Part 1 Introduction to scattering theory: the crossed beam experiment waves and particles trajectories, wave packets and stationary states semi-classical theory laboratory and centre of mass coordinates summary of systems to be examined. Part 2 Elastic scattering: classical trajectories for the central force problem collision cross-sections quantum scattering by a central force a semi-classical view of elastic scattering comparison of classical, semi-classical and quantum cross-sections the inversion problem. Part 3 Inelastic collisions: the classical treatment of atom-diatomic molecule numerical integration of trajectories and action-angle variables the multi-channel equations quantum treatment of collinear atom-diatomic molecule collisions the semi-classical approach to inelastic collisions approximate solutions of the coupled channel equations. Part 4 Rotationally inelastic collisions: classical rotational energy transfer classical trajectories for reactions potential energy functions and reaction cross-sections quantum theory of reactive scattering statistical theories. Part 6 Electronic transitions: beyond the Born-Oppenheimer approximation atom-atom collisions classical trajectory methods. Part 7 Scattering from surfaces: atomm-rigid surfaces scattering more complicated problems. Appendices: the JWKB approximation the partial wave expansion jost functions numerical methods effective impact parameter for a three-dimensional surface Hamilton's equations for the A+BC classical trajectory.

Coalescent resonances are investigated in the He/LiF(001) collisions. The giant resonance is found when the incident energy of the He atom is scanned. Similar resonance is not found when the incidence azimuthal angle is scanned. This is primarily due to the presence of other resonances which are degenerate with the coalescent ones.

Coalescent resonances are investigated in the He/LiF(001) collisions. The giant resonance is found when the incident energy of the He atom is scanned. Similar resonance is not found when the incidence azimuthal angle is scanned. This is primarily due to the presence of other resonances which are degenerate with the coalescent ones.

Time delay in collisions is analyzed when zero-angular-momentum resonances are present. It is shown that very large delay comes from an orbiting wave. This is reflected in rapid change with energy of the phase of the S-matrix residue. In addition, we show the proper definition of time delay in terms of the scattering amplitude.

In atom-surface collisions, there are pairs of resonances which merge into a single resonance for special values of initial parameters of atomic beam. They display an unusual broadening effect when they are close to each other. In this paper we describe some of their properties based upon a model example.

Conditions are given under which two resonance poles of the S matrix for atom–surface scattering coalesce into a single pole leading to increased structure in resonance cross sections. The conditions are applied to He–LiF (001) elastic scattering.

The eigenvalues of a hard-walled parallelogram-shaped enclosure were investigated using quantum perturbation theory, the perturbation being a small angle distortion of a pair of parallel sides of the rectangle. A comparison of perturbation theory results and exact computations for low-lying states showed good agreement. The distribution of eigenvalues grossly disturbed from their value in the nearby regular system was studied and found to be systematic.

A recently determined intermolecular potential for HF has been used to calculate the second virial coefficient of the gas in the temperature range 275-9000 K and the rotational inelastic cross sections for HF-HF collisions at a collision energy of 300 cm-1. The virial coefficients calculated in the temperature range 292·5-329 K are in better agreement with an empirical estimate made by Redington than values calculated from other potentials. We have shown that at least seven terms in the bipolar expansion of the potential are necessary to obtain converged scattering cross sections. However, computational limitations have prevented us from concluding that even the seven term expansion has fully converged. We predict large cross sections for transitions which are dipolar coupled (for example (0, 0) →(1, 1)) and some that are not (for example (0, 1) →(1, 1)). The transition (0, 0) →(0, 2) is predicted to have a very small cross section.