Reaction operators for the relative coordinates treatment of atom-diatom collinear collisions

The reaction operator K is used to treat the collinear collision between an atom and a diatom in relative coordinates representation. With this choice of coordinates the coupling between the zeroth-order channels is due to a kinetic crossing term. The inadequacy of the channel functions to describe properly the asymptotic motion can be partially corrected by a renormalization procedure consisting of a shift of the energies. An analytical solution for arbitrary inter-continuum couplings can be given for the T matrix when the diatom is approximated by a harmonic oscillator. Calculations are presented for two types of atom-diatom interaction potential: an exponential or a Morse function. The results are compared with the exact available numerical calculations and with the linearized distorted wave approximation. The treatment in relative coordinates with renormalization is found to yield, for many cases of physical significance, very good results.