Quantum Theory of Reactive Collisions for $1/r^n$ Potentials

We develop a general quantum theory for reactive collisions involving power-law potentials ($-1/r^n$) valid from the ultracold up to the high-temperature limit. Our quantum defect framework extends the conventional capture models to include the nonuniversal case when the short-range reaction probability $P^{\mathrm{re}}<1$. We present explicit analytical formulas as well as numerical studies for the van der Waals ($n=6$) and polarization ($n=4$) potentials. Our model agrees well with recent merged beam experiments on Penning ionization, spanning collision energies from 10 mK to 30 K [Henson et al., Science 338, 234 (2012)].