Probability distributions of atomic scattering lengths

The probability distribution of the real and imaginary parts of atomic scattering lengths a are derived, in a two-channel model that allows for inelastic scattering to occur. While the real part of a remains Cauchy-distributed, as predicted for single channel scattering in the classic work of Gribakin and Flambaum, the imaginary part of a is seen to be strongly peaked near zero. Two-body inelastic scattering rates may therefore be smaller in general than a naive estimate would suggest.