CHAPTER 2: Cold Molecular Collisions: Quantum Scattering Calculations and Their Relevance in Astrophysical Applications

In this chapter, we review the theory of quantum close coupling inelastic scattering calculations starting from the Born–Oppenheimer approximation and going all the way to the determination of the inelastic and elastic cross sections and rate coefficients. We first discuss the separation of electronic and nuclei motion done within the Born-Oppenheimer approximation that is, most of the time, used to study cold inelastic collisions. Then, we derive the scattering Schrödinger equation and discuss its almost exact solution with the close coupling approach. Decoupling approximations that are frequently used are also discussed. The application of quantum close coupling scattering theory to open-shell molecules is also briefly reviewed. In the second part of chapter, we discuss the importance and interest of having accurate collisional data for astrophysical applications. In particular, we show how they impact the radiative transfer calculations needed to analyze emission spectra from interstellar molecular clouds and to derive the physical condition of the interstellar matter. Finally, we illustrate the theory by recent results obtained on benchmark collisional systems, the CO and OH molecules in collisions with both He and H₂.