projection of the projectile and the quantum state of the N-electron target, which may be bound or ionised.

The reaction mechanism is studied by considering targets whose description is simple and, at least from the spectroscopic point of view, believable within an accuracy appropriate to the scattering experiment. Hydrogen is the obvious example, although experiments are difficult because of the need to make the atomic target by dissociating molecules. Sodium is a target for which a large quantity of experimental data is available and whose structure can be quite well described for the lower-energy states. When the reaction mechanism is sufficiently understood the reaction may be used as a probe for the structure of more-complicated target or residual systems.

Formulation of the problem

Scattering theory concerns a collision of two bodies, that may change the state of one or both of the bodies. In our application one body (the projectile) is an electron, whose internal state is specified by its spin-projection quantum number v.

The problem of N bound electrons interacting under the Coulomb attraction of a single nucleus is the basis of the extensive field of atomic-spectroscopy. For many years experimental information about the bound eigenstates of an atom or ion was obtained mainly from the photons emitted after random excitations by collisions in a gas. Energy-level differences are measured very accurately. We also have experimental data for the transition rates (oscillator strengths) of the photons from many transitions. Photon spectroscopy has the advantage that the photon interacts relatively weakly with the atom so that the emission mechanism is described very accurately by first-order perturbation theory. One disadvantage is that the accessibility of states to observation is restricted by the dipole selection rule.

Photon spectroscopy associates two numbers with the pair of states involved in a transition, the energy-level difference and the transition rate. The correlated emission directions of photons in successive transitions are determined trivially by the dipole selection rule. In most cases it is impossible to solve the many-body problem accurately enough to reproduce spectroscopic data within experimental error and we are left wondering how good our theoretical methods really are.

Because our description of differential cross sections for momentum transfer in a reaction initiated by an electron beam depends on our ability to describe both the structure and the reaction mechanism, scattering provides much more information about bound states. This is even more true of ionisation. The information is less accurate than from photon spectroscopy and is obtained only after a thorough understanding of reactions, the subject of this book, is achieved. The understanding of structure and reactions is of course achieved iteratively.

Quantitative studies of the scattering of electrons by atoms began in 1921 with Ramsauer's measurements of total collision cross sections. Ramsauer (1921) with his single-collision beam technique showed that electron–atom collision cross sections for noble gas targets pass through maxima and minima as the electron energy is varied, and can have very low minima at low electron energies. The marked transparency of rare gases over a small energy range to low energy (~1 eV) electrons was also noted by Townsend and Bailey (1922) in swarm experiments. This result was in total disagreement with the classical theory of scattering, which predicts a monotonic increase in the total collision cross section with decreasing energy. The Ramsauer–Townsend effect provided a powerful impetus to the development of quantum collision theory.

Although the history of electron impact cross-section measurements is quite long, the instrumentation and the experimental techniques used have continued to evolve, and have improved significantly in recent years. Part of the motivation for this progress has been the need for electron collision data in such fields as laser physics and development, astrophysics, plasma devices, upper atmospheric processes and radiation physics. The development of electron–atom collision studies has also been strongly motivated by the need of data for testing and developing suitable theories of the scattering and collision processes, and for providing a tool for obtaining detailed information on the structure of the target atoms and molecules and final collision products.

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.