  Experiments are starting to probe collisions and chemical reactions between
atoms and molecules at ultra-low temperatures. We have developed a new
theoretical procedure for studying these collisions using the R-matrix method.
Here this method is tested for the atom -- atom collisions described by a Morse
potential. Analytic solutions for continuum states of the Morse potential are
derived and compared with numerical results computed using an R-matrix method
where the inner region wavefunctions are obtained using a standard nuclear
motion algorithm. Results are given for eigenphases and scattering lengths.
Excellent agreement is obtained in all cases. Progress in developing a general
procedure for treating ultra-low energy reactive and non-reactive collisions is
discussed.
