Inelastic collisions between atoms I. General theoretical considerations

Source abstract

Abstract The probability of slow inelastic collisions between two atomic systems is investigated theoretically using the perturbed stationary state method (p.s.s. method) in which the kinetic energy of the relative motion is treated as the perturbation responsible for the transitions. The p.s.s. method has been extended to include cases in which resonance degeneracy occurs and when the transition concerned involves a change of the axial component of angular momentum. The scope and limitations of the method are examined in detail and compared with those of Born’s approximation. It is shown that two modifications of the latter approximation are of comparable importance in most cases, one involving a change in the effective transition potential, the other the distortion of the plane waves representing the relative motion of the colliding systems. The first of these is the only one included in previous applications. It is shown that, under semi-classical conditions, the formulae of the p.s.s. method reduce to Mott’s impact parameter formulae provided the important distortion effect is neglected. New semi-classical formulae, including this effect as well as the effect of resonance degeneracy, are derived in a form suitable for numerical application.