Heavy-particle collisions

Historically, the theoretical tool-box used to study heavy-particle atomic collisions was divided into two broad areas of research: (i) Close-coupling methods based on an expansion of wavefunctions in terms of a set of functions chosen to describe the electronic coordinates of the colliding atomic systems. (ii) Perturbative methods such as the Born series. The first approach was generally believed to be valid for low-energy collisions and the second for high-energy-collisions. However, the terms low and high are quite ambiguous in this context and require further clarification. The ratio of the projectile velocity, υ, to that of the orbital electron of interest in the target, υe, provides adequate guidance in categorising low- and high-energy collisions, that is low refers to υ/υe <∼ 1 a.u. for high, υ/υe >∼ 1 a.u. In high-energy heavy particle collisions, ionization is the dominant process followed by possible excitation of the target. In contrast, in low- to intermediate-energy collisions it is not possible to single out a dominant channel in general, because often many inelastic channels couple with one another, exchanging flux and phase in a complex manner. In this thesis we examine these two areas of heavy-particle collisions. In part I we concentrate on low-energy collisions. Chapter one introduces the Stokes phenomenon and the JWKB approximation. The JWKB method is considered a valuable tool within the theoretical treatment of atomic processes. Very often, when tracing JWKB solutions through the complex plane, one will encounter the apparent discontinuities that give rise to the Stokes phenomenon. In chapter one we discuss such situations within the context of a one-dimensional problem. Then in chapter two, after introducing the equations of motion for low-energy charge exchange for ion-atom collisions, we consider the four- transit ion-point model and the Zwaan-Stueckelberg phase-integral method. This leads to the derivation of the semiclassical two-state S matrix within diabatic and adiabatic representations. In chapter 3 we examine the four-transition-point exponential model of Nikitin which is used to approximate certain types of low-energy ion-atom collisions. Analytic approximations for the generalised transition probability are obtained and compared with numerical calculations. Similarly, in chapter 4 we consider another four-transition-point model, namely the Parabolic model. A completely new four-transition-point model is introduced in chapter 5. This model is initially developed within the context of one-dimensional scattering. This then allows us to attempt to construct suitable Hamiltonian interactions that satisfy our model. Part II of this thesis is concerned with the single-ionization of atomic and molecular targets by ion impact at intermediate energies. In chapter 6 we introduce basic descriptions of the problem and discuss the main mechanisms involved in the ionization process. The obvious starting point is to examine the First-Born approximation and consider its deficiencies. To account for these deficiencies we then examine distorted-wave theories such as the continuum-distorted-wave approximation and the eikonal-initial-state model. Chapter 7 concentrates on the continuum-distorted-wave eikonal-initial-state model and its application to the single-ionization of atomic and molecular hydrogen and helium by proton impact at intermediate energies. We study the ejected-electron spectrum by calculating double-differential cross sections and focus attention on the role of saddle-point trapping of ejected-electrons during the ionization process. (author)