Two-body loss rates for reactive collisions of cold atoms

We present an effective two-channel model for reactive collisions of cold atoms. It augments elastic molecular channels with an irreversible, inelastic loss channel. Scattering is studied with the distorted-wave Born approximation and yields general expressions for angular momentum resolved cross sections as well as two-body loss rates. Explicit expressions are obtained for piece-wise constant potentials. A pole expansion reveals simple universal shape functions for cross sections and two-body loss rates in agreement with the Wigner threshold laws. This is applied to collisions of metastable ${^{20}}$Ne -- ${^{21}}$Ne atoms, which decay primarily through exothermic Penning-, or Associative- ionization processes. From a numerical solution of the multichannel Schr\"odinger equation using the best currently available molecular potentials, we have obtained synthetic scattering data. Using the two-body loss shape functions derived in this paper, we can match these scattering data very well.