Collinear Collisions of an Atom and a Morse Oscillator: An Approximate Semiclassical Approach

The semiclassical treatment by Heidrich, Wilson, and Rapp of atom–harmonic oscillator collinear collisions with exponential and Morse repulsive potentials, is extended to include collisions, with the same potentials, between an atom and a Morse oscillator. The classical equations of motion for the Morse oscillator system lead to a differential equation which can be solved in the same form as the harmonic oscillator system by an iterative method. It is found that for vibrational transitions between low lying levels and for relative translational energies on the order of several oscillator quanta only one or two iterations are necessary for convergence to within a few percent. The results are compared with a calculation for harmonic oscillator systems.