Ultracold collisions of molecules

This paper deals with the theory of collisions between two ultracold particles with a special focus on molecules. It describes the general features of the scattering theory of two particles with internal structure, using a time-independent quantum formalism. It starts from the Schr\"odinger equation and introduces the experimental observables such as the differential or integral cross sections, and rate coefficients. Using a partial-wave expansion of the scattering wavefunction, the radial motion of the collision is described through a linear system of coupled equations, which is solved numerically. Using a matching procedure of the scattering wavefunction with its asymptotic form, the observables such as cross sections and rate coefficients are obtained from the extraction of the reactance, scattering and transition matrices. The example of the collision of two dipolar molecules in the presence of an electric field is presented, showing how dipolar interactions and collisions can be controlled.