  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 non-universal case when the short-range reaction
probability P^{re} < 1. We present explicit analytical formulas as well as
numerical studies for the van der Waals (n = 6) and polarization (n = 4)
potentials, and relate our work to recent merged beam experiments on Penning
ionization for collision energies below 0.1 meV [Henson et al, Science 338,
234(2012)].
