Nuclear Spin Effects in the Reactions of H$_3^+$ with H$_2$ and Electrons

H$_3^+$ is the simplest polyatomic molecule. It is widely used as a benchmark for theoretical calculations of molecular spectroscopy and reaction dynamics, and also plays a pivotal role as the cornerstone of interstellar chemistry. In Urbana, we have investigated the proton hop/exchange reaction H$_3^+$ + H$_2$ $\rightarrow$ (H$_5^+$)$^*$ $\rightarrow$ H$_2$ + H$_3^+$ for the first time at low temperatures. This reaction is the simplest bimolecular reaction involving a polyatomic, and is also the most common bimolecular reaction in the universe. Our experiments have revealed the branching ratio between proton hop and exchange, and appear to explain the observed {\em ortho:para} ratio of H$_3^+$ in diffuse interstellar clouds. At the TSR storage ring of the Max Planck Institute for Nuclear Physics in Heidelberg, we have performed high-resolution measurements of the dissociative recombination (DR) cross sections of cold H$_3^+$ in different mixtures of its lowest {\em ortho} and {\em para} quantum states. These measurements represent an important step towards the first state-selected DR measurements.