Field-theoretical approach to vibrational excitation in atom—diatom collinear collisions

The field-theoretical atom—diatom scattering equations of Csanak have been tested numerically, assuming a collinear collision model, with an exponential repulsive interaction potential and with a harmonic oscillator approximation for the molecule. Dyson's equation, in its integral form, has been solved obtaining orbitals representing the elastic scattering of an atom off the target and these Dyson's orbitals have been used to evaluate a matrix element containing a transition potential. This has been obtained by approximating Bethe—Salpeter's equation and yields directly the transition amplitudes for inelastic scattering. The results for single and multiple-jumps compare favourably with the exact values of Secrest and Johnson, and refinements of the model are suggested for further improvements.