Written for graduate students, this book provides an overview of fundamental cold collision physics together with applicable numerical techniques, with an emphasis on the research frontiers emerging based on recent advances in cold atomic physics.

The book introduces readers to the description of standard scattering theory at low energy including multichannel scattering and the distinction between Coulomb and non-Coulomb scattering with their underlying boundary conditions. To supplement the gap between understanding of formal theory and its practical implementation, it presents in some detail the relevant atomic structure and the effects of external fields on the atomic and molecular states. A unique feature of the book is a discussion on the manipulation of quantum correlations by controlled cold collisions, highlighting the quantum information aspect of the collision theory. Numerous kinds of scattering resonances and their connection with a low-energy bound state are discussed, with particular emphasis on the external field control of atomic collisions at low energy. New spectroscopic techniques based on the field controlled atomic collisions are explained, detailing how knowledge about low energy collision theory can be applied in such new spectroscopic techniques. One chapter in the book introduces low energy collision theory in lower dimensions and a special three-body bound state known as Efimov state which was theoretically predicted 50 years ago and recently discovered in the context of ultracold atomic collisions. The concluding chapter introduces various numerical and computational techniques used to simulate and model ultracold states and collisions. Exercises and worked examples are found in every chapter, whilst appendixes recap relevant angular momentum algebra, partial-wave analysis, spin-spin interactions, Green function methods, partial-wave expansion of Green function, and also to derive important mathematical relations or formulas.