Theory of low energy collisions

The basic notions of low-energy quantum scattering theory are introduced (cross sections, phase shifts, resonances,... ), in particular for positively-charged particles, in view of nuclear physics applications. An introduction to the reaction-matrix (or R-matrix) method is then proposed, as a tool to both solve the Schroedinger equation describing collisions and fit experimental data phenomenologically. Most results are established without proof but with a particular emphasis on their intuitive understanding and their possible analogs in classical mechanics. Several choices are made consequently: (i) the text starts with a detailed reminder of classical scattering theory, (ii) the concepts are first introduced in ideal theoretical cases before going to the more complicated formalism allowing the description of realistic experimental situations, (iii) a single example is used throughout nearly the whole text, (iv) all concepts are established for the elastic scattering of spinless particles, with only a brief mention of their multichannel generalization at the end of the text. (author)