Multichannel Cold Collisions: Simple Dependences on Energy and Magnetic Field

The scattering matrices needed to describe cold collision processes are shown to have a simple dependence on energy and magnetic field, controlled by single-channel dynamics in the appropriate long-range field. A frame transformation describes the energy and field dependences entirely in terms of a standard recoupling matrix and single-channel parameters, giving adequate accuracy for many systems. The formulas in this paper should permit experimentalists to reproduce the results of hitherto complicated coupled channels calculations, through small, simple matrix manipulations.